i hate statistics sm

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null hypothesis (Ho)

"no effect" -the statement being tested in a statistical test.

alternative hypothesis (Ha)

"some effect" -the researcher is trying to gather evidence to support

Based on data taken from airline fares and distances flown, it is determined that the equation of the least-squares regression line is ŷ = 102.50 + 0.65x, where ŷ is the predicted fare and x is the distance, in miles. One of the flights was 350 miles and its residual was -105.00. What was the fare for this flight?

$102.50 $435.00 -$225.00 $330.00

A math club is researching a golf tournament fund-raiser. It will cost $1,000 to host the tournament. If it rains, the club will lose the investment. If it is sunny, it is expected that the club will collect $4,500 from the participants. If the chance of rain is 20%, what is the expected value for the tournament?

$2,600

A real estate agent has 4 homes for sale: A, B, C, and D. Here are the listing prices. Home A: $150,000Home B: $250,000Home C: $190,000Home D: $550,000 The agent wants to randomly select 2 of the 4 homes to show in an open house this coming weekend. This means the agent may show home A and B, A and C, A and D, B and C, B and D, or C and D. If homes A and B are selected, what is the sample mean listing price for this particular selection?

$200,000

Market researchers were interested in the relationship between the number of pieces in a brick-building set and the cost of the set. Information was collected from a survey and was used to obtain the regression equation ŷ = 0.08x +1.20, where x represents the number of pieces in a set and ŷ is the predicted price (in dollars) of a set. What is the predicted price of a set that has 500 pieces?

$41.20

A basketball roster is shown in the table. Which variable would be classified as a continuous quantitative variable?

height

A couple is thinking about having 3 children. Assume that each child is equally likely to be a girl or a boy. What is the probability that exactly 2 of the children are girls?

0.375

The owner of an apple orchard knows that the average weight of Granny Smith apples is 380 grams. Which of the following sample sizes would have the greatest variability?

In a test of significance, if all else is held constant, what can be done to increase the power of a test?

D- Increase the sample size or increase the significance level.

The relative frequency table below displays the proportion of colors of cars for sale at a dealership. What proportion of cars are yellow? 0.04 0.1 0.15 0.4

his scatterplot shows the study time, in hours, versus test score for 20 students. Complete each statement.

high leverage unusual observation unusual observation

A conference consists of 5 sessions: A, B, C, D, and E. Here are the costs of the sessions. Session A: $50Session B: $50Session C: $100Session D: $150Session E: $200 A participant plans to attend 3 sessions. Here is a list of all possible samples of size 3 sessions from this population of 5 sessions: ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, and CDE. If sessions A, B, and C are selected, what is the sample minimum session cost?

$50

A dealership tracks the correlation between the age of its used cars and asking price for a car. The regression line is ŷ = 12,338 - 930x, where x is the age of the car, in years. If someone was interested in buying a used car that is about 4 years old, what would be a reasonable price for the car?

$8618

There are four blood types, and not all are equally likely to be in blood banks. In a certain blood bank, 49% of donations are Type O blood, 27% of donations are Type A blood, 20% of donations are Type B blood, and 4% of donations are Type AB blood. A person with Type B blood can safely receive blood transfusions of Type O and Type B blood. What is the probability that the 4th donation selected at random can be safely used in a blood transfusion on someone with Type B blood?

(0.31)³(0.69)

A random sample of adults was surveyed about their exercise habits. Of the 100 surveyed, 56 stated they exercise regularly. Which of the following is the 95% confidence interval for p, the proportion of all adults who exercise regularly?

(0.46, 0.66)

A random sample of adults was surveyed about whether they shop online. Of the 90 adults surveyed, 72 stated they shop online. What is the 99% confidence interval for p, the proportion of adults who shop online?

(0.69, 0.91)

71% of the surface of the Earth is covered in water. A random number generator uses latitude and longitude to select a random location on Earth. If such locations are generated, what is the probability that the first of those locations that is over land is on the 8th location?

(0.71)⁷(0.29)

In a certain board game, a 12-sided number cube showing numbers 1-12 is rolled. If three such number cubes are rolled, what is the probability that all three show a number 10 or larger?

(3/12)3

A manufacturing company has 5 vice presidents: Andrew, Beth, Charles, Diane, and Eric. Their regional responsibilities are shown in the table. The president of the company wants to select 2 of the 5 vice presidents randomly to send to a conference. Which of the following gives a correct list of all possible samples of size 2 selected from this population of 5 vice presidents without replacement?

(Andrew, Beth), (Andrew, Charles), (Andrew, Diane), (Andrew, Eric), (Beth, Charles), (Beth, Diane), (Beth, Eric), (Charles, Diane), (Charles, Eric), (Diane, Eric)

A store manager wanted to see the relationship between the number of computers sold, x, and store profit, y, on a daily basis. The regression line is ŷ = -150 + 24x, where x is the number of computers sold for the day. What is the predicted store profit if 0 computers are sold for the day?

-$150

Market researchers were interested in the relationship between the number of pieces in a building-brick set and the cost of the set. The researchers collected information from a survey and used it to obtain the regression equation ŷ = 0.08x + 1.20, where x represents the number of pieces in a set and ŷ is the predicted price (in dollars) of the set. What is the predicted price of a set that has 2,520 pieces?

-$202.80 $2,017.20 $3,024.08 $31,485

A statistics student wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The given data lists the number of absences and GPAs for 15 randomly selected students. Using technology, the slope of the least-squares regression line is

-0.10, which means for each additional absence, the GPA is predicted to decrease by 0.10 points.

Agriculturists in a certain state claim that 43% of the residents in the northern portion of the state prefer flour tortillas over corn tortillas, while 59% of the residents in the southern portion of the state prefer flour tortillas over corn tortillas. Suppose random samples of 33 northerners and 41 southerners are selected. Let and be the sample proportions of northern and southern residents of this state, respectively, who would prefer flour tortillas over corn tortillas. Which of the following is the mean of the sampling distribution of PN-PS?

-0.16

Alex's times for running a mile are Normally distributed with a mean time of 5.28 minutes and a standard deviation of 0.38 seconds. Chris's times for running a mile are Normally distributed with a mean time of 5.45 seconds and a standard deviation of 0.2 seconds. Ten of Alex's times and 15 of Chris's times are randomly selected. Let represent the difference in the mean times for Alex and Chris. Which of the following represents the mean of the sampling distribution for xa-xc?

-0.17

The number of pieces of cat food in a one-cup scoop is approximately Normally distributed with a mean of 344 pieces and a standard deviation of 16 pieces. If a random sample of 28 scoops of cat food is selected, what is the probability that the mean number of pieces will be more than 350 pieces?

0.0236

The arm span and foot length were measured (in centimeters) for each of the 19 students in a statistics class and displayed in the scatterplot. An analysis was completed and the computer output is shown. PredictorCoefSE Coeft-ratiopConstant-7.6112.5672.9650.046Arm span0.1860.0355.3770.000 S = 1.61R-Sq = 63.0%R-Sq(Adj) = 62.7% Using the computer output, what is the correlation?

-0.630 0.649 0.794 0.806

A snack-size bag of carrots has a mean weight of 1.75 ounces and a standard deviation of 0.1 ounce. Kendra bought a snack-size bag of carrots to measure and found that it weighed 1.68 ounces. What is the z-score for the snack-size bag of carrots that Kendra measured?

-0.70

The scatterplot shows the number of bacteria in a petri dish for different temperatures. The least-squares regression equation is ŷ= 25 - 1.5x. Calculate and interpret the residual at a temperature of 6ºF.

-1 1 less

Two machines, X and Y, produce earbuds. Let X represent the diameter of an earbud produced by machine X, and let Y represent the diameter of an earbud produced by machine Y. X has a mean of 14 mm with a standard deviation of 0.6 mm, and Y has a mean of 15.2 mm with a standard deviation of 0.2 mm. Which answer choice correctly calculates and interprets the mean of the difference, D = X - Y?

-1.2; earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X and Y, on average, to be -1.2 mm.

The least-squares regression equation ŷ = 100 + 25x can be used to predict the amount of money raised at a fundraiser when x donors donated money. Suppose $3,725 was raised at a fundraiser with 150 donors. Calculate and interpret the residual for this fundraiser with 150 donors.

-125 125 less negative overestimated

A choir director collected data about the number of members in the choir for the last 20 years. The mean number of choir members is 52.68 with a standard deviation of 2.35. This year. The choir has 46 members. The choir director wants to find and interpret the z-score for 46 choir members. Complete the statements about the z-score and its interpretation. The z-score for 46 choir members is about

-2.843 2.843 below fewer

A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation ŷ = 4.9x + 15.2, where x represents the attendance (in thousands) and ŷ is the predicted number of wins. What is the predicted number of wins for a team that has an attendance of 2,100?

-25.49 wins 31.92 wins 36.82 wins 10,305.2 wins

A sports analyst determines that the number of points scored in a basketball game is related to the number of shots taken during the game. The least-squares regression line is ŷ = 5.0 + 1.2x, where ŷ is the predicted number of points scored and x is the number of shots taken. In one game, a team takes 50 shots and scores 75 points. What is the residual for this team during this game?

-33 5 =10 65

A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation ŷ = 4.9x + 15.2, where x represents attendance (in thousands) and ŷ is the predicted number of wins. Which statement best describes the meaning of the slope of the regression line?

-For each increase in attendance by 1,000, the predicted number of wins increases by 4.9. For each increase in attendance by 1,000, the predicted number of wins increases by 15.2. For each increase in the number of wins by 1, the predicted attendance increases by 4,900. For each increase in the number of wins by 1, the predicted attendance increases by 15,200.

A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers placed an ad online asking for volunteers to participate in the study, and 100 subjects replied. They are informed that one group will receive a new cream and the other group will receive a cream with no active ingredient. The researchers believe that sun exposure may affect the cream's effectiveness. The subjects are then asked about their outdoor activities, and 42 of the subjects state they spend more than 50% of their day outside. All subjects are exposed to poison ivy and given their cream. They are asked to return in three days and report their level of irritation. Which of the following describes a randomized block design?

-The subjects are grouped based on their outdoor activity. The 42 subjects are randomly assigned to the two treatment groups. The remaining 58 subjects are also randomly assigned to the two treatment groups. The subjects are numbered 1-100, and these numbers are entered into a random number generator. Fifty numbers, ignoring repeats, are generated and these subjects receive the new cream. The remaining 50 receive the inactive cream. The subjects are paired based on similar age. Two marbles, one red and one blue, are placed in a bag and mixed. If the first subject picks a red marble, then that subject will receive the new cream and the other subject will receive the inactive cream. If it is blue, then the opposite will occur. This is done for all 50 pairs. The subjects are grouped based on their outdoor activity. The researchers flip a coin and if it lands on heads, then the group with the most sun exposure will receive the new cream and the other group will receive the inactive cream. If the coin lands on tails, then the group with the most sun exposure will receive the inactive cream and the other group will receive the new cream.

In a large urban high school, 68% of the students take public transportation to and from school. Annette takes a random sample of 75 students from this school. What is the probability that more than 70% of the students in the sample take public transportation to and from school?

0.356

A shoe company wants to test an updated model of a running shoe on its wear after one month of running. They recruit 50 people who run on a regular basis to participate in the study. Twenty-five runners will receive a pair of the new model and the remaining 25 will receive a pair of the current model. After one month, the wear on the shoes will be determined using the depth of the tread and the flexibility of the toe box. The wear between the new and current models will then be compared. Which of the following describes a completely randomized design for this experiment?

-The subjects are numbered 1-50 and these numbers are put into a random number generator. The first 25 random numbers, ignoring repeats, represent the subjects assigned to the new model group. The remaining 25 subjects will wear the current model. The subjects' names are written on equal-sized slips of paper and placed into a hat. A researcher then reaches in and pulls out 25 slips of paper. These subjects are assigned to the new model group. The remaining 25 subjects will be assigned to the current model group. The 50 subjects are paired based on running ability. The fastest two runners are paired together, the next fastest, etc. For each pair of runners, the researcher will flip a coin. If the coin lands on heads, the first runner will receive the new model and the second runner will receive the original model. The 50 subjects are grouped based on running ability. Twenty runners classify themselves as competitive runners and the remaining 30 classify themselves as recreational runners. For the competitive group, the runners' names are written on equal-sized slips of paper and placed into a hat. The slips are shuffled, and the first 10 runners wear the new model and the other 10 wear the current model. The same procedure is used to assign the shoes to the recreational group.

To investigate the influence of distracted driving, 13 volunteers were asked to participate in a study involving a driving simulator. The participants drove at a safe speed but were told to stop the car at a random moment during the simulation. The scatterplot shows the reaction time and the simulated car's stopping distance (in feet) for each volunteer. The value of r for the scatterplot is 0.935. How would the correlation change if the stopping distances were recorded in meters, rather than feet?

-The value of the correlation coefficient would not change. Since the points would be more spread out, the value of the correlation coefficient would decrease. Since the number of meters would be less than the number of feet, the value of the correlation coefficient would increase. Since the number of meters would be less than the number of feet, the value of the correlation coefficient would decrease.

A therapist wants to study the effects of yoga and meditation on stress relief. She has 60 volunteers who experience varying levels of stress. Half of the participants will be assigned to practice yoga for one month and the other half will practice meditation. Before the experiment begins, all of the participants will be asked to rate their stress levels on a scale from 0 to 10, with 0 representing "no stress" and 10 representing "highest level of stress." At the end of one month, the participants will be asked to rate their stress level again. The differences in stress levels will be compared. Which of the following describes a completely randomized design for this experiment?

-The volunteers' names are all placed on equal-sized slips of paper and these slips are put into a hat. The therapist draws 30 slips of paper and the corresponding volunteers are placed into the yoga group. The remaining 30 volunteers are placed in the meditation group. After one month, the stress levels between the two groups are measured and compared. Volunteers are put together based on stress level in groups of two. For each group of two, a coin is flipped and if it is heads, then the first person is placed in the yoga group, and if it is tails, then the first person is placed in the meditation group. The other person will be placed in the other group. After one month, the stress levels between the two participants are measured and compared. The volunteers' names are all placed on equal-sized slips of paper and these slips are put into a hat. After the hat is shaken, a slip of paper is drawn without replacement and the corresponding volunteer is placed in the yoga group. This is repeated until the yoga group has 30 volunteers. The remaining 30 volunteers are placed in the meditation group. After one month, the stress levels between the two groups are measured and compared. The volunteers are grouped based on their current stress level. The 30 volunteers with the highest level of reported stress are placed in one group and the remaining 30 volunteers are placed in another group. The therapist flips a coin and if it lands on heads, then the group with the highest stress levels will receive the yoga treatment. If it lands on tails, then this group will receive the meditation treatment. After one month, the stress levels will be compared between the two groups.

A tire company wants to determine if tires made with a new type of tread will last longer than the tires made with the original type of tread. The company has access to 24 different vehicles. The vehicles will be driven for one year and the depth of the remaining tread will be measured. The average depth for the new type of tread will be compared to the average depth of the original type of tread. Which of the following describes a randomized block design for this experiment?

-There are six vehicles of each vehicle type: sedan, SUV, minivan, and truck. For each type, three vehicles will be randomly selected to receive tires with the new tread and the other three vehicles will receive tires with the original tread. Each vehicle is numbered 1-24, and these numbers are put into a random number generator. The first 12 unique numbers represent the vehicles that will receive the tires with the new tread. The remaining 12 vehicles will receive the tires with the original tread. The vehicles will be put in groups of two based on the size of the vehicle, with the largest two put together, the next largest two, etc. For each of the 12 pairs, the largest vehicle will get tires with the original type of tread and the other vehicle in the pair will get the new type of tread. There are six vehicles of each vehicle type: sedan, SUV, minivan, and truck. Each vehicle type is numbered 1-4, and these numbers are entered into a random number generator. The first two unique numbers selected will represent the group of vehicles that will receive tires with the new type of tread. The remaining 2 groups will receive tires with the original tread.

A biology student wants to determine if using a fertilizer would help promote the growth of new babies in spider plants. The student chooses 100 baby spider plants to be used in the study. They all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light. Half of the plants are randomly assigned to the group that receives fertilizer every three months and the remaining plants are assigned to the group that does not receive fertilizer. After one year, the shoots are counted for each plant. The average number of shoots for the plants receiving fertilizer is compared with the average number of shoots for the plants that did not receive fertilizer. Is this a completely randomized design?

-Yes, the plants were randomly assigned each treatment. Yes, the plants received the same amount of soil, water, and light. No, only spider plants were used. No, the plants did not all receive the same treatment.

Lynnetta gets paid weekly for completing household chores. The amount of money she earns for doing dishes, D, is approximately Normally distributed with a mean of $53 and a standard deviation of $3.60. The amount of money she earns for doing laundry, L, is approximately Normally distributed with a mean of $47 and a standard deviation of $4.10. Assume that D and L are independent random variables. What is the probability that Lynnetta will earn more than $110 in a randomly selected week?

0.034

At a carnival game, the chance of winning a prize is 0.45. Elijah plays the game 5 times. What is the probability that he wins 1 prize in 5 games?

0.04

A tire company wants to determine if tires made with a new type of tread will last longer than tires made with the original type of tread. The company decides to put tires with the new tread on 10 different vehicles and tires with the original tread on 10 different vehicles. "New" is written on one slip of paper and "Original" is written on another slip of paper. The two slips are placed in a bag and thoroughly mixed. A vehicle is selected and a slip is drawn. The corresponding tread of tires is assigned to the vehicle. The slip is put back into the bag and mixed. The next vehicle is selected and a slip is drawn. The corresponding tread is assigned to the vehicle. This procedure continues until all 20 vehicles have been assigned tires of the new or original types of tread. Does this procedure describe a completely randomized design for this experiment?

-Yes, the tires are randomly assigned to each vehicle. Yes, there are two treatments, new and original treads. No, even though randomness is used, the procedure does not ensure that an equal number of vehicles are in both groups. No, the company did not use 20 of the same type of vehicle to receive both treatments, the new and original treads.

summarize the t-test for matched pairs

-find the differences between the measurements (find "d") -apply all other t procedures

what can hinder interference in practice?

-practical problems (nonresponse, dropouts) -not using random data

what do we do when the population standard deviation (σ) is unknown?

-use the t-statistic -use table C

what do we conclude if the p-value is larger than the significance level(α)

-we can accept the null hypothesis -the data are not statistically significant

what do we conclude if the p-value is the same or smaller than the significance level(α)

-we can reject the null hypothesis -the data are statistically significant at level α

In bags of Happy Trail Mix, the number of raisins is skewed left with a mean of 33.6 and a standard deviation of 8.4, while in bags of a generic trail mix, the number of raisins is skewed right with a mean of 28.8 and a standard deviation of 12.7. What is the probability in a sample of 17 randomly selected Happy Trail Mix bags and a sample of 17 randomly selected generic bags that the mean number of raisins in the Happy Trail Mix is more than the mean number of raisins in the generic mix?

.9032

At a carnival, a customer notices that a prize wheel has 5 equal parts, one of which is labeled "winner." She would like to conduct a simulation to determine how many spins it would take for the wheel to land on "winner." She assigns the digits to the outcomes. 0, 1 = winner 2-9 = not a winner Here is a portion of a random number table. Beginning at line 1 and starting each new trial right after the previous trial, carry out 5 trials of this simulation. What proportion of the 5 trials takes more than 10 spins to win a prize?

The graph shows the number of states and Washington, DC, within each range of electoral votes for the 2020 presidential election. What is the variability of electoral votes that states will have for the 2020 presidential election?

0 to 21 electoral votes

Tennis balls must have a high rebound, or bounce, that is approved by the International Tennis Federation. Rebound is measured by dropping a ball from a height of 100 inches and measuring how high it bounces. Approved balls must bounce back up 53 to 58 inches. A tennis coach tested 50 tennis balls and found that the mean bounce was 56.2 inches and the standard deviation was 1.8 inches. The z-score of a ball that bounces 56.2 inches is - . This ball has a bounce that is - the mean.

0.0 equal to

The number of turns of a pencil sharpener needed to sharpen a brand W pencil is approximately Normally distributed with a mean of 4.6 and a standard deviation of 0.67. The number of turns needed to sharpen a brand H pencil is approximately Normally distributed with a mean of 5.2 and a standard deviation of 0.33. If 30 pencils of each brand are randomly selected and sharpened, what is the probability that the brand W pencils will have a higher mean number of turns needed to sharpen than brand H?

0.0005

The times a musician spends performing a rock song and a country song are approximately Normally distributed. The rock song has a mean time of 133 seconds with a standard deviation of 3.5 seconds, and the country song has a mean time of 126 seconds with a standard deviation of 3.3 seconds. If the musician randomly selects 4 times the rock song is played and 3 times the country song is played, what is the probability that the mean time for the rock song is less than the mean time for the country song?

0.0034

A course for a snail race has times that are skewed right with a mean of 5.18 minutes and a standard deviation of 2.34 minutes. If a random sample of 38 snails is selected, what is the probability that the mean race time is less than 4.3 minutes?

0.0102

The number of pieces of dog food in a one-cup scoop is approximately Normally distributed with a mean of 205 pieces and a standard deviation of 9.2 pieces. If a random sample of 15 scoops of dog food is selected, what is the probability that the mean number of pieces of food will be less than 200 pieces?

0.0177

A group of students is writing a phone message app to provide better word suggestions based on the context of the word and the words the person used in the past. They will earn an A on the project if their teacher is convinced that their program suggests the correct word at least 54% of the time. The current success rate for this app is 54%. The teacher randomly selects 100 words and finds that the students' program correctly suggests 64 of the words. To determine if this data provide convincing evidence that the proportion of correct words is more than 54%, 150 trials of a simulation are conducted. The results are shown in the dotplot. The teacher is testing the hypotheses: H0: p = 54% and Ha: p > 54%, where p = the true proportion of words the app will correctly predict. Based on the results of the simulation, what is the estimate of the P-value of the test?

0.02

multiple analyses

if you actually run the test many times, there is a low probability that the confidence interval will actually capture the true mean

Hans has two route options to drive to work. When he travels Hampton Road, the distribution of times is approximately Normal with a mean of 23.9 minutes and a standard deviation of 3.1 minutes. When Hans travels Route 8, the distribution of times is approximately Normal with a mean of 20.8 minutes and a standard deviation of 5.4 minutes. Hans randomly selects 11 times he drove Hampton Road and 11 different times that he drove Route 8. What is the probability the mean time of the Hampton Road trips will be less than the mean of the Route 8 trips?

0.0493

A commuter train is late to a station 5% of the time. Last week, the train was late on 2 of the 7 days. If the train being late can be considered a random event, what is the probability that the train would be late 2 times in 7 days?

0.050

A large company boasts in their promotional literature that 74% of their employees have college degrees. Assume this claim is true. What is the probability that if people are selected at random from this company, that the first person to have a college degree is the 3rd person selected?

0.0500

A jar contains 11 red marbles, 12 blue marbles, and 6 white marbles. Four marbles from this jar are selected, with each marble being replaced after each selection. What is the probability that the first red marble chosen is on the 5th selection?

0.0563

Devon's tennis coach says that 72% of Devon's serves are good serves. Devon thinks he has a higher proportion of good serves. To test this, 50 of his serves are randomly selected and 42 of them are good. To determine if these data provide convincing evidence that the proportion of Devon's serves that are good is greater than 72%, 100 trials of a simulation are conducted. Devon's hypotheses are: H0: p = 72% and Ha: p > 72%, where p = the true proportion of Devon's serves that are good. Based on the results of the simulation, what is the estimate of the P-value of the test?

0.06

A medical device company knows that the percentage of patients experiencing injection-site reactions with the current needle is 11%.What is the probability that an injection-site reaction occurs for the first time on the 6th patient of the day?

0.0614

At a certain pizzeria, it is known that 12% of orders are for extra-large pizzas. What is the probability that the 6th pizza ordered is the first extra-large pizza?

0.0633

Hannah has a chicken coop with six hens. Let X represent the total number of eggs the hens lay on a random day. The distribution for X is given in the table. What is the probability that the hens lay a total of two eggs?

0.07

The owner of an apple orchard has learned from previous experience that, on average, 5% of the harvested apples have blemishes. The owner randomly selects 10 apples from this year's harvest. What is the probability that 2 of the apples have blemishes?

0.07

The weight of panda bears, P, is approximately Normally distributed with a mean of 185 pounds and a standard deviation of 12.3 pounds. The weight of koala bears, K, is approximately Normally distributed with a mean of 21.5 pounds and a standard deviation of 4.8 pounds. Suppose a zookeeper randomly chooses a panda and a koala bear, where P and K are independent random variables. What is the probability that the total weight for the two animals is 225 pounds or more?

0.081

A fair six-sided number cube is rolled 60 times. What is the probability that fewer than 10% of the rolls are a five?

0.082

A computer technician notes that 40% of computers fail because of the hard drive. If he repairs many computers a day, what is the probability that the first computer that has failed due to the hard drive is his 4th computer of the day?

0.0864

The total number of forks dropped by customers per day at a busy restaurant is multimodal with a mean of 24.5 and a standard deviation of 3.3. If a random sample of 80 days is selected, what is the probability that the mean number of forks dropped during those days will be more than 25?

0.088

The table shows the number of cars sold per day at a dealership during a promotional sale. What is the equation of the least-squares regression line, where is the predicted number of cars sold and xis the day? Round each coefficient or constant to the nearest tenth.

0.1 1.8

0.1032

0.13

At a manufacturing plant, it is known that 8% of the computer chips produced are defective. A random sample of 20 chips is taken. What is the probability that 3 of those chips are defective?

0.14

The owner of a local movie theater keeps track of the number of tickets sold in each purchase. The owner determines the probabilities based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table. What is the probability that a randomly selected purchase has less than two tickets?

0.17

A shipping company claims that 90% of its packages are delivered on time. Jenny noticed that out of the last 10 packages shipped, 2 were late. What is the probability that 2 out of 10 randomly selected shipments would be late?

0.19

At West High School, 10% of the students participate in sports. A student wants to simulate the act of randomly selecting 20 students and counting the number of students in the sample who participate in sports. The student assigns the digits to the outcomes. 0 = student participates in sports 1-9 = student does not participate in sports Here is a portion of a random number table. In the first trial, line 1, two of the 20 digits are zeros, meaning that two of the 20 selected students participate in sports. Starting at line 2 and using a new line for each trial, carry out 4 more trials to determine the number of students who participate in sports in random samples of size 20. In what proportion of all 5 trials do we find that 0 students participate in sports?

0.2

At a local coffee shop, the manager has determined that 56% of drink orders are for specialty espresso drinks and 44% are for plain coffee. The manager also noted that 40% of customers order food. For customers who purchase the specialty espresso drinks, 35% also purchase a food item, and for customers who purchase plain coffee, 30% also purchase a food item. What is the probability that a randomly chosen customer will purchase a specialty espresso drink and a food item?

0.20

Renee and Thomas live at the beach and collect seashells. The number of shells Renee collects on any given day, R, is approximately Normal with a mean of 58.2 shells and a standard deviation of 12.8 shells. The number of shells Thomas collects on any given day, T, is approximately Normal with a mean of 47.9 shells and a standard deviation of 11.5 shells. Assume the two random variables are independent of each other. What is the probability that on a randomly selected day the total number of shells collected by Renee and Thomas is 120 or more?

0.209

One professional basketball player typically attempts eight free throws per game. Let X represent the number of free throws made out of eight. The distribution for X is shown in the table. What is the probability that the basketball player will make six free throws out of the eight attempts?

0.21

At a certain high school, 38% of freshmen and 31% of sophomores walk to school. Suppose that random samples of 40 freshmen and 45 sophomores are chosen. Let S = the proportion of sophomores who walk to school and F = the proportion of freshmen who walk to school. What is the probability that the proportion of sophomores who walk to school is greater than the proportion of freshmen?

0.248

On any given day, 34% of sales at Ruby's jewelry store are from necklaces, while 28% of sales at Nugget Jewels are from necklaces. Suppose Ruby's has 50 customers and Nugget Jewels has 60 customers on a randomly selected day. Let R = the proportion of sales that are from necklaces at Ruby's and N = the proportion of sales that are from necklaces at Nugget Jewels. What is the probability that the proportion of sales from necklaces at Ruby's will be less than the proportion of sales from necklaces at Nugget Jewels?

0.250

In a large local high school, 19% of freshmen have had their wisdom teeth removed and 24% of seniors have had their wisdom teeth removed. Suppose that a random sample of 60 freshmen and 50 seniors is selected. Let F = the proportion of freshmen who have had their wisdom teeth removed and S = the proportion of seniors who have had their wisdom teeth removed. What is the probability that the proportion of freshmen who have had their wisdom teeth removed is greater than the proportion of seniors?

0.263

A business has an opportunity to invest $35,000. If the investment is a success, the business earns a profit of $150,000. Otherwise, the investment will result in a total loss of all monies. If the investment has 0.27 chance of success, which equation correctly models the expected value of this investment?

0.27(150,000) + 0.73(-35,000) = E(X)

In a beach town, 13% of the residents own boats. A random sample of 100 residents was selected. What is the probability that less than 11% of the residents in the sample own boats?

0.276

A quarterback's pass-completion percentage is 70%. Eight of his passes are randomly selected. What is the probability that 6 of them were successful passes?

0.30

The grade distribution for students in the introductory statistics class at a local community college are displayed in the table. In this table, A = 4, B = 3, etc. Let X represent the grade for a randomly selected student. What is the probability that a randomly selected student got a B?

0.31

0.32

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let X represent the score on a randomly selected exam. The distribution of scores for one subject's standardized test is given in the table. What is the probability of earning a score lower than 3?

0.38

Ricardo and Tammy practice putting golf balls. Ricardo makes 47% of his putts and Tammy makes 51% of her putts. Suppose that Ricardo attempts 25 putts and Tammy attempts 30 putts. Let R = the proportion of putts Ricardo makes and T = the proportion of putts Tammy makes. What is the probability that Ricardo makes a higher proportion of putts than Tammy?

0.384

A placekicker for a football team makes field goals 85% of the time when kicking from the 20-yard line. Assuming that field goal attempts can be considered random events, what is the probability that the placekicker will make 4 of his next 5 attempts from the 20-yard line?

0.39

A large hotel has five elevators. On any given day, there is an 8% chance that one elevator is broken The elevators operate independently of one another. The Robertsons are staying in this hotel for five days. Let X represent the number of days one elevator is broken during their stay. What are the mean and standard deviation of X?

0.4, 0.61

Carol and Diane are axe throwers. Carol hits the board on 44% of her throws, while Diane hits the board on 42% of her throws. Suppose that Carol throws 25 axes at the board and Diane throws 28. Let C = the proportion of axes that hit the board when Carol throws and D = the proportion of axes that hit the board when Diane throws. What is the probability that Diane's proportion of axes hitting the board is higher than Carol's?

0.442

One study of 91 bald eagle eggs found that the eggs had a mean length of 73.6 millimeters and standard deviation of 2.9 millimeters. One of the bald eagle eggs found was 74.9 millimeters long. Which is closest to the z-score for the egg?

0.45

The owner of a used car dealership is trying to determine if there is a relationship between the price of a used car and the number of miles it has been driven. The owner collects data for 25 cars of the same model with different mileage and determines each car's price using a used car website. The analysis is given in the computer output. Using the computer output, what is the value of the coefficient of determination?

0.46 -0.68 0.70 0.82

In an urban area, 31% of dog owners pay for someone to walk their dogs. Morgan asks a random sample of 50 dog owners in this urban area if they pay for someone to walk their dog. What is the probability that more than 30% of the owners in the sample pay for someone to walk their dog?

0.561

A placekicker for a football team makes field goals 55% of the time when kicking from the 35-yard line. Assume that field goal attempts can be considered random events. Using the table, what is the probability that the placekicker will make at least 3 of his next 5 attempts from the 35-yard line?

0.60

The heights of five-year-olds are Normally distributed with a mean of 42.5 inches and a standard deviation of 2.5 inches. A random sample of 16 five-year-olds is taken and the mean height is recorded. What would be the standard deviation of the sampling distribution of all possible samples of size 16?

0.63

Among the senior class at a high school, 55% of Ms. Keating's students plan on majoring in a branch of STEM, while 49% of Ms. Lewis's students plan on majoring in a branch of STEM. Suppose Ms. Keating chooses 25 of her students at random and Ms. Lewis chooses 23 of her students at random. Since nKpK, nK (1 - pK) and nLpL, nL (1 - pL) are all greater than 10, the Normal condition is met. Let K = the proportion of Ms. Keating's students from the sample who plan on majoring in a branch of STEM, and let L = the proportion of Ms. Lewis's students from the sample who plan on majoring in a branch of STEM. What is the probability that the proportion of students who plan on majoring in a branch of STEM is greater for Ms. Keating?

0.662

A student decides to spin a dime and determine the proportion of times it lands on heads. The student spins the dime 25 times and records that it lands on heads 17 times. Let p = the true proportion of times the dime would land on heads when spun. If the true proportion is 0.5, which of the following sample proportions is the least likely to occur?

0.7

The table shows how surveyed drivers obtained their current vehicle and how they plan to get their next vehicle. What proportion of the drivers who said they currently lease a vehicle plan to lease their next vehicle?

0.72

Driving instructors Mr. Adams and Mr. Bateman teach class independently of each other. Among Mr. Adams's students, 68% pass the driving test on the first try, while 74% of Mr. Bateman's students pass the driving test on the first try. Suppose there are 40 students in Mr. Adams's class and 50 students in Mr. Bateman's class. Let A = the proportion of students who pass the driving test on the first try from Mr. Adams's class and B = the proportion of students who pass the driving test on the first try from Mr. Bateman's class. What is the probability that Mr. Bateman's class has more students who pass on the first try?

0.734

You are challenged to a lucky draw game. If you draw a face card (K, Q, J) from a standard deck of cards, you earn 10 points. If you draw any other card, you lose 2 points. What is the expected value of a draw?

0.77

A spinner with four equal sectors labeled "purple," "blue," "orange," and "green" is spun 45 times. What is the probability that the spinner will land on "purple" in fewer than 20% of the spins?

0.779

A statistics teacher has a large container of beads that she says contains 60% blue beads. A student randomly selects 50 beads. Let p = the true proportion of blue beads in the container. If the true proportion of blue beads is 0.60, which value of p is least likely to occur?

0.80

A certain standardized test measures students' knowledge in English and math. The English and math scores for 10 randomly selected students are given in the table. Using technology, what is the value of r2?

0.83

0.91

Latisha owns two spas, one in Pine township and the other in Adams township. Each spa offers a 30-minute face, head, and neck massage to reduce muscle tension. However, therapists first ask each patient questions about their type of tension and stop about five minutes before the end of the 30 minutes to have time to prepare for the next patient. The number of minutes each therapist massages the patients at both spas is approximately Normally distributed, with the Pine spa having a mean of 22.6 minutes and a standard deviation of 1.7 minutes and the Adams spa having a mean of 21.0 minutes and a standard deviation of 2.8 minutes. If Latisha randomly selects 8 massage times from Pine and 9 from Adams, what is the probability that the mean time for Pine is longer than the mean time for Adams?

0.9252

Claire flips a coin 4 times. Using the table, what is the probability that the coin will show tails at least once?

0.94

The owner of a local movie theater keeps track of the number of tickets sold in each purchase and makes a probability distribution based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table. What is the standard deviation of the distribution?

0.95

The table shows the number of kilograms a newborn pig weighs during its first week. What is the equation of the least-squares regression line, where is the predicted weight and x is the day? Round each coefficient or constant to the nearest hundredth.

0.96 0.18

Chris makes a smoothie for breakfast every day. When he makes smoothies with bananas, the distribution of calories is skewed right with a mean of 248.6 and a standard deviation of 39.1. His berry smoothies have a distribution of calories that is approximately Normal with a mean of 279.1 calories and a standard deviation of 60.8. Random samples of 35 of each type of smoothie are selected. What is the probability of the banana smoothies having fewer mean calories than the berry smoothies?

0.9937

The probability that a mature hen will lay an egg on a given day is 0.80. Hannah has 6 hens. Using the table, what is the probability that at least 2 of the hens will lay eggs on a given day?

0.998

The distribution of the number of blocks a young child can stack before their tower falls is approximately Normally distributed with a mean of 12.7 blocks and a standard deviation of 1.4 blocks. If 6 of the child's towers are randomly selected, what is the probability that the mean number of blocks is more than 11 blocks?

0.9985

A farmer sows 100 seeds of a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the crop when it has matured. He decides to take a simple random sample of the crop. Which of the following correctly labels the population?

00-99

A candy manufacturer is testing new brands of sugar and needs to assign 150 recipes to two treatment groups. A table of random digits will be used to generate the sample. Select the appropriate way to number the experimental units.

000-149

A school principal wants to conduct a survey of student electronic use in her high school. She wants to select an SRS of 50 from the 690 students in the school using a random number table. Which of the following are correct methods for labeling the population? Check all that apply.

000-689 001-690

A greenhouse owner wants to test the effectiveness of a new fertilizer on African violets. She has 60 violet seedlings that were grown for 8 weeks. She wants to test the new fertilizer on 10 of the plants, and decides to use a random number table to select a simple random sample. Which of the following correctly labels the population of violets?

01-60

Several members of a running club would like to survey the rest of the members to determine which 5K races the club should enter. They decide to use a random number table to sample 10 of the 78 members. Which of the following correctly labels the population?

01-78

Based upon historical data, it is known that 8% of 12-egg cartons contain at least one broken egg. A grocery store manager would like to carry out a simulation to estimate the number of cartons, in a sample of 10, that would contain at least one broken egg. She assigns the digits to the outcomes: 01-08 = carton contains a broken egg 09-99, 00 = carton does not contain a broken egg Here is a portion of a random number table. Beginning at line 1, carry out one trial of this simulation. Use additional lines as needed. How many cartons in this random sample of 10 cartons contain at least one broken egg?

A real estate company wanted to see the relationship between home prices and square footage of homes for sale. The regression line is ŷ = -802,456 + 144x, where x is the square footage of a home.

1 144

A politician estimates that 61% of his constituents will vote for him in the coming election. How many constituents are required for a random sample to obtain a margin of error of at most 0.03 with 95% confidence?

1,016

how to calculate the p-values for each of the t tests

1. For Ha:μ≠μo, calculate 2P(T>|n|) 2. For Ha:μ>μo, calculate P(T>t) 3. For Ha:μ<μo, calculate P(T<t)

What are the three basic types of hypothesis tests for the population mean(μ)? -one-sided or two-sided?

1. Ho:μ=μo vs. Ha:μ>μo (one-sided) 2. Ho:μ=μo vs. Ha:μ<μo (one-sided) 3. Ho:μ=μo vs. Ha:μ≠μo (two-sided)

summarize how to use hypothesis tests on the population mean (μ)

1. State H0 and Ha 2. Calculate the test statistic z = x - population mean 0) / (standard deviation/square root of n) 3. Calculate the p-value for the test. 4. Make a decision based on the p-value. If p-value is less then or equal to the decisive value, we reject H0 and accept Ha. If p-value is greater than the decisive value, we do not reject H0.

summarize the t-test

1. state Ho vs. Ha 2. decide on one-sided or two-sided test 3. choose significance level 4. calculate t and its degrees of freedom 5. use table C to find the area under the curve 6. state p-value and interpret result

what are the 2 circumstances where only a very large p-value is convincing evidence against Ho

1. the Ho has been believed for years 2. if rejecting Ho means making a costly changeover

In a statistics class, students were asked how many siblings they have. Their responses are shown. 2, 3, 1, 3, 5, 3, 3, 3, 6, 3, 5, 0, 3 What is the z-score for the student with five siblings?

1.19

A certain standardized test measures students' knowledge in English and math. The English and math scores for 10 randomly selected students were recorded and analyzed. The results are shown in the computer output. Which of the following represents the standard deviation of the residuals?

1.223 -34.55 78.712 124.13

Hannah has a chicken coop with 6 hens. Let X be the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table. What is the standard deviation of the distribution?

1.39

A professional basketball player typically attempts 8 free throws per game. Let X represent the number of free throws made out of 8. The distribution for X is shown in the table. What is the standard deviation of the distribution?

1.40

What is the z* critical value for constructing an 88% confidence interval for a proportion?

1.55

What is the z* critical value for constructing a 90% confidence interval for a proportion?

1.65

What is the z* critical value for constructing a 92% confidence interval for a proportion?

1.75

Twenty-four pairs of adult brothers and sisters were sampled at random from a population. The difference in heights, recorded in inches (brother's height minus sister's height), was calculated for each pair. The 95% confidence interval for the mean difference in heights for all brother-and-sister pairs in this population was (-0.76, 4.34). What was the sample mean difference from these 24 pairs of siblings?

1.79 inches

The length (in inches) and weight (in ounces) for a type of bass were measured for a random sample of 10 bass from a lake. These measurements were then analyzed and the results are given in the computer output. Which of the following represents the average distance between the actual weight and the predicted weight of the bass?

1.80

What is the z* critical value for constructing a 94% confidence interval for a proportion?

1.88

A manufacturing company has 5 vice presidents: Andrew, Beth, Charles, Diane, and Eric. Their regional responsibilities are shown in the table. The president of the company wants to randomly select 2 of the 5 vice presidents to send to a conference. How many distinct groups of 2 vice presidents can be selected without replacement from this small population of 5 vice presidents?

The stemplot shows the years of experience for several teachers at Sycamore High School. What is the IQR of the data?

10 years

A random sample of 40 seniors reveals that 10% of those sampled have assigned parking spaces in the high school's main lot. This is surprising because, according to the main office of a large high school, 45% of seniors have assigned parking spaces in the high school's main lot. Which of the following statements is true?

10% is a statistic and 45% is a parameter.

The list shows the mileage rating (in mpg) for some 2019 vehicles with all-wheel or four-wheel drive. 11, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 27, 28, 29, 30, 31, 32, 33, 34 Which intervals are most appropriate for a histogram displaying the mileage ratings?

10-15, 15-20, 20-25, 25-30, 30-35

Based on data taken from airline fares and distances flown, it is determined that the equation of the least-squares regression line is ŷ = 102.50 + 0.65x, where ŷ is the predicted fare and x is the distance, in miles. One of the flights was 500 miles and its residual was 115.00. What was the fare for this flight?

102.50 312.50 427.50 -542.50

Two local hotels, X and Y, rent out rooms nightly. Let X represent the number of rooms hotel X rents out nightly, and let Y represent the number of rooms hotel Y rents out nightly. The mean of X is 49, and the mean of Y is 58. Which answer choice correctly calculates and interprets the mean of the sum, S = X + Y?

107; the hotels can expect to rent out 107 rooms, on average, each night.

The scatterplot shows the relationship between the number of participants in a fundraiser and the amount of money raised. The regression equation is ŷ = 67.79 + 6.72x. How many participants are needed in order for the school to raise $800?

109

The fare charged for a rideshare service is a function of the distance traveled. However, the fare differs according to the time of day, availability, and other variables. The distance and fares for 10 rides are shown in the table. The equation of the least-squares regression line is ŷ = 5.20 + 2.33x, where ŷ is the predicted fare and x is the distance. What is the residual for the rideshare cost with a distance of 16 miles?

11.35

120.4

An arena manager tallies the number of snack items (hot dogs, nachos, and popcorn) sold at each of three concession stands in the arena. Snack Item Hot DogsNachosPopcornTotalConcessionStandsStand A1256540230Stand B21811952389Stand C655213130 Total408236105749 What is the probability that a customer purchased popcorn, given that they purchased from stand B?

13.4%

The table shows how surveyed drivers obtained their current vehicle and how they plan to get their next vehicle. What percent of drivers surveyed bought their current vehicle new and will buy a new vehicle again next time? Round your answer to the nearest whole number; you do not need to enter the percent symbol.

The probability of an archer hitting her target is 83%. Suppose she has 20 shots to take, and each shot is independent of the others. Let X represent the number of targets hit. What is the mean of X? 4.1 8.3 16.6 83

16.6

Carlos notices he usually pushes the clear button on his calculator more than once each time he wants to clear the screen. Carlos' teacher suggests that about 20% of all students have this habit, but Carlos thinks it might be greater. He randomly selects 100 students in his school and finds that 25 of them push the clear button more than once. To determine if these data provide convincing evidence that the proportion of students who push the clear button more than once is greater than 20%, 100 trials of a simulation are conducted. Carlos is testing the hypotheses: H0: p = 20% and Ha: p > 20%, where p = the true proportion of students who push the clear button more than once. Based on the results of the simulation, what is the estimate of the P-value of the test?

17%

A farmer determines that, on average, his chickens lay a total of 16 eggs each day. A random sample of 10 days was taken, and the mean number of eggs was determined. Let μ = the true mean number of eggs the chickens lay each day. Which of the following values for the sample mean is the least likely to occur?

The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. An analysis was completed and the computer output is shown. PredictorCoefSE Coeft-ratiopConstant-14.714.3171.6890.046Handspan1.5850.3105.1140.000 S = 3.05R-Sq = 52.1%R-Sq(Adj) = 51.7% Using the computer output, what is the predicted number of pretzels a person with a handspan of 21 cm could grab?

18.58 pretzels

2.95

The final exam grade distribution for all students in the introductory statistics class at a local community college is displayed in the table, with A = 4, B = 3, C = 2, D = 1, and F = 0. Let X represent the grade for a randomly selected student from the class. What is the mean of the distribution?

2.98

A farmer sows 100 seeds of a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the crop when it has matured. He decides to take a simple random sample of the crop by using a random digit table. What is the fewest number of digits that should be used, given that there are 100 plants in total?

At West High School, 10% of the students participate in sports. A student wants to simulate the act of randomly selecting 20 students and counting the number of students in the sample who participate in sports. The student assigns the digits to the outcomes. 0 = student participates in sports 1-9 = student does not participate in sports Here is a portion of a random number table. Beginning at line 1, carry out one trial of this simulation. Use additional lines as needed. How many students in this random sample of 20 students participate in sports?

At a carnival, a customer notices that a prize wheel has 5 equal parts, one of which is labeled "winner." She would like to conduct a simulation to determine how many spins it would take for the wheel to land on "winner." She assigns the digits to the outcomes. 0, 1 = winner 2-9 = not a winner Here is a portion of a random number table. Beginning at line 1, carry out one trial of this simulation. Use additional lines as needed. How many spins does it take until the first prize is won?

hypothesis tests (tests of significance)

2 hypotheses about the population and the null and alternative hypothesis

A spinner is divided into six equal-sized sectors labeled 1 through 6. Dwayne spins this spinner 12 times. Let X represent the number of 1s that are spun. What are the mean and standard deviation of X?

2, 1.29

A jar contains 11 red marbles, 12 blue marbles, and 6 white marbles. Four marbles from this jar are selected, with each marble being replaced after each selection. What is the standard deviation of X, the number of draws until the first red marble?

2.0770

A local charity holds a carnival to raise money. In one activity, participants make a $3 donation for a chance to spin a wheel that has 10 spaces marked with the values 0, 1, 2, 5, and 10. The participant wins the dollar amount marked on the space on which the wheel stops. Let X represent the value of a spin. The distribution of X is given in the table. What is the expected value of the distribution?

2.1

The dotplot shows the number of hours per day 20 high school students spent watching television shows one summer. Use the dotplot to answer the questions. The median number of hours is -. This median number of hours indicates that -.

2.5 the same number of students spend less than and more than 2.5 hours

What is the z* critical value for constructing a 99% confidence interval for a proportion?

2.58

The table shows the number of smartphones sold at an electronics store each day. To the nearest tenth, what is the standard deviation of the data? Use this formula:

2.7 smartphones

A cafeteria purchases milk from one of three providers each week, depending on what other items need to be purchased. The probability of shopping at each store and the cost of one gallon of milk are shown in the table below.

2.90

The list shows the mileage rating (in mpg) for some 2019 vehicles with all-wheel or 4-wheel drive. 11, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 27, 28, 29, 30, 31, 32, 33, 34 Which interval has the greatest frequency?

20-25

The table shows the horsepower and top speeds of a variety of boat motors. What is the equation of the least-squares regression line, where ŷ is the predicted top speed and x is the horsepower?

21.2 .14 35

Natalia estimates that she wins a board game 72% of the time. How large of a random sample is required to obtain a margin of error of at most 0.06 with 95% confidence?

216

The stemplot below displays the times, in seconds, for 25 students to run 100 meters. Which of the following is the correct five-number summary?

22, 24.5, 26, 28, 30

A recent study estimated that 68% of US adults enjoy reading a book while relaxing. How many adults are required for a random sample to obtain a margin of error of at most 0.05 with 90% confidence?

236

25.49 wins

A scientist wants to sample fish from a large aquarium to estimate the true proportion of striped fish. How many fish are required for a random sample to obtain a margin of error of at most 0.06 with 95% confidence?

267

A game of "Doubles-Doubles" is played with two dice. If a player rolls doubles, the player earns 3 points and gets another roll. If the player rolls doubles again, the player earns 9 more points. How many points should the player lose for not rolling doubles in order to make this a fair game?

27/35

In a certain breed of cattle, the length of gestation has a mean of 284 days and a standard deviation of 5.5 days. What is the length of the gestation period, to the nearest whole number, that is 0.7 standard deviations below the mean?

280 days

A researcher needs to assign 45 subjects, numbered 01 to 45, to one of three treatment groups: A, B, or C. Use the table of random digits, starting with the first row and first column, to carry out the random assignment. Which subjects will be in group A?

29, 17, 37, 20, 45, 27, 12, 23, 26, 25, 19, 30, 11, 28, 31

A researcher is comparing the effectiveness of three devices designed to help people who snore. There are 60 people who snore participating in the experiment who are labeled 01-60. Using a table of random digits, the researcher will randomly place the participants into three equally sized treatment groups suitable for comparison. Carry out the random assignment using the given selection from a table of random digits, starting with the first row and first column. Which list assigns the first eight people to the device 1 group?

29, 17, 37, 48, 20, 27, 12, 23

A shipping company claims that 95% of packages are delivered on time. A student wants to conduct a simulation to estimate the number of packages that would need to be randomly selected to find a package that was not delivered on time. The student assigns the digits to the outcomes. 00-04 = package not delivered on time 05-99 = package delivered on time Here is a portion of a random number table. Beginning at line 1, carry out one trial of this simulation. Use additional lines as needed. How many packages need to be selected at random in order to find one that is not delivered on time?

At a large university, 20% of students are enrolled in the nursing program. The dean of students selects a random sample of 20 students and records n = the number of students enrolled in the nursing program. The dean decides to simulate this random process by using a random number table. He assigns the digits to the outcomes. 1, 2 = student is enrolled in nursing program 3-9, 0 = student not enrolled in nursing program Here is a portion of a random number table. Beginning at line 1, carry out one trial of this simulation. Use additional lines as needed. How many students in this random sample of 20 students are enrolled in the nursing program?

Mrs. Bready has a large bag filled with red and green cards. She tells the class that 15% of the cards are red and 85% are green. At the end of each class, she mixes the cards, reaches inside the bag, and draws out one card at random. If a red card is drawn, the students will not be assigned homework. She shows the class the card, and then places the card back in the bag. Carla would like to carry out a simulation to estimate the number of days it will take in order to get a "no homework" day. She assigns the digits to the outcomes. 00-14 = red 15-99 = green Here is a portion of a random number table. Beginning at line 1, carry out one trial of this simulation. Use additional lines as needed. How many days does it take to find the first "no homework" day?

The graph shows the number of states and Washington, DC, within each range of electoral votes for the 2020 presidential election. Which interval contains 11 states? Check all that apply.

3 to 6 6 to 9

A local charity holds a carnival to raise money. In one activity, participants make a $3 donation for a chance to spin a wheel that has 10 spaces marked with the values 0, 1, 2, 5, and 10. The participant wins the dollar amount marked on the space on which the wheel stops. Let X be the value of a random spin. The distribution of X is given in the table. What is the standard deviation of the distribution?

3.01

There are frogs and koi in a pond, and the number of frogs and the number of koi in the pond are independent. Let X represent the number of frogs in any given week, and let Y represent the number of koi in any given week. X has a mean of 28 with a standard deviation of 2.7, and Y has a mean of 15 with a standard deviation of 1.6. Which answer choice correctly calculates and interprets the standard deviation of the difference, D = X - Y?

3.1; this pond can expect the difference of frogs and koi to vary by approximately 3.1 from the mean.

The daily temperatures for the winter months in Virginia are Normally distributed with a mean of 59°F and a standard deviation of 10°F. A random sample of 10 temperatures is taken from the winter months and the mean temperature is recorded. What is the standard deviation of the sampling distribution of the sample mean for all possible random samples of size 10 from this population?

3.2

During the 2016 Rio Olympics, Simone Biles scored 62.366 points in the women's all-around competition, and Oleg Verniaiev scored 91.964 points in the men's all-around competition. Both Biles and Verniaiev won gold medals. Which athlete had a stronger performance? Round to the nearest hundred, if necessary.

3.257 greater than 2.433 simone biles oleg v

According to records at the guidance office, the mean GPA of all juniors is 3.45 and the mean GPA of all seniors is 3.62. Which of the following statements is true?

3.45 is a parameter and 3.62 is a parameter.

The probability of a high school basketball team winning any game is 58%. This team is in a six-game tournament, and the games are played independently of one another. Let X represent the number of games the team might win in this tournament. What are the mean and standard deviation of X?

3.48, 1.21

The weights of bunches of bananas in the grocery store are Normally distributed with a mean weight of 3.54 pounds and a standard deviation of 0.64 pounds. A random sample of four bunches is taken and the mean weight is recorded. Which of the following is the mean of the sampling distribution for the mean of all possible samples of size four?

3.54

he histogram shows the heights of flowers in a greenhouse. The interval - contains the median height of the flowers. This median height indicates that -.

30-40 ✔ about the same number of flowers are shorter than and taller than the interval of 30-40 inches.

The owner of an apple orchard knows that the average weight of Granny Smith apples is 380 grams. A random sample of 40 apples was selected and the mean weight was calculated. Let μ = the true mean weight of the Granny Smith apples in the orchard. Which of the following means is least likely to occur if the true mean weight is 380 grams?

300 grams

Mr. Jackson gave an exam worth 50 points. The mean score on the exam was 38, and the standard deviation was 4. Mr. Jackson also reported his students' z-scores. Corey's z-score was -1.75. This means that Corey scored

31 points on the exam

A student wants to investigate the proportion of students who would support a fundraiser at a large high school. Which of the following sample sizes would have the least variability?

When sampling, which of the following sample sizes will yield the smallest variability in results obtained from repeated sampling from the population?

Hannah has a chicken coop with 6 hens. Let X represent the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table. What is the median of the distribution?

Hannah has a chicken coop with 6 hens. Let X represent the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table. What is the mean of the distribution?

4.2

The value of s for a relationship between the number of hours and the number of gallons of water remaining in a tank is calculated using computer software. Identify and interpret the value of s by completing the sentence.

4.80079 gallons 5

The weight of infants follows a bell-shaped distribution with mean 7.5 pounds and standard deviation 1.75 pounds. A baby born two weeks early has a standardized score of -1.5. What is the baby's actual weight? Round your answer to the nearest hundredth.

4.88 pounds at birth

The daily temperatures for the winter months in Virginia are Normally distributed with a mean of 59°F and a standard deviation of 10°F. The daily temperatures for the winter months in California are Normally distributed with a mean of 64°F and a standard deviation of 12°F. Random samples of 10 temperatures are taken from the winter months for both Virginia and California. The mean temperature is recorded for both samples. Let represent the difference in the mean temperatures for the winter months in Virginia and California. Which of the following represents the standard deviation of the sampling distribution for xv-xc?

4.9

In a certain board game, a 12-sided number cube showing numbers 1 through 12 is rolled. In this game, a number cube must be rolled until a number 9 or higher appears. What is the probability that the first such number is on the 3rd roll?

4/27

Vehicles passing over a bridge have two options for paying their bridge toll: paying with a live cashier or using a Speed Pass device affixed to the dashboard. Data on a busy day for cars and trucks passing over the bridge are shown here. Payment Method Live CashierSpeed PassTotalVehicle TypeCar3567102Truck184765 Total53114167 What percentage of vehicles are trucks, given that they use Speed Pass?

41.2%

The heights of five-year-olds are Normally distributed with a mean of 42.5 inches and a standard deviation of 2.5 inches. A random sample of 16 five-year-olds is taken and the mean height is recorded. What would be the mean of the sampling distribution of all possible samples of size 16?

42.5

Market researchers were interested in the relationship between the price of bobbleheads and the demand of bobbleheads. Information was collected from a market research survey and was used to obtain the regression equation ŷ = -0.227x + 50.455, where x represents the price of a bobblehead (measured in dollars) and ŷ is the predicted demand of bobbleheads (in units). What is the predicted demand of a bobblehead that has price of $29.99?

43.64727 units

A sports analyst determines that the number of points scored in a basketball game is related to the number of shots taken during the game. The least-squares regression line is ŷ = 5.0 + 1.2x, where ŷ is the predicted number of points scored and x is the number of shots taken. In one game, a team takes 50 shots and the residual is -10. How many points were scored by this team in this game?

45 -55 65 75

The histogram shows the amount of time Mr. Crawford's students spent on homework. The mean of the data could be - minutes. This mean time indicates that - on homework.

45 on average, students spend 41 to 60 minutes

The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. The times to pop a mini bag of microwave popcorn without burning it are Normally distributed with a mean time of 90 seconds and a standard deviation of 15 seconds. Suppose two independent random samples, 25 of each, are taken and the mean popping times are calculated. Let R = the popping time of a randomly selected regular-sized bag and M = the popping time of a mini-sized bag. Which of the following best describes the standard deviation of the sampling distribution of xr-xm?

5 seconds

The graph displays the vacation preferences of people in relation to their states of residency. Use the drop-down menu to complete the statement based on the bar graph. Kansas residents prefer big city vacations about -more than nature vacations and about - less than beach vacations.

5% 30%

A local sandwich shop makes an Italian sandwich that contains ham, salami, and pepperoni meats. Let X represent the weight of ham, Y represent the weight of salami, and Z represent the weight of pepperoni for each Italian sandwich made. The mean of X is 2 ounces, the mean of Y is 1.25 ounces, and the mean of Z is 1.75 ounces. What is the mean of the sum, S = X + Y + Z?

5.0 ounces

Tropical islands have many rainstorms during the afternoon heat. One particular tropical island has a 79% chance of a rainstorm on any given afternoon. Abraham is planning a weeklong stay on this tropical island. Let X represent the number of days there is an afternoon tropical storm that week. What are the mean and standard deviation of X?

5.53, 1.08

5.79 cm 22.15 cm - 29.76 cm 29.80 cm

A beauty product company conducts a study to test the effectiveness of a new shampoo to control split ends. One hundred subjects have volunteered to take part in the study, and will be split into a treatment group and a placebo group. The study leader will randomly assign the subjects to the groups using slips of paper. How many slips of paper will the researcher need to draw in order to randomly assign subjects to the treatment groups?

A telemarketing company is conducting a study of new calling scripts. Seventy-five employees will be randomly assigned to three new scripts using a table of random digits. The study leader will assign the subjects to the groups using a table of random digits. How many unique two-digit numbers within the range of 01 to 75 will the study designer need to select from the table?

The pie chart shows the favorite type of book of the more than 50,000 high school students. About what percent of favorite type of book is drama? About what percent is mystery?

50% 25%

The owner of a tire company wants to determine how long a new type of tire tread will last by measuring the length of time, in days, it takes for the tire tread to reach 2 mm. Let μ = the true mean number of days it takes for the tire tread to wear to 2 mm. Which of the following sample sizes will have the least variability in the sampling distribution of the sample mean?

The height of the 10-year-old girls at Franklin Elementary School follows a bell-shaped distribution with mean 54.5 inches and standard deviation 2.7 inches. Jazmin's height has a standardized score of 1.5. What is Jazmin's actual height? Round your answer to the nearest hundredth. Jazmin's actual height is

58.55 inches

This scatterplot shows the study time, in hours, versus test score for 17 students. Which combinations of study times and test scores would be considered unusual observations? Check all that apply.

6 hours; score of 35 9 hours; score of 40 14 hours; score of 55

A zoo collected data on the diving times of turtles. Based on the data, the regression line is ŷ = 0.010 + 2.515x, where x is the time of the dive, in minutes. Based on the regression equation, what is the predicted dive depth in meters at 150 seconds? Give your answer to three decimal places.

6.298 meters

The table shows the weight and gas mileage of several vehicles. What is the equation of the least-squares regression line, where ŷ is the predicted gas mileage and x is the weight? According to the regression equation, a car that weighs 1.8 tons would have a gas mileage of about

64.6 -20.2 28

Incorrect data: 43 46 48 48 49 50 50 52 53 57 57 60 Corrected data: 34 46 48 48 49 50 50 52 53 57 57 60 IQR (incorrect data) = IQR (corrected data) = The IQR - measure

7 7 a resistant

This scatterplot is used to predict when the next eruption event will happen. The regression equation is ŷ = 30.33 + 11.44x. Use the scatterplot and regression equation to complete the statement. If the duration of a future eruption event is 210 seconds, guests can expect the next event to happen in approximately

70 minutes

An anthropologist is interested in the relationship between fathers' and sons' heights. She collects a simple random sample of 25 fathers and 25 sons and determines that the least-squares regression line is ŷ =-2.8 + 1.1x, where ŷ is the predicted height of each son and x is the height of his father (both measured in inches). One father is 70 inches tall and the residual for his son's height is 2.5. What is the son's actual height?

71.7 inches 74.2 inches -76.7 inches 82.3 inches

8.10 pretzels 10.83 pretzels -18.58 pretzels 75.95 pretzels

At a certain pizzeria, it is known that 12% of orders are for extra-large pizzas. What is the expected number of pizzas that will be ordered until the first extra-large pizza is ordered?

8.33

A medical device company knows that the percentage of patients experiencing injection-site reactions with the current needle is 11%. What is the standard deviation of X, the number of patients seen until an injection-site reaction occurs?

8.5763

This scatterplot is used to predict when the next eruption event will happen. The regression equation is ŷ = 30.33 + 11.44x. Use the scatterplot to complete the statements. Prediction 1: If the duration of an event is 4.5 minutes, guests can expect about

82 more than prediction one

9.1

A teacher has two large containers filled with blue, red, and green beads. He wants his students to estimate the difference in the proportion of red beads in each container. Each student shakes the first container, randomly selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container. One student sampled 13 red beads from the first container and 16 red beads from the second container. Assuming the conditions for inference are met, what is the 95% confidence interval for the difference in proportions of red beads in each container?

Joe takes part in math competitions. A particular contest consists of 25 multiple-choice questions, and each question has 5 possible answers. It awards 6 points for each correct answer, 1.5 points for each answer left blank, and 0 points for incorrect answers. Joe is sure of 12 of his answers. He ruled out 2 choices before guessing on 4 of the other questions and randomly guessed on the 9 remaining problems. What is his expected score?

90.8

The value of r2 for a relationship between distance (in miles) and the cost (in dollars) of a shuttle bus from a hotel to an airport is calculated using computer software. Identify and interpret the value of r2 by completing the sentence.

96.80% 97% cost distance (in miles)

A doctor would like to estimate the mean difference in height of pairs of identical twins. The doctor randomly selects 8 pairs of identical twins and determines the current height, in inches, of each twin. The data are displayed in the table. What is the mean difference (twin 1 - twin 2) and the standard deviation of the differences?

A drug manufacturing company believes it has found a new medication to alleviate pain for headache sufferers. Twenty people with chronic headaches are asked to take a placebo pill or a pill containing the new medication during their next headache episode. The pill they take is determined by a coin flip. An hour later, the participants are asked to rate their headache pain level on a scale from 1 (no pain) to 5 (severe pain). During their next headache episode, the subjects are asked to take the other pill. The difference in pain ratings (new pill - placebo) is calculated for each subject. What are the hypotheses the company should use?

A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1-10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Let pA = = the true proportion of clothes receiving a rating of 7 or higher for detergent A and pB = the true proportion of clothes receiving a rating of 7 or higher for detergent B. Which of the following are the correct hypotheses to test the company's claim?

A local school board wants to determine if the proportion of households in the district that would support starting the school year a week earlier has changed from the previous year. Last year, the school board determined that 65% of households supported starting school earlier. They ask a random sample of 100 households this year, and 70% state they would support starting the school year earlier. Which hypotheses would determine if the proportion of households that support starting school earlier has changed this year?

A nutritionist believes that 10% of teenagers eat cereal for breakfast. To investigate this claim, she selects a random sample of 150 teenagers and finds that 25 eat cereal for breakfast. She would like to know if the data provide convincing evidence that the true proportion of teenagers who eat cereal for breakfast differs from 10%. What are the values of the test statistic and P-value for this test?

A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likely voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (-0.014, 0.064). What was the difference (pre-debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate?

A restaurant is interested in the relationship between the number of people in a party and the bill for their dinner. An owner of a restaurant records the number of people in the party and the bill for 10 groups of people as shown in the table. The equation of the least-squares regression line isŷ = 16.5 + 8.51x, where ŷ is the bill for the dinner and xis number of people in the party. Which shows the residual plot?

A statistics student believes that black cars are less likely to receive tickets for moving violations. Black cars make up 19% of all cars manufactured. The student randomly selects 70 moving violation records and finds that 10 of them involve black cars. Which hypotheses would test the student's claim?

A statistics teacher is interested in whether there is a difference in the accuracy of dominant versus nondominant hands. She asks her students to roll a ball, once with each hand, toward a target. The students then measure the distance, in centimeters, between the ball and the target. Students will determine which hand they use first by tossing a coin. The differences (nondominant - dominant) in the distances for each student are listed. 28, -33, 25, 41, -14, 21, 12, -30, 17, 26, 32, 27, -25, 18, 10, 22, -19, 4, 31, 19 What are the hypotheses the teacher should use?

A used car dealership is interested in the age of a used car and the price of the vehicle. The manager collects a simple random sample of vehicles as shown in the table. The equation of the least-squares regression line isŷ = 19.2 - 0.868x, where ŷ is the price of the vehicle (in thousands of dollars) and x is the age (in years). Which shows the residual plot?

After a hailstorm, a large car dealership wants to determine the proportion of cars that have damage. The service department randomly selects 50 cars on the dealership lot, examines them, and determines that 18 have damage. Assuming all conditions have been met, they construct a 99% confidence interval for the true proportion of cars with damage from the storm. What are the calculations for this interval?

College administrators noticed that students who had higher high school GPAs tend to have higher college GPAs. The data in the table show various high school GPAs and college GPAs for a sample of students. Which scatterplot represents the student data?

In a statistics activity, students are asked to spin a penny and a dime and determine the proportion of times that each lands with tails up. The students believe that since a dime is lighter, it will have a lower proportion of times it will land tails up compared to the penny. The students are instructed to spin the penny and the dime 30 times and record the number of times each lands tails up. For one student, the penny lands tails side up 18 times, and the dime lands tails side up 20 times. Let pD = the true proportion of times a dime will lands tails up and pP = the true proportion of times a penny will land tails up. Which of the following are the correct hypotheses to test the student's claim?

Machine engineers are designing a new ice cube machine. They notice that designs that use cubes containing higher volumes of water take longer to freeze. The data in the table show various volumes (in milliliters) and freezing times (in hours) for a sample of machine designs. Which scatterplot represents the data?

The following are the winning times, in seconds, for the Kentucky Derby from 1997 to 2016. Select the boxplot that represents the data. 122.4, 124.2, 123.2, 121, 119.97, 121.1, 121.19, 124.06, 122.75, 121.36, 122.17, 121.82, 122.66, 124.04, 122.04, 121.83, 122.89, 123.66, 123.02, 121.3

The mean price of houses in the US is $383,500. A real estate agent believes the mean price of houses in a local neighborhood is less than the national mean. The agent takes a random sample of 30 houses and finds the mean price to be $295,089 with a standard deviation of $156,321. Do the data provide convincing evidence at the =0.05 level that the mean price of the houses in the area is less than $383,500? What hypotheses should the real estate agent use to conduct a significance test?

The owner of a popular coffee shop wants to determine if there is a difference between the proportion of customers who use their own cups when they purchase a coffee beverage, and the proportion of customers who use their own cups when they purchase an espresso beverage. Customers using their own cups get a 5% discount, which is displayed on the receipt. The owner randomly selects 50 receipts from all coffee purchases and 50 receipts from all espresso purchases. For coffee purchases, 24 receipts showed that the customer used their own cup. For espresso purchases, 18 receipts showed that the customer used their own cup. Assuming the conditions for inference have been met, what is the 99% confidence interval for the difference in proportion of customers who use their own cups?

The president of the company wants to select 2 of the 5 vice presidents to send to a conference. The 10 possible samples of size 2 that can be selected from this population without replacement are (Andrew, Beth), (Andrew, Charles), (Andrew, Diane), (Andrew, Eric), (Beth, Charles), (Beth, Diane), (Beth, Eric), (Charles, Diane), (Charles, Eric), and (Diane, Eric). Which of the following gives the sampling distribution of the sample proportion of east regional responsibility for all possible samples of size 2 from this population?

The stemplot below displays the grades (out of 30) that 26 students received on a quiz. Which of the following boxplots correctly displays the distribution of quiz grades?

The table shows the number of vehicles by gas mileage rating (mpg) for all 2019 vehicles with all-wheel or four-wheel drive. Which histogram best displays the data? Use this graphic to answer the question.

Which residual plot shows data that would appear to be most appropriate to represent with a linear model?

Read each scenario and choose the type of bias that is exhibited.

A college professor has a colleague administer a survey to each member of his class about the effectiveness of his teaching strategies. This exhibits nonresponseX responseX undercoverage✔ no bias. At the end of a lecture, a college professor polls his lecture class of 200 students about the importance of attending his lectures. This exhibits nonresponseX response✔ undercoverageX no bias.

The table shows how surveyed drivers obtained their current vehicle and how they plan to get their next vehicle. Complete the table by selecting the missing counts for each letter.

A = 39 B = 9 C = 5

A plant in Alamo, TN, manufactures complex transformer components that must meet specific guidelines for safety. One such component is constructed to deliver 1,000 volts of electricity. A component creates a critical safety hazard if it absorbs humidity at a level above 3%. Any components that absorb too much humidity will be destroyed. A quality control inspector uses a random sample of components to conduct a hypothesis test with H0: The humidity level absorbed is 3%, and Ha: The humidity level absorbed is more than 3%. What is a Type I error in this context?

A Type I error would result in rejecting a true null hypothesis. This means the company would believe the humidity level is more than 3%, when in fact it is not more than 3%.

A coach surveyed a random sample of 200 college athletes about their height. Which statements are correct about the data in the table? Check all that apply.

A bar graph is an appropriate display. A pie chart is not appropriate because the categories do not add to 100%. A bar graph is appropriate because the frequencies are given.

Read each scenario and choose the type of bias that is exhibited.

A college professor polls each student as they leave the final exam about the effectiveness of his teaching strategies. This exhibits response✔ bias. A college professor hands out a notecard the last day of class asking each student to write comments about the effectiveness of his teaching strategies. This exhibits ✔ nonresponse

Identify the sampling designs that use convenience sampling. Check all that apply.

A grocery chain uses information from customer purchases to select products for future promotions. The first three people arriving at a movie theater are asked about their favorite movie genre. The drama club interviews patrons of the play about their interests in fine arts.

An inspector selects a random sample of 25 wireless keyboards from today's production line to assess whether or not they work properly. He finds that 24 of the 25 wireless keyboards do work properly. Which of the following conclusions can we draw from this study? A: We can infer that about 96% of the wireless keyboards produced by the manufacturer that day will work properly. B: We can draw conclusions about cause and effect for the population of all wireless keyboards produced today by this manufacturer.

A only

Identify the sampling designs that use voluntary response sampling. Check all that apply.

A pharmaceutical company advertises for subjects to participate in an online survey about insulin pumps for diabetics. An online poll is created for sports fans to vote on the winner for the Super Bowl. After each customer service call, callers are asked to stay on the line to complete a brief satisfaction survey.

To determine if carrot juice helps improve heart conditions, a juicing company asks a random sample of 100 adults about whether or not they drink carrot juice and their heart condition. The company finds an association between drinking carrot juice and healthy heart conditions. Which statement is true about a possible confounding variable?

A possible confounding variable is the amount of exercise. Those that drink carrot juice may be more concerned about their health and exercise more, which explains the healthy heart conditions.

Identify the sampling designs that use convenience sampling. Check all that apply.

A restaurant surveys all its breakfast customers about meal quality. A company that produces natural food flavorings conducts taste tests with all its employees. A veterinarian collects information from his or her clients about dog food brand preferences.

Which statement about stratified random sampling is true?

A stratified random sample is a combination of simple random samples selected from each of several strata.

A statistics teacher has 20 students in her class. Here is a graph showing the scores of the 20 students on a recent test. The teacher selects a random sample of 5 students from the class. Here is a graph displaying the scores of the students she selected. The teacher calculates the mean of this sample of 5 scores and plots it on a number line. She then repeats this process 100 times. Here are the results. Which of the following gives the correct order of the graphs of the population distribution, distribution of a single sample, and an approximate sampling distribution, respectively?

A, B, C

A manufacturing company has 5 vice presidents: Andrew, Beth, Charles, Diane, and Eric. Their regional responsibilities are shown in the table. Which of the following gives the correct order of the graphs of the population distribution, distribution of a single sample, and sampling distribution, respectively?

A, C, B

A manufacturer of cell phones would like to estimate how much longer the battery lasts in their model 10 phone than in their model 9 phone. To estimate this difference, they randomly select 40 cell phones of each model from the production line. They subject each phone to a standard battery life test. The 40 model 10 phones have a mean battery life of 14.4 hours with a standard deviation of 2.1 hours. The 40 model 9 phones have a mean battery life of 12.8 hours with a standard deviation of 2.3 hours. The conditions for inference have been met. What is the correct 95% confidence interval for the difference in the population means?

A- (0.594, 2.606)

In a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let and be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class. Which of the following is the mean of the sampling distribution of ?

A- -0.52

Can a person train to become better at holding their breath? An experiment was designed to find out. A group of 12 volunteers were randomly assigned to 1 of 2 groups. The 6 volunteers assigned to group 1 were given breath-holding exercises to perform for 2 weeks. The other group was not given any information about the experiment. At the end of the 2 weeks, all 12 volunteers were individually tested to determine how long they could hold their breath. Here are the data (in seconds): Group 1: 90, 88, 70, 110, 75, 105 Group 2: 40, 48, 35, 50, 55, 62 The researcher would like to determine if these data provide convincing evidence that the true mean amount of time volunteers who were given training held their breath is greater than the true mean amount of time volunteers without training held their breath. The researcher tests H0: μ1 - μ2 = 0, Ha: μ1 - μ2 > 0, where μ1 = the true mean amount of time that volunteers who were given training held their breath and μ2 = the true mean amount of time that volunteers without training held their breath. The conditions for inference are met. The standardized test statistic is t = 5.44. What is the P-value of this test closest to?

A- 0

A music professor is interested in the effects of listening to music while memorizing a list of words. She asks 14 volunteers to memorize two different lists of words: one list while listening to music in the background and the other list with no music in the background. The order of the treatments is determined by a coin toss. The mean difference (music - no music) in the number of words memorized is 4.1 words with a standard deviation of 3.8 words. Assuming that the conditions for inference are met, what is the P-value for testing the hypotheses H0 :μdiff = 0; Ha :μdiff > 0?

A- 0.0007

The time needed to broil cauliflower is approximately Normally distributed with a mean of 6 minutes and a standard deviation of 1.9 minutes. If a random sample of 100 batches of cauliflower is selected, what is the probability the mean broiling time is more than 6.5 minutes?

A- 0.0042

A nurse at a local hospital wonders if the firstborn twin is taller than the second-born. He randomly selects the medical records of 33 sets of twins and finds the differences (firstborn - second-born) in the twins' heights, in centimeters. The mean of the differences is 1.1 centimeters with a standard deviation of 2.3 centimeters. Assuming the conditions for inference are met, what is the P-value for testing the hypotheses H0 :μdiff = 0; Ha :μdiff > 0?

A- 0.0049

A student claims that statistics students at her school spend, on average, an hour doing statistics homework each night. In an attempt to substantiate this claim, she selects a random sample of 6 of the 62 students who are currently taking statistics and asks them how much time they spend completing statistics homework each night. She would like to know if there is convincing statistical evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than 1 hour. The student plans to test the hypotheses, = 1 versus < 1, where μ = the true mean amount of time that statistics students spend doing statistics homework each night. Assume all conditions have been met. The student discovers that the power of this test to reject the null hypothesis when μ = 0.75 is not very high. Which value of the alternative hypothesis would yield the greatest power of this test?

A- 0.25

Hal and Jose are avid crossword puzzle solvers. Hal solves 48% of his crossword puzzles in under 30 minutes, while Jose solves 39% of his crossword puzzles in under 30 minutes. Suppose that Hal solves 22 crossword puzzles and Jose solves 26 crossword puzzles. Because nJpJ, nJ (1-pJ), and nH (1-pH) are all greater than 10, the Normal condition is met. Let H = the proportion of Hal's crossword puzzles solved in under 30 minutes and J = the proportion of Jose's crossword puzzles solved in under 30 minutes. What is the probability that Jose's proportion of crossword puzzles solved in under 30 minutes is greater than Hal's?

A- 0.265

Some stores print multiple coupons and advertisements on their receipts, making the receipts unusually long. A curious shopper makes the same purchase at a random sample of 10 stores and measures the length of each receipt (in inches). Here are the results: 8.25, 7.5, 5, 9.5, 12, 5.5, 9, 14, 11.5, 18 What is the value of the standard error of the mean?

A- 1.256

A store manager claims that 60% of shoppers who enter her store make a purchase. To investigate this claim, she selects a random sample of 40 customers and finds that 40% of them make a purchase. She wants to know if the data provide convincing evidence that the true proportion of all customers who enter her store that will make a purchase differs from 60%. The P-value of this test is 0.0098. Interpret the P-value.

A- Assuming the true population proportion of shoppers who will make a purchase is 0.60, the probability of obtaining a sample statistic of 0.40 in a random sample of 40 customers is 0.0098.

From previous experience, the owner of an apple orchard knows that the mean weight of Gala apples is 140 grams. There has been more precipitation than usual this year. The owner believes the weights of the apples will be heavier than usual, and therefore the crop will be more profitable. The owner takes a random sample of 30 apples and records their mean weight. What is a Type I error in this situation?

A- Based on the sample mean, the owner concludes that the mean weight of apples is greater than 140 grams when the true mean weight is not greater than 140 grams.

A carnival game is designed so that approximately 10% of players will win a large prize. If there is evidence that the percentage differs significantly from this target, then adjustments will be made to the game. To investigate, a random sample of 100 players is selected from the large population of all players. Of these players, 19 win a large prize. The question of interest is whether the data provide convincing evidence that the true proportion of players who win this game differs from 0.10. The computer output gives the results of a z-test for one proportion.

A- Because the P-value < α = 0.05, the correct decision is to reject H0.

A local school board wants to determine if the proportion of households in the district that would support starting the school year a week earlier has changed from the previous year. Last year, the school board determined that 65% of households supported starting school earlier. They ask a random sample of 100 households this year, and 75% state they would support starting the school year earlier. The P-value for the test of the hypotheses, and , is 0.04. What is the correct conclusion given ?

A- Because the P-value is less than 0.05, the school board should reject H0.

A teacher has a large container of blue, red, and green beads. She reports to the students that the proportion of blue beads in the container is 0.30. The students feel the proportion of blue beads is lower than 0.30. A student randomly selects 60 beads and finds that 12 of the beads are blue. The P-value for the test of the hypotheses, and , is 0.045. What is the correct conclusion given

A- Because the P-value is less than a=0.05 , the student should reject H0.

Researchers wonder if practicing yoga reduces stress levels in adults. They select a random sample of 32 adults and assess their current stress levels. The participants are told to practice 60 minutes of yoga each day for one week. At the end of the week, their stress levels are assessed again. The mean difference (pre-yoga - post-yoga) in stress scores is 2.68 points with a standard deviation of 5.58 points. A positive value indicates that the subject's stress level decreased. Assuming the conditions for inference have been met, is there statistical evidence that practicing yoga is associated with lower stress levels in adults like the ones in the study? Use a significance level of α = 0.05.

A- Because the P-value is less than α, there is evidence that practicing yoga is associated with lower stress levels, on average, in adults like the ones in the study.

A researcher is interested in whether parents and their children share the same opinion on topics. She selects a random sample of 31 pairs of mothers and their daughters. Each mother/daughter pair is shown a commercial and asked to rate the likelihood that they would purchase the product on a scale of 1 (not likely) to 5 (very likely). The mean difference (mother - daughter) of the ratings is 0.85 with a standard deviation of 1.59. Assuming all the conditions for inference have been met, is there evidence that, on average, mothers and daughters like those in the study would have different opinions about purchasing the product? Use a significance level of α = 0.05.

A- Because the P-value is less than α, there is evidence that, on average, mothers and daughters like those in the study would have different opinions about purchasing the product.

Simone read online that the failure rate in Arizona for the first attempt of the written driver's test is 60%. Simone thinks the Arizona rate is less than 60%. To investigate, she selects an SRS of 50 Arizona drivers and finds that 27 failed their first written driving test. To determine if this provides convincing evidence that the failure rate for Arizona is less than 60%, 200 trials of a simulation are conducted. Simone's hypotheses are: H0: p = 60% and Ha: p < 60%, where p = the true proportion of Arizona drivers who fail the first attempt of the written driver's test. Based on the results of the simulation, the estimated P-value of this test is 0.035. Using ∝ = 0.05, what conclusion should Simone reach?

A- Because the P-value of 0.035 < a , Simone should reject H0. There is convincing evidence that the Arizona written driver's test has a true first-attempt failure rate less than 60%.

A study was conducted to determine the true mean number of hours of television watched on school nights by teenagers. A 99% confidence interval for the true mean is 0.8 hours to 2.1 hours. Based upon this interval, what conclusion should be made about the hypotheses: =2.5 versus 2.5 where μ = the true mean number of hours of television watched on school nights by teenagers at α = 0.01?

A- Reject H0. Since 2.5 falls outside the 99% confidence interval, there is convincing evidence that the true mean number of hours of television watched on school nights by teenagers differs from 2.5 hours.

A- Because the P-value of 0.06 < , Devon should reject H0. There is convincing evidence that the proportion of serves that are good is greater than 72%.

Lucy recently asked the servers at her restaurant to only give straws to customers who request them. She thinks that about half of the customers will ask for straws but hopes that the rate will be less than half. She randomly selects 100 customers and finds that 43 of them ask for a straw. To determine if these data provide convincing evidence that the proportion of customers who will ask for a straw is less than 50%, 150 trials of a simulation are conducted. Lucy is testing the hypotheses: H0: p = 50% and Ha: p < 50%, where p = the true proportion of customers who will ask for a straw. Based on the results of the simulation, the estimated P-value is 0.0733. Using = 0.10, what conclusion should Lucy reach?

A- Because the P-value of 0.0733 < , Lucy should reject H0. There is convincing evidence that the proportion of customers who will ask for a straw is less than 50%.

Derek Jeter challenges Albert Pujols to a batting battle. Each will earn 1 point for a hit other than a home run and 4 points for a home run in each round. Which player should you back given the statistics in the table below? Note that home runs are included as hits in the table.

A- E(Jeter) = 0.38 and E(Pujols) = 0.45, so back Pujols.

A- H0: p = 0.80 versus Ha: p < 0.80, where p = the true proportion of all American adults who do not have an emergency fund.

A school guidance counselor is concerned that a greater proportion of high school students are working part-time jobs during the school year than a decade ago. A decade ago, 28% of high school students worked a part-time job during the school year. To investigate whether the proportion is greater today, a random sample of 80 high school students is selected. It is discovered that 37.5% of them work part-time jobs during the school year. The guidance counselor would like to know if the data provide convincing evidence that the true proportion of all high school students who work a part-time job during the school year is greater than 0.28. The power of this test to reject the null hypothesis if p = 0.747 is 0.59 using a significance level of α = 0.05. What is the interpretation of the power of this test?

A- If the true proportion of high school students who work a part-time job during the school year is p = 0.747, there is a 0.59 probability that the guidance counselor will find convincing evidence for Ha: p > 0.28.

A- Let 00-04 = not delivered on time. Let 05-99 = delivered on time.

A random sample of 100 customers is selected, and the mean difference in their satisfaction rating for company A and company B is calculated. A rating of 1 indicates that a customer is highly dissatisfied, and a rating of 5 indicates that a customer is highly satisfied. A 90% confidence interval for the true mean difference (company A - company B) in satisfaction ratings is -2.5 to 1.5. Based on the confidence interval, the owner of company B claims that customers are more satisfied with his company than with company A. Is this claim supported by the 90% confidence interval?

A- No, the confidence interval does not consist entirely of positive numbers.

A teacher claims that his coffee cools to a temperature of 100 degrees Fahrenheit in 5 minutes after he brews it at home in his single-cup coffee brewer. To further investigate this claim, the teacher measures how long it takes for his coffee to cool to 100 degrees for each of the next 30 days. He would like to carry out a t-test for one mean to determine if there is convincing evidence that the true mean amount of time it takes for his coffee to cool to 100 degrees is less than 5 minutes. Are the conditions for inference met?

A- No, the random condition is not met.

To estimate the true mean speed of vehicles traveling on a particular section of roadway, a speed-detection device is programmed to measure the speed of the first 100 vehicles that pass it. Are the conditions for constructing a t confidence interval met?

A- No, the random condition is not met.

A local athletic facility offers a four-week training course, hoping to increase athletes' running speeds. Thirty-five volunteer athletes are timed, in seconds, running a 50-yard dash before the training program begins and then again after the program is complete. The difference in running times (before training - after training) is calculated for each athlete. Are the conditions for inference met?

A- No. This is not a random sample of athletes

It is claimed that 95% of teenagers who have a cell phone never leave home without it. To investigate this claim, a random sample of 300 teenagers who have a cell phone was selected. It was discovered that 273 of the teenagers in the sample never leave home without their cell phone. One question of interest is whether the data provide convincing evidence that the true proportion of teenagers who never leave home without a cell phone is less than 95%. The standardized test statistic is z = -3.18 and the P-value is 0.0007. What decision should be made using the = 0.01 significance level?

A- Reject H0 because the P-value is less than = 0.01.

The mayor of a local town wants to determine if there is support for a certain proposal. The mayor's assistant randomly selects 100 households and asks whether they would support the mayor's proposal. Sixty responded that they would support it. What type of sampling is described in this study?

A- one sample

A student claims that statistics students at her school spend, on average, an hour doing statistics homework each night. In an attempt to substantiate this claim, she selects a random sample of 6 of the 62 students who are taking statistics currently and asks them how much time they spend completing statistics homework each night. Here are the data (in hours): 0.75, 0.75, 0.75, 0.5, 1, 1.25. She would like to know if the data provide convincing statistical evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour. The student plans to test the hypotheses, H0: μ = 1 versus Ha: μ < 1, where μ = the true mean amount of time that statistics students spend doing statistics homework each night. The conditions for inference are met. The test statistic is t = -1.58 and the P-value is between 0.05 and 0.10. What conclusion should be made at the significance level, ?

A- Reject H0. There is convincing evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour.

A pool supply company sells 50-pound buckets of chlorine tablets. A customer believes that the company may be underfilling the buckets. To investigate, an inspector is hired. The inspector randomly selects 30 of these buckets of chlorine tablets and weighs the contents of each bucket. The sample mean is 49.4 pounds with a standard deviation of 1.2 pounds. The inspector would like to know if this provides convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds, so he plans to test the hypotheses H0: μ = 50 versus Ha: μ < 50, where μ = the true mean weight of all 50-pound buckets of chlorine tablets. The conditions for inference are met. The test statistic is t = -2.74 and the P-value is between 0.005 and 0.01. What conclusion should be made at the significance level, ?

A- Reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.

A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1-10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Let pA = the true proportion of clothes receiving a rating of 7 or higher for detergent A and pB = the true proportion of clothes receiving a rating of 7 or higher for detergent B. The P-value for this significance test is 0.007. Which of the following is the correct conclusion for this test of the hypotheses

A- Researchers should reject the null hypothesis since 0.007 < 0.05. There is sufficient evidence that the true proportion of clothes receiving a rating of 7 or higher is significantly greater for the new formula of detergent.

A social scientist collects information about study time for a random sample of 40 students with the intention of testing the hypotheses = 2 hours per night versus 2 hours per night where = the true mean number of hours of study time per night for students. Rather than test these hypotheses, she computes the 90% confidence interval, (1.5, 1.8). Based upon the confidence interval, what conclusion can be made using = 0.10?

A- She should reject the null hypothesis. Since 2 falls outside of the 90% confidence interval, there is convincing evidence that the true mean number of hours of study time per night for students differs from 2 hours per night.

A- The company believes the humidity absorption is more than 3% when in fact it is not. Correctly functioning components will be destroyed, at great expense to the company.

An emergency fund is defined as a savings account that has a balance equal to at least two months' living expenses. An article in a financial magazine claims that 80% of American adults do not have an emergency fund. To investigate this claim, a financial advisor selects a random sample of 150 Americans and finds that 112 do not have an emergency fund. The financial advisor would like to know if the data provide convincing evidence that the true proportion of American adults who do not have an emergency fund is less than 80%. The power of this test to reject the null hypothesis if p = 0.747 is 0.49 using a significance level of α= 0.05. What are two ways the financial advisor could increase the power of this test?

A- The financial advisor could use a sample size that is larger than 150 and use a significance level that is larger than α = 0.05.

A local school board believes there is a difference in the proportion of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school-aged children that would support starting the school year a week earlier. They survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 38 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 25 respond yes. Let ps= the true proportion of households with school-aged children that would support starting the school year a week early and pw= the true proportion of households without school-aged children that would support starting the school year a week earlier. The P-value for this significance test is 0.000034. Which of the following is the correct conclusion for this test of the hypotheses

A- The local school board should reject the null hypothesis since 0.000034 < 0.05. There is sufficient evidence that the true proportion of households with school-aged children that would support starting the school year a week early is significantly different from the true proportion of households without school-aged children.

Nina would like to estimate the difference in the mean amount of time students spend on math homework at her public school versus her cousin Sharon's private school. To do so, each girl selects a random sample of 30 students from their large schools and asks the selected students how much time they spent doing math homework the previous night. Nina and Sharon would like to construct a 90% confidence interval for the true difference in the population means. Are the conditions for inference met?

A- Yes, all three conditions for inference are met.

The maintenance crew of a hotel has to monitor the temperature of the hotel pool and hot tub. To enhance comfort, the management team requests that the mean pool temperature and the mean hot tub temperatures not differ by more than 15 degrees. To estimate the difference in these mean temperatures the maintenance crew selects a random sample of 8 times to check the hot tub temperature and a random sample of 10 times to check the pool temperature. A 95% confidence interval for the difference in the population means is (11.97, 18.03). What is the interpretation of this interval?

A- The maintenance crew can be 95% confident that the interval from 11.97 to 18.03 captures the true difference in the mean temperatures (hot tub - pool).

An engineer would like to design a parking garage in the most cost-effective manner. The garage must be able to fit pickup trucks, which have an average height of 76.4 inches. To double-check this figure, the engineer employs a statistician. The statistician selects a random sample of 50 trucks, which will be used to determine if there is convincing evidence that the true mean height of all trucks is greater than 76.4 inches. The statistician plans to test the hypotheses, = 76.4 versus > 76.4, where μ = the true mean height of all trucks. The power of this test to reject the null hypothesis when μ = 77 inches is 0.97. What is the interpretation of 0.97?

A- The probability of rejecting H0: = 76.4 when = 77 inches is 0.97.

A teacher has two large containers filled with blue, red, and green beads, and claims the proportion of red beads is the same in each container. The students believe the proportions are different. Each student selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container. One student's samples contained 13 red beads from the first container and 16 red beads from the second container. Let p1= the true proportion of red beads in container 1 and p2= the true proportion of red beads in container 2. Which of the following is a correct statement for the conditions for this test?

A- The random condition is not met.

The daily temperatures in fall and winter months in Virginia have a mean of 62oF. A meteorologist in southwest Virginia believes the mean temperature is colder in this area. The meteorologist takes a random sample of 15 daily temperatures from the fall and winter months over the last five years in southwest Virginia. The mean temperature for the sample is 58oF with a standard deviation of 4.12oF. A significance test at an alpha level of produces a P-value of 0.001. What is the correct interpretation of the P-value?

A- There is a 0.1% chance that a sample mean temperature of at most 58oF will occur by chance if the true mean temperature is 62oF.

The distribution of the heights of five-year-old children has a mean of 42.5 inches. A pediatrician believes the five-year-old children in a city are different. The pediatrician selects a random sample of 40 five-year-old children and measures their heights. The mean height of the sample is 41.7 inches with a standard deviation of 3.3 inches. A significance test at an alpha level of produces a P-value of 0.133. What is the correct interpretation of the P-value?

A- There is a 13.3% chance that a sample mean at least as extreme as 41.7 inches will occur by chance if the true mean height of five-year-old children is 42.5 inches.

A major car dealership has several stores in a big city. The owner wants to determine if there is a difference in the proportions of SUVs that are sold at stores A and B. The owner gathers the sales records for each store from the past year. A random sample of 55 receipts from store A shows that 30 of the sales were for SUVs. Another random sample of 60 receipts from store B shows that 45 of the sales were for SUVs. Based on the 99% confidence interval, (-0.43, -0.02), is there convincing evidence of a difference in the proportions of sales that are SUVs for the two stores?

A- There is convincing evidence because the entire interval is below 0.

A manufacturer of cell phones would like to estimate how much longer the battery lasts in their model 10 phone than in their model 9 phone. To estimate this difference, they randomly select 40 cell phones of each model from the production line. They subject each phone to a standard battery life test. The 40 model 10 phones have a mean battery life of 14.4 hours with a standard deviation of 2.1 hours. The 40 model 9 phones have a mean battery life of 12.8 hours with a standard deviation of 2.3 hours. A 95% confidence interval for the difference in the population means is (0.594, 2.606). What is the interpretation of this interval?

A- We can be 95% confident that the interval from 0.594 to 2.606 captures μ1 − μ2 = the true difference in the mean battery life for all model 9 and model 10 cell phones.

A doctor would like to estimate the mean difference in the number of hours of sleep for seniors in high school and seniors in college. To do so, he selects a random sample of 50 high school seniors from all high schools in his county. He also selects a random sample of 50 seniors from the colleges in his county. He would like to construct a 95% confidence interval for the true mean difference in the number of hours of sleep for seniors in high school and seniors in college. Are the conditions for inference met?

A- Yes, all three conditions for inference are met.

An experiment is conducted to estimate the difference in work productivity for employees under two conditions: with and without music playing in the background. Twenty employees volunteered to be part of the study. Ten of the volunteers were randomly assigned to work for one week with music playing in the background. The other 10 volunteers worked for one week without music playing in the background. Productivity is measured by counting the number of units produced for the week. Here are dotplots, which display the data: Are the conditions for inference met?

A- Yes, all three conditions for inference are met.

From previous experience, the owner of an apple orchard knows that the mean weight of gala apples is 140 grams. This year there has been more precipitation than usual and the owner believes the weights of the apples are heavier than usual. The owner takes a random sample of 30 apples and records their weights. What type of sampling is described in this study?

A- one sample

The maintenance crew of a hotel must monitor the temperature of the hotel pool and hot tub. To enhance comfort, the management team requests that the mean pool temperature and the mean hot tub temperatures not differ by more than 15 degrees. To estimate the difference in these mean temperatures the maintenance crew selects a random sample of 8 times for checking the hot tub temperature and a random sample of 10 times for checking the pool temperature. Although the sample sizes are small, the distribution of temperature for the pool and for the hot tub does not show strong skewness or any outliers. Are the conditions for inference met?

A- Yes, all three conditions for inference are met.

A 95% confidence interval for the true proportion of math students who prefer to use a handheld calculator versus computer software for computations is (0.751, 0.863). Is it reasonable to believe more than 75% of math students prefer to use a handheld calculator versus computer software for computations?

A- Yes, because the entire interval is greater than 0.75.

It is claimed that 75% of puppies are house-trained by the time they are 6 months old. To investigate this claim, a random sample of 50 puppies is selected. It is discovered that 42 are house-trained by the time they are 6 months old. A trainer would like to know if the data provide convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old. Are the conditions for inference met?

A- Yes, the conditions for inference are met

A- Yes, the conditions for inference are met.

A restaurant manager believes that a majority of customers who dine at his restaurant would rate the food as excellent. To investigate this belief, he sends an email survey to a random sample of 50 customers from the large list of customers who have signed up for his frequent diner club. To encourage the customers to complete the survey, he offers a $10 gift card upon completion of the survey. He receives 22 responses, of which 20 rated the food as excellent. He would like to know if these data provide convincing evidence that more than 50% of customers who dine at his restaurant would rate the food as excellent. Are the conditions for inference met?

A- Yes, the conditions for inference are met.

After a hailstorm, a large car dealership wants to determine the proportion of cars that have damage. The service department randomly selects 50 cars on the dealership lot, examines them, and finds that 11 cars have damage. They want to construct a 99% confidence interval for the true proportion of cars with damage from the storm. Are the conditions for inference met?

A- Yes, the conditions for inference are met.

In a children's story, a young girl finds that one bowl of soup is too hot, another is too cold, and a third bowl is just right. Further study reveals that the temperature of the soup bowl that the young girl declared to be just right was 100°F. A researcher would like to test the hypotheses =100 versus 100 where μ = the true mean temperature of all bowls of soup. A 95% confidence interval based on a random sample of 30 bowls of soup is (100.9, 102.3). Using this interval, can the researcher reject the null hypothesis?

A- Yes, the null hypothesis can be rejected at the significance level α = 0.05, because 100 is not contained in the 95% confidence interval.

A carnival game is designed so that approximately 10% of players will win a large prize. If there is evidence that the percentage differs significantly from this target, then adjustments will be made to the game. To investigate, a random sample of 100 players is selected from the large population of all players. Of these players, 19 win a large prize. The question of interest is whether the data provide convincing evidence that the true proportion of players who win this game differs from 0.10. Are the conditions for inference met for conducting a z-test for one proportion?

A- Yes, the random, 10%, and large counts conditions are all met.

A school guidance counselor is concerned that a greater proportion of high school students are working part-time jobs during the school year than a decade ago. A decade ago, 28% of high school students worked a part-time job during the school year. To investigate whether the proportion is greater today, a random sample of 80 high school students is selected. It is discovered that 37.5% of them work part-time jobs during the school year. The guidance counselor would like to know if the data provide convincing evidence that the true proportion of all high school students who work a part-time job during the school year is greater than 0.28. Are the conditions for inference met for conducting a z-test for one proportion?

A- Yes, the random, 10%, and large counts conditions are all met.

A company that sells hair-care products wants to determine if a product that combines shampoo and conditioner works better than a shampoo and conditioner used separately. A researcher recruits 60 volunteers and pairs them according to age, hair color, and hair type. For each pair, the researcher flips a coin to determine which volunteers will use the shampoo/conditioner combination and which ones will use the separate shampoo and conditioner. After using the products for one month, the subjects are asked to rate their satisfaction with the hair products on a scale of 1-10 (1 = highly dissatisfied and 10 = highly satisfied). What type of sampling is described in this study?

A- one sample

A student wants to determine the proportion of times a spun penny will land on heads. She spins a penny 50 times and records the number of times it lands on heads. What type of sampling is described in this study?

A- one sample

The manager of a large manufacturing company wants to estimate the proportion of items that have been manufactured with defects. How many items are required for a random sample to obtain a margin of error of at most 0.04 with 90% confidence?

B- 423

The mayor of a large town wants to estimate the proportion of households in the town that would support a proposal. The mayor's assistant randomly selects 100 households and asks whether they would support the mayor's proposal. Sixty households responded that they would. What is the appropriate inference procedure?

A- one-sample z-interval for p

A manufacturing company packages shipments in either large or small boxes. A random sample of 40 shipments that are packaged in large boxes is found to have a mean of 15 pounds and a standard deviation of 2.8 pounds. A separate random sample of 50 shipments that are packaged in small boxes is found to have a mean of 10 pounds and a standard deviation of 1.5 pounds. The manager would like to know if the data provide convincing evidence that the true mean weight of all shipments that are packaged in small boxes is less than the true mean weight of all shipments that are packaged in large boxes. The manager tests H0: μS - μL = 0, Ha: μS - μL < 0, where μL = the true mean weight of all shipments that are packaged in large boxes and μS = the true mean weight of all shipments that are packaged in small boxes. The conditions for inference have been met. What are the values of the test statistic and P-value for a t-test about a difference in means?

A- t = -10.19. The P-value is less than 0.0005.

The distribution of professional baseball player salaries has a mean of $3.2 million. An analyst believes that the mean salary for teams on the East Coast is different. The analyst randomly selects 30 baseball players from teams on the East Coast and records their annual salaries. The mean salary for the players in the sample is $3.9 million with a standard deviation of $2.1 million. Do the data provide convincing evidence at the level that the mean salary for the baseball players on the East Coast is different from $3.2 million? What are the test statistic and P-value for this significance test?

A- t = 1.83 and 0.05 < P-value < 0.10

An emergency fund is defined as a savings account that has a balance equal to at least two months' living expenses. An article in a financial magazine claims that 80% of American adults do not have an emergency fund. To investigate this claim, a financial advisor selects a random sample of 150 Americans and finds that 112 do not have an emergency fund. The financial advisor would like to know if the data provide convincing evidence that the true proportion of American adults who do not have an emergency fund is less than 80%. The conditions for inference are met. What is the value of the test statistic and P-value for this test?

A- z = -1.62, P-value = 0.0526

A- z = 1.47, P-value = 0.0708

A-1.3

A researcher needs to assign 10 subjects, numbered 0 to 9, to one of two treatment groups: A and B. Use the table of random digits, starting with the first row and first column, to carry out the random assignment. Select the correct random assignment using the table.

A: 0, 7, 5, 8, 1 B: 3, 4, 2, 6, 9

A runner would like to know what percentage of people clean up after their dog while walking on public trails. For the next week, he keeps track every time he observes a person cleaning up after their dog (or not) while he runs on the public trail. He found that four out of 20 dog owners do not clean up after their dog. Which of the following conclusions can we draw from this study?

A: We can infer that about 25% of all dog owners do not clean up after their dog while walking on the public trail. B: We can draw conclusions about cause and effect for the population of all people who walk their dog on the public trail. We can conclude neither A nor B

The data points in the table show minutes on phone calls per day, x, and text messages sent per day, y. The least-squares regression line for the data is ŷ = 100 - 0.5x. Use this table to answer the question. Identify the missing values in the table.

A=5 B=0 C=50 D=-5

A real estate agent has 4 homes for sale: A, B, C, and D. Here are the listing prices. Home A: $150,000Home B: $250,000Home C: $190,000Home D: $550,000 The agent wants to randomly select 2 of the 4 homes to show in an open house this coming weekend. Which of the following gives a complete list of all possible samples of size 2 selected from this population of 4 homes without replacement?

AB, AC, AD, BC, BD, CD

The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis. Which of the following is the best interpretation of the coefficient of determination r2?

About 37% of the variation in arm span is accounted for by the linear relationship formed with the foot length. About 65% of the variation in foot length is accounted for by the linear relationship formed with the arm span. About 63% of the variation in arm span is accounted for by the linear relationship formed with the foot length. -About 63% of the variation in foot length is accounted for by the linear relationship formed with the arm span.

The value of r2 for a relationship between gallons of gasoline used (explanatory) and the number of miles driven (response) by a certain car is calculated as 96.78%. Which of the following statements is the best interpretation of r2?

About 96.78% of the variation in the gallons of gasoline of the car is accounted for by the linear relationship created with the number of miles driven.

The table shows the production budgets and worldwide gross revenues of eight 2018 films. Which statement gives the correct value and interpretation of r?

As budgets increased, the gross revenue increased; r = 0.62.

A statistics student believes that black cars are less likely to receive tickets for moving violations. Black cars make up 19% of all cars manufactured. The student randomly selects 70 moving violation records and finds that 10 of them involved black cars. The P-value for the test of the hypotheses, . What is the correct interpretation of this value?

Assuming the true proportion of black cars that receive moving violations is 0.19, there is a 24% probability that the sample proportion would be 0.15 or less by chance alone.

A certain oat cereal manufacturer boasts that adults who eat its cereal every day have lower cholesterol levels. To test this claim, a nurse measures the cholesterol levels of 18 patients. These patients are instructed to eat the oat cereal every day for four weeks. At the end of this four-week period, the nurse measures the cholesterol levels again. The differences in cholesterol levels (before - after) are listed. A negative difference means that a patient's cholesterol level increased over the four weeks. -18, 5, 9, -1, 0, 4, 3, -2, 0, 11, 5, 12, -5, 1, -3, 4, 8, 9 Assuming the conditions for inference are met, what is the test statistic for testing the hypotheses

A charity is holding a raffle to raise money. There is one car worth $30,000 and five $100 gift cards being raffled off. Each ticket costs $20, and there are a total of 5,000 tickets being sold. Which equation correctly depicts the calculation of the expected value for a ticket?

A computer company wants to determine if there is a difference in the proportion of defective computer chips in a day's production from two different production plants, A and B. A quality control specialist takes a random sample of 100 chips from the first hour of production from plant A and determines that there are 12 defective chips. The specialist then takes a random sample of 100 chips from the last hour of production from plant B and determines that there are 10 defective chips. Assuming conditions for inference are met, what is the 90% confidence interval for the true difference in proportions of defective chips from a day's production between the two plants?

A group of six students decides to conduct an experiment about "brain freeze," a phenomenon that often occurs when eating something cold. The students each flip a coin. If they flip heads, they eat a cup of Italian ice as fast as they can while sitting in an air-conditioned car. If they flip tails, they eat a cup of Italian ice as fast as they can while sitting outside in the sunshine. After a recovery period, they each complete the opposite treatment. The students record the amount of time it takes, in seconds, for them to experience brain freeze under each condition. The data are displayed in the table. What is the mean difference (sun - car) and the standard deviation of the differences?

A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1-10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Assuming the conditions for inference are met, what is the 90% confidence interval for the difference in proportions of clothes that receive a rating of 7 or higher for the two detergents?

A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likely voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (-0.014, 0.064). What is the margin of error for this confidence interval?

A real estate agent has 4 homes for sale: A, B, C, and D. Here are the listing prices. Home A: $150,000Home B: $250,000Home C: $190,000Home D: $550,000 The agent wants to randomly select 2 of the 4 homes to show in an open house this coming weekend. This means the agent may show home A and B, A and C, A and D, B and C, B and D, or C and D. Which of the following gives the sampling distribution of the sample mean listing price for all possible samples of size 2 from this population of 4 homes?

A researcher is studying the relationship between fathers' and sons' heights. He collects a simple random sample of eight pairs of fathers and sons and records their heights as shown in the table. The equation of the least-squares regression line isŷ = 2.7 + 1.042x, where ŷ is each son's height and x is his father's height. Which shows the residual plot?

A student claims that statistics students at her school spend, on average, an hour doing statistics homework each night. In an attempt to substantiate this claim, she selects a random sample of 6 of the 62 students that are taking statistics currently and asks them how much time they spend completing statistics homework each night. Here are the data (in hours): 0.75, 0.75, 0.75, 0.5, 1, 1.25. She would like to know if the data provide convincing statistical evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour. The student plans to test the hypotheses, H0: μ = 1 versus Ha: μ < 1, where μ = the true mean amount of time that statistics students spend doing statistics homework each night. The conditions for inference are met. What are the appropriate test statistic and P-value?

A study found that 80% of teenagers use social media on a regular basis. John wants to investigate if the proportion of students at his large high school who use social media is different. He takes a random sample of 90 students and finds that 63 of them use social media on a regular basis. Which hypotheses would test if the proportion of students at his high school who use social media on a regular basis is different than 0.80?

Can a person train to become better at holding their breath? An experiment was designed to find out. Twelve volunteers were randomly assigned to 1 of 2 groups. The 6 volunteers assigned to group 1 were given breath-holding exercises to perform for 2 weeks. The other group was not given any information about the experiment. At the end of the 2 weeks, all 12 volunteers were individually tested to determine how long they could hold their breath. Here are the data (in seconds) Group 1: 90, 88, 70, 110, 75, 105 Group 2: 40, 48, 35, 50, 55, 62 The researcher would like to determine if these data provide convincing evidence that the true mean amount of time volunteers who were given training held their breath is greater than the volunteers without training. The researcher tests H0: μ1 - μ2 = 0, Ha: μ1 - μ2 > 0, where μ1 = the true mean amount of time that volunteers who were given training held their breath and μ2 = the true mean amount of time that volunteers without training held their breath. The conditions for inference are met. What is the value of the test statistic for a t-test about a difference in means?

If a raffle has a winning prize of $100 and each ticket costs $5 with a total of 500 tickets sold, which equation would calculate the expected value?

It is believed that 80% of adults are honest. An honesty experiment was conducted on a random sample of 50 adults. It was discovered that 42 of the adults were honest. The researcher would like to know if the data provide convincing evidence that more than 80% of adults are honest. What are the values of the test statistic and P-value for this test?

Katie selects a simple random sample of 25 students at her large school and finds that 5 of them are planning to try out for the soccer team next year. She wants to construct a confidence interval for p = the proportion of all students at her school who plan to try out for the soccer team next year, but she realizes she hasn't met all the conditions for constructing the interval. Which condition for this procedure has she failed to meet?

One professional basketball player typically attempts eight free throws per game. Let X represent the number of free throws made out of eight. The distribution for X is shown in the table. Which of the following histograms correctly displays the distribution?

The daily temperatures in fall and winter months in Virginia have a mean of 62oF. A meteorologist in southwest Virginia believes the mean temperature is colder in this area. The meteorologist takes a random sample of 30 daily temperatures from the fall and winter months over the last five years in southwest Virginia. The mean temperature for the sample is 59oF with a standard deviation of 6.21oF. Do the data provide convincing evidence at the level that the mean temperature in fall and winter months in southwest Virginia is less than 62o F? What hypotheses should the meteorologist use to conduct a significance test?

The data points in the table show (minutes on phone calls per day, text messages sent per day). The least-squares regression line for the data is ŷ = 100 - 0.5x. Which shows the residual plot? Use this table to answer the question.

The dotplot below displays the number of math classes taken by a random sample of 35 students at a high school. Which letter represents the approximate location of the mean number of math classes?

The owner of a computer company claims that the proportion of defective computer chips produced at plant A is higher than the proportion of defective chips produced by plant B. A quality control specialist takes a random sample of 100 chips from production at plant A and determines that there are 12 defective chips. The specialist then takes a random sample of 100 chips from production at plant B and determines that there are 10 defective chips. Let pA = the true proportion of defective chips from plant A and pB = the true proportion of defective chips from plant B. Which of the following are the correct hypotheses to test the owner's claim?

The principal of a large high school wants to improve student test scores, so he asks one of his science teachers to try a new method of teaching. Thirty-one students take a pretest on the first day of science class. After 6 weeks using the new instruction, the same students take a posttest. The mean difference (posttest - pretest) in scores is 4.8 points with a standard deviation of 9.7 points. Assuming the conditions for inference are met, what is the test statistic for testing the hypotheses ?

Twenty-four pairs of adult brothers and sisters were sampled at random from a population. The difference in heights, recorded in inches (brother's height minus sister's height), was calculated for each pair. The 95% confidence interval for the mean difference in heights for all brother-and-sister pairs in this population was (-0.76, 4.34). What is the margin of error for the confidence interval?

Which of the following displays is a relative frequency bar graph?

The histogram shows the resting pulse rates of students in a high school health class. Use the histogram to answer the questions. The most likely location for the mean of the data is - . The most likely location for the median of the data is -.

B B

The owner of a smart watch would like to estimate the mean number of steps they take per day. To do so, they select a random sample of 30 days from the previous year's data and record the number of steps they took on each of those days. The mean number of steps taken per day was 8,575 with a standard deviation of 2,125 steps. What is the value of the standard error of the mean?

B- 387.970

Twenty people who claimed to have trouble sleeping volunteered to participate in a sleep study. Half of them were randomly assigned to take 10 mg of melatonin 20 minutes before bed and the other half were randomly assigned to listen to soothing music when they went to bed. The volunteers adhered to their treatments for two weeks. At the end of two weeks, the individuals who listened to soothing music reported a greater improvement to their sleep than those who took melatonin. Which of the following conclusions can we draw from this study? A: We can make inferences based on the results of this study to the population of all people who have trouble sleeping. B: We can draw conclusions about cause and effect for people like those who participated in the study.

B only

A teacher attempts to make a number cube unfair by drilling out the spots on one side and inserting lead weights. To determine if she was successful, she rolls the number cube 50 times and keeps track of the number of times she rolls a 1. She rolls a 1 15 times. She would like to know if the data provide convincing evidence that the proportion of rolls that will land on a 1 is greater than one-sixth. Are the conditions for inference met?

B or D

A teacher wants to estimate the mean height of seniors who attend a large high school. He randomly selects 35 students from this school and records the height, in inches, of these students. The average height is 65.3 inches with a standard deviation of 3.6 inches. Which of the following is the 95% confidence interval for the true mean height of students at this school?

B- (64.06, 66.54)

B- 0.02

An auto body shop receives 70% of its parts from one manufacturer. If parts from the shop are selected at random, what is the probability that the first part not from this manufacturer is the 6th part selected?

B- 0.0504

The weights of bunches of bananas in the grocery store are Normally distributed with a mean weight of 3.54 pounds and a standard deviation of 0.64 pounds. A random sample of four bunches is taken and the mean weight is recorded. Which of the following is the standard deviation of the sampling distribution for the mean of all possible samples of size four?

B- 0.32

Dan and Glenn are swimming buddies who love to challenge themselves while diving. The amount of time Dan can hold his breath underwater, D, is 111 seconds with a standard deviation of 12.5 seconds. The amount of time Glenn can hold his breath underwater, G, is 105 seconds with a standard deviation of 10.9 seconds. Assume that D and G are independent random variables and X = D - G. What is the probability that on any given dive Dan holds his breath for less time than Glenn?

B- 0.359

What is the z* critical value for constructing a 95% confidence interval for a proportion?

B- 1.96

The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. The times to pop a mini bag of microwave popcorn, without burning it, are Normally distributed with a mean time of 90 seconds and a standard deviation of 15 seconds. Suppose two independent random samples, 25 of each, are taken and the mean popping times are calculated. Let R = the popping time of a randomly selected regular-sized bag and M = the popping time of a mini-sized bag. Which of the following best describes the mean of the sampling distribution of ?

B- 50

A local school board wants to determine if the proportion of households in the district that would support starting the school year a week earlier has changed from the previous year. Last year, the school board determined that 65% of households supported starting school earlier. They ask a random sample of 100 households this year, and 70% state they would support starting the school year earlier. The P-value for the test of the hypotheses, , is 0.29. What is the correct interpretation of this value?

B- Assuming 65% of households would support starting school earlier, there is a 0.29 probability of getting a sample proportion of 0.70 or more different from 0.65.

A political pollster claims that 55% of voters prefer candidate A. To investigate this claim, a random sample of 75 voters is polled. The pollster finds that 39 of those polled prefer candidate A. He would like to know if the data provide convincing evidence that the true proportion of all voters who prefer candidate A is less than 55%. The P-value of this test is 0.3015. Interpret the P-value.

B- Assuming that the true population proportion of voters who prefer candidate A is 0.55, the probability of obtaining a sample statistic of 0.52 or less in a random sample of 75 voters is 0.3015.

It is believed that 80% of adults are honest. An honesty experiment was conducted on a random sample of 50 adults. It was discovered that 42 of the adults were honest. The researcher would like to know if the data provide convincing evidence that more than 80% of adults are honest. The standardized test statistic is z = 0.71 and the P-value is 0.2389. What conclusion should be made using the = 0.10 significance level?

B- Because the P-value is greater than = 0.10, there is not convincing evidence that more than 80% of adults are honest.

Consider the given probability histogram of a binomial random variable. What are the center and shape of the distribution?

B- Center: 2.4Shape: skewed right

B- H0: p = 0.28 versus Ha: p > 0.28, where p = the proportion of all high school students who work a part-time job during the school year.

According to a soccer coach, 75% of soccer players have had at least one sprained ankle. An athletic trainer would like to investigate this claim. To do so, the trainer selects a random sample of 125 college soccer players from across the country and finds that 99 of them have had at least one sprained ankle. The trainer would like to know if the data provide convincing evidence that the true proportion of college soccer players who have had at least one sprained ankle is greater than 75%. What are the appropriate hypotheses for this test?

B- H0: p = 0.75 versus Ha: p > 0.75, where p = the true proportion of all college soccer players who have had at least one sprained ankle.

An engineer would like to design a parking garage in the most cost-effective manner. He reads that the average height of pickup trucks, which is the largest type of vehicle that should be expected to fit into the parking garage, is 76.4 inches. To double-check this figure, the engineer employs a statistician. The statistician selects a random sample of 100 trucks and finds the mean height of the sample to be 77.1 inches with a standard deviation of 5.2 inches. The statistician will determine if these data provide convincing evidence that the true mean height of all trucks is greater than 76.4 inches. What are the appropriate hypotheses?

B- H0: μ = 76.4 versus Ha: μ > 76.4, where μ = the true mean height of all trucks

A student claims that professional male basketball players are taller, on average, than college male basketball players. To investigate this claim, the student selects a random sample of 30 professional basketball players and 30 college basketball players. The mean height of the sample of professional male basketball players is 76 inches with a standard deviation of 3.5 inches. The mean height of the sample of college male basketball players is 74.5 inches with a standard deviation of 5.5 inches. The student would like to determine if there is convincing evidence that the true mean height of all professional male basketball players is greater than the true mean height of all college male basketball players. Let μ1 = the true mean height of all professional male basketball players and μ2 = the true mean height of all college male basketball players. What are the appropriate hypotheses?

B- H0: μ1 - μ2 = 0, Ha: μ1 - μ2 > 0

Can a person train to become better at holding their breath? An experiment was designed to find out. Twelve volunteers were randomly assigned to 1 of 2 groups. The 6 volunteers assigned to group 1 were given breath-holding exercises to perform for 2 weeks. The other group was not given any information about the experiment. At the end of the 2 weeks, all 12 volunteers were individually tested to determine how long they could hold their breath. Here are the data (in seconds). Group 1: 90, 88, 70, 110, 75, 105 Group 2: 40, 48, 35, 50, 55, 62 The researcher would like to determine if these data provide convincing evidence that the true mean amount of time volunteers who were given training held their breath is greater than volunteers without training. Let μ1 = the true mean amount of time that volunteers who were given training held their breath and μ2 = the true mean amount of time that volunteers without training held their breath. What are the appropriate hypotheses?

B- H0: μ1 - μ2 = 0, Ha: μ1 - μ2 > 0

Jocelyn believes that the amount of sleep she tends to get on weekends differs from the amount of sleep she tends to get during the school week. To investigate this claim, she randomly selects 10 weekend days and 10 school days. She consults her smart watch to determine the number of hours she slept for each of the selected days. Here are the data. School week: 7, 7.5, 8, 6.5, 8, 7.5, 7, 6.5, 7, 8 Weekend: 9.5, 9.5, 8.25, 8.5, 7.5, 10.25, 8, 7, 9.5, 10 Jocelyn would like to determine if these data provide convincing evidence that the true mean amount of sleep she gets on weekends differs from the true mean amount of sleep she gets during the school week. Let μW = the true mean amount of sleep Jocelyn gets on weekends and μS = the true mean amount of sleep she gets during the school week. What are the appropriate hypotheses?

B- H0: μS - μW = 0, Ha: μS - μW ≠ 0

A trainer would like to estimate the number of runs of the same length and same speed it takes for an individual's body to adjust to the activity. To do this, the trainer selects a random sample of 30 adults who do not currently run and assigns them to run 1 mile at a 12-minute pace every day until they can do so easily. The trainer finds that the standard error of the mean is 2.2 days. What is the interpretation of the standard error of the mean?

B- If we select many random samples of adults who do not currently run and assign them to this training program, the sample mean amount of time needed to adjust to this workout would typically vary by about 2.2 days from the population mean.

A bottled water company bottles varying sizes of water, from 8-ounce to 1-gallon containers. The company has determined that the mean quantity in their 20-ounce bottles is 20.8 ounces with a standard deviation of 0.6 ounces. The bottling plant manager believes his machines are overfilling the bottles. A random sample of 30 bottles is taken, and the mean number of ounces of water is determined to be 21. Under the assumption that the true mean ounces of water is 20.8, 100 simulated means for samples of size 30 are shown in the dotplot What does the dot above 21 represent?

B- In one simulated random sample of 30 bottles of water, the mean number of ounces was 21

A cell phone manufacturer would like to estimate the mean difference in battery lifespan for a phone in full-power versus power-saver mode. They randomly select eight phones and determine the battery lifespan, in hours, for each phone using each power mode. A 90% confidence interval for the true mean difference (full power - low power) in battery life is 5.42 hours to 6.71 hours. A journalist claims that battery lifespan is, on average, 5 hours longer when the phone is used under low-power mode as opposed to full-power mode. Is this claim supported by the 90% confidence interval?

B- No, 5 is not a plausible value in the 90% confidence interval.

A statistics student wants to survey a high school of 910 students concerning support for increasing the number of student parking spots. The student randomly selects 100 students to construct a 95% confidence interval for the true proportion of students who support increasing the number of student parking spots, and finds that 77 students are in support. Are the conditions for inference met?

B- No, the 10% condition is not met.

A teacher claims that 55% of her statistics students have a strong understanding of inference for one proportion. To investigate this claim she randomly selects 25 of her 50 statistics students and provides them with an inference problem about one proportion. Of the 25 selected students, 14 demonstrate a strong understanding of inference for one proportion. The teacher would like to know if the data provide convincing evidence that more than 55% of her students have a strong understanding of this topic. Are the conditions for inference met?

B- No, the 10% condition is not met.

The cafeteria manager at a high school that has 910 students and 75 teachers is considering adding a baked potato bar to the lunch menu. The manager randomly surveys 90 students and 25 teachers, and finds that 50 of the 90 students and 13 of the 25 teachers would purchase from the potato bar. The manager constructs a 99% confidence interval for the difference in the proportions of students and teachers who would purchase lunch on the day the potato bar option is available. Are the conditions for inference met?

B- No, the 10% condition is not met.

A student at a large high school wants to estimate the number of texts seniors send, on average, each day. This student randomly selects 15 seniors at this school and asks them how many texts they sent yesterday. Use the data to construct a 95% confidence interval to estimate the true mean number of texts seniors at this school send each day. 26, 28, 33, 45, 45, 53, 57, 58, 60, 62, 66, 80, 90, 115, 150 Have the conditions for inference been met?

B- No, the graph of the data shows skewness and has at least one outlier

A college professor would like to estimate the difference in the mean amount of time spent completing a particular homework assignment by the top students in her large lecture hall literature class and the students in this class who do not perform as well. She identifies the three students in the class with the highest grades and the three students in the class with the lowest grades and asks each of them how long it took them to complete the particular homework assignment. Although the sample sizes are small, the distribution of the amount of time spent to complete the assignment by the students in each sample shows no signs of strong skewness or outliers. Are the conditions for inference met?

B- No, the random condition is not met for both samples.

A researcher is 95% confident that the interval from 5.2 hours to 7.8 hours captures the true mean amount of time it takes to fully charge a battery pack. Is it plausible that the true mean number of hours to charge all battery packs of this type may be 5?

B- No, this is not a plausible value for the population mean, because 5 is not within the 95% confidence interval.

A government agency constructs a 95% confidence interval to estimate the mean amount of pollution in a city's river. Assume that all conditions have been met. The one-sample t-interval is (1.26, 3.91). Water with 4.00 units of pollution or more, on average, of this type of measure is said to be contaminated. Is it reasonable to believe that this city's river is contaminated?

B- No. Because the interval representing the mean amount of pollution is entirely below 4.00, it is reasonable to believe the river is not contaminated.

Hannah has a chicken coop with six hens. Let X represent the total number of eggs the hens lay on a random day. The distribution for X is given in the table. Which of the following represents the probability of the hens laying at least four eggs?

B- P(X ≥ 4)

A study was conducted to determine the true mean hourly wage of all working high school students. A 95% confidence interval for the true mean hourly wage of high school students is ($6.50, $13.00). Based upon this interval, what conclusion should be made about the hypotheses: = 15 versus where = the true mean hourly income of all working high school students at α = 0.05?

B- Reject H0. Since 15 falls outside the 95% confidence interval, there is convincing evidence that the true mean hourly income of all working high school students is different than $15.

The amount of time it takes students to travel to school can vary greatly depending on how far a student lives from the school and what mode of transportation they take to school. A student claims that the average travel time to school for his large district is 20 minutes. To further investigate this claim, he selects a random sample of 50 students from the school and finds that their mean travel time is 22.4 minutes with a standard deviation of 5.9 minutes. He would like to conduct a significance test to determine if there is convincing evidence that the true mean travel time for all students who attend this school is greater than 20 minutes. The student would like to test H0: μ = 20 versus Ha: μ > 20, where μ = the true mean travel time for all students who attend this school. The conditions for inference are met. The test statistic is t = 2.88 and the P-value is between 0.0025 and 0.005. What conclusion should be made at the significance level, ?

B- Reject H0. There is convincing evidence that the true mean travel time for all students who attend this school is greater than 20 minutes.

A study seeks to estimate the difference in the mean fuel economy (measured in miles per gallon) for vehicles under two treatments: driving with underinflated tires versus driving with properly inflated tires. To quantify this difference, the manufacturer randomly selects 12 cars of the same make and model from the assembly line and then randomly assigns six of the cars to be driven 500 miles with underinflated tires and the other six cars to be driven 500 miles with properly inflated tires. A 90% confidence interval for the true difference in the mean fuel economy for cars of this make and model driven with underinflated tires versus properly inflated tires is -3.339 mpg to -0.585 mpg. Interpret this interval.

B- The manufacturer can be 95% confident that the interval from -3.339 to -0.585 captures the true mean difference in fuel economy (underinflated - properly inflated).

A refrigeration unit at a restaurant is supposed to be kept at 40°F. An inspector would like to test the hypotheses = 40 versus 40 where μ = the true mean temperature for all times of the day. A 98% confidence interval based upon a random sample of 40 temperatures is 40.5 degrees to 42.1 degrees. Using the interval, what decision should be made?

B- The null hypothesis should be rejected at the = 0.02 level.

A professional basketball player typically attempts 8 free throws per game. Let X represent the number of free throws made out of 8. The distribution for X is shown in the table. Which is the correct interpretation of the standard deviation?

B- The number of free throws made out of 8 typically varies from the expected value by 1.4 free throws.

The mean weight for a typical bunch of bananas in grocery stores is 3.54 pounds. The owner of a grocery store will reject a shipment of bananas if the mean weight of the banana bunches is less than 3.54 pounds. The owner randomly selects and weighs 30 bunches of bananas. A significance test at an alpha level of tests the hypotheses pounds; pounds. What is the consequence of a Type II error in this situation?

B- The owner accepts a shipment of bananas that has a mean weight less than 3.54 pounds.

The owner of a popular coffee shop believes that customers who drink espresso are less likely to use their own cup compared with customers who drink coffee. Customers using their own cups get a 5% discount, which is displayed on the receipt. The owner randomly selects 50 receipts from all espresso purchases and 50 receipts from all coffee purchases. For espresso purchases, 15 receipts showed that the customer used their own cup. For coffee purchases, 24 receipts showed the customer used their own cup. Let pEspresso= the true proportion of customers who drink espresso and use their own cup and pCoffeee = the true proportion of customers who drink coffee and use their own cup. The P-value for this significance test is 0.033. Which of the following is the correct conclusion for this test of the hypotheses

B- The owner should reject the null hypothesis since 0.033 < 0.05. There is convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.

A headache medication is supposed to contain 500 mg of active ingredient. A researcher would like to test the hypotheses =500 versus 500 where μ = the true amount of active ingredient for all pills. A 99% confidence interval based on a random sample of 60 pills is (505, 511). Based on the interval, what decision should be made at α = 0.01?

B- The researcher should reject the null hypothesis because 500 falls outside the 99% confidence interval.

A teacher has two large containers filled with blue, red, and green beads, and claims the proportion of red beads are the same in each container. The students believe the proportions are different. Each student shakes the first container, selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container. One student's samples contain 13 red beads from the first container and 16 red beads from the second container. Let p1= the true proportion of red beads in container 1 and p2= the true proportion of red beads in container 2. The P-value for this significance test is 0.171. Which of the following is the correct conclusion for this test of the hypotheses level?

B- The student should fail to reject the null hypothesis since 0.171 > 0.05. There is insufficient evidence that the true proportion of red beads is significantly different between the two containers.

The mean weight for a typical bunch of bananas in grocery stores is 3.54 pounds. Quinn believes the weights of the bananas at the local grocery store this year are different. He randomly selects and weighs 30 bunches of bananas for which the mean weight is 3.27 pounds and the standard deviation is 0.89 pounds. A significance test at an alpha level of produces a P-value of 0.107. What is the correct interpretation of the P-value?

B- There is a 10.7% chance that a sample mean of 3.27 pounds or one more extreme will occur by chance if the true mean weight is 3.54 pounds.

Miguel Cabrera has had 369 at bats, and he has 127 hits and 21 home runs. (Note: The home runs are included in the hits data.) If he is challenged to a batting battle, what is the expected score of each at bat if he earns 1 point for each hit that is not a home run and 5 points for each home run?

C- 0.57

A doctor would like to estimate the mean difference in height of pairs of identical twins. The doctor randomly selects 8 pairs of identical twins and determines the current height, in inches, of each twin. The data are displayed in the table. A 95% confidence interval for the mean difference (twin 1 - twin 2) in height is (-0.823, 0.573). Based on the confidence interval, is it reasonable to claim there is no difference in the heights of twins?

B- Yes, 0 is contained in the 95% confidence interval

A racecar driver has a 0.05 probability of winning any given race in a season. There are 16 races in a season, and whether or not the driver wins one race is independent of whether he wins any other race. Let X represent the number of races the driver wins in the season. Have the conditions for a binomial setting been met for this scenario?

B- Yes, all four conditions in BINS have been met.

A school newspaper article claims that the mean weight of student backpacks is 20 pounds. A student of this school would like to test the hypotheses = 20 versus where = the true mean weight of all backpacks. A 95% confidence interval based upon a random sample of 50 students is (18.5, 19.75). Using the interval, can the researcher reject the null hypothesis?

B- Yes, the null hypothesis can be rejected at the significance level = 0.05 because 20 is not contained in the 95% confidence interval.

A certain size of tires is supposed to be inflated to 35 psi. The owner of a vehicle repair shop would like to test the hypotheses =35 versus 35 where μ = the true mean tire pressure for all customers with this tire size. A 90% confidence interval based upon a random sample of 40 customers is (32.1, 34.3). Using the interval, can the owner reject the null hypothesis?

B- Yes, the null hypothesis can be rejected at the significance level α = 0.10 because 35 is not contained in the 90% confidence interval.

B- approximately Normal because the expected number of successes and failures for each sample are all at least 10

The owner of an apple orchard wants to estimate the mean weight of the apples in the orchard. She takes a random sample of 30 apples, records their weights, and calculates the mean weight of the sample. What is the appropriate inference procedure?

B- one-sample t-interval for u

A student wants to determine if the proportion of times a spun penny lands on heads is different from 0.5. She spins a penny 50 times and records the number of times it lands on heads. What is the appropriate inference procedure?

B- one-sample z-test for p

The mayor of a large town wants to determine if a majority of the households in the town support a proposal. The mayor's assistant randomly selects 100 households and asks whether they would support the mayor's proposal. Sixty households responded that they would. Is there evidence that a majority of the households would support the proposal? What is the appropriate inference procedure?

B- one-sample z-test for p

What critical value of t* should be used for a 80% confidence interval for the population mean based on a random sample of 38 observations?

B- t* = 1.310

What critical value of t* should be used for a 99% confidence interval for the population mean based on a random sample of 34 observations?

B- t* = 2.750

A company would like to estimate the effectiveness of two dish detergents using cleanliness ratings. Fifty dirty dishes are randomly selected and randomly divided into two groups. In one group, each dirty dish will be placed in a container of hot water with Brand A detergent and in the other group, each dirty dish will be placed in a container of hot water with Brand B detergent. The dishes will sit for two hours, and then the cleanliness of the dishes will be measured using a scale of 1-10 (1 = the least clean and 10 = most clean). The difference in mean cleanliness ratings for the two detergents (A - B) will then be calculated. What is the appropriate inference procedure?

B- two-sample t-interval for UA-UB

A television newscaster from a 24-hour news station wants to estimate the number of hours per day its viewers watch programming on this channel. The newscaster randomly selects 100 viewers and asks them how many hours per day they watch this station. The newscaster constructs an 85% confidence interval for the true mean number of hours viewers watch this station. Which of the following would decrease the margin of error?

B- using a sample of size 200

A principal at a large high school wants to estimate the number of days freshmen regularly ride the bus to school. The principal randomly selects 35 freshmen and asks them how many days per week they ride the school bus. The principal constructs a 90% confidence interval for the true mean number of days freshmen ride the bus to school per week. Which of the following would decrease the margin of error?

B- using a sample of size 40

An experiment is conducted to estimate the difference in work productivity for employees under two conditions: with and without music playing in the background. Twenty employees volunteered to be part of the study. Ten of the volunteers were randomly assigned to work for one week with music playing in the background. The other 10 volunteers worked for one week without music playing in the background. Productivity is measured by counting the number of units produced for the week. A 99% confidence interval for the difference in the population means, without music - with music, is (1.525, 7.275). Does the confidence interval support the claim that employees who listen to music while working are less productive than employees who work without listening to music?

B- yes because the confidence interval consists entirely of positive numbers

It is common knowledge that a fair penny will land heads up 50% of the time and tails up 50% of the time. It is very unlikely for a penny to land on its edge when flipped, so a probability of 0 is assigned to this outcome. A curious student suspects that 5 pennies glued together will land on their edge 50% of the time. To investigate this claim, the student securely glues together 5 pennies and flips the penny stack 100 times. Of the 100 flips, the penny stack lands on its edge 46 times. The student would like to know if the data provide convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5. The conditions for inference are met. What is the value of the test statistic and P-value for this test?

B- z = -0.80, P-value = 0.4238

A store manager claims that 60% of shoppers who enter her store make a purchase. To investigate this claim, she selects a random sample of 40 customers and finds that 40% of them make a purchase. She wants to know if the data provide convincing evidence that the true proportion of all customers entering her store who make a purchase differs from 60%. What are the values of the test statistic and P-value for this test?

B- z = -2.58, P-value = 0.0098

It is claimed that 95% of teenagers who have a cell phone never leave home without it. To investigate this claim, a random sample of 300 teenagers who have a cell phone was selected. It was discovered that 273 of the teenagers in the sample never leave home without their cell phone. One question of interest is whether the data provide convincing evidence that the true proportion of teenagers who never leave home without a cell phone is less than 95%. What are the values of the test statistic and P-value for this test?

B- z = -3.18, P-value = 0.0007

To be considered 18-karat (18K) gold, a piece of jewelry must be made of 75% pure gold. The higher the karats, the more valuable a piece of jewelry. A jewelry designer is purchasing a large quantity of 18K gold from a new supplier. To see if the new supplier is being dishonest about the karat rating in the shipment, the designer melts a random sample of the gold and conducts a hypothesis test with H0: The proportion of metal that is gold is 75%, and Ha: The proportion of metal that is gold is less than 75%. What is a Type II error and its consequence in this context?

B-The gold shipment truly is made of less than 75% gold, but the designer concludes that it is made of 75% gold. The designer will accept the shipment of gold and produce inferior jewelry.

A statistics student believes that black cars are less likely to receive tickets for moving violations. Black cars make up 19% of all cars manufactured. The student randomly selects 70 moving violation records and finds that 10 of them involved black cars. The P-value for the test of the hypotheses, and , is 0.24. What is the correct conclusion given ?

Because the P-value is greater than 0.05, the student should fail to reject H0.

A popular restaurant chain will open a new franchise if a study shows that more than 60% of residents in an area would purchase food from the restaurant. An analyst of a particular area randomly selects 500 residents and surveys them about their interest in the restaurant. Of the 500 residents, 320 stated they would purchase food from the restaurant. The P-value for the test of the hypotheses, and , is 0.03. What is the correct conclusion given ?

Because the P-value is less than 0.05 , the analyst should reject H0.

A computer company wants to determine if the proportion of defective computer chips from a day's production is more than 10%. A quality control specialist randomly selects 200 chips from a day's production and finds that 30 chips are defective. The P-value for the test of the hypotheses, and , is 0.009. What is the correct conclusion given ?

Because the P-value is less than 0.05, the specialist should reject H0.

Because the P-value of 0.035 > α, Simone should fail to reject H0. There is not convincing evidence that the Arizona written driver's test has a true first-attempt failure rate less than 60%.

Because the P-value of 0.0733 > , Lucy should fail to reject H0. There is not convincing evidence that the proportion of customers who will ask for a straw is less than 50%.

Graduation rate is one measure used to compare colleges in national publications. One such publication compared semester tuition against graduation rate, defined as the percentage of students who graduate within four years. The value of r for the scatterplot is 0.856. Which statement best describes how the circled point influences the correlation shown in the scatterplot?

Because the point lies outside the linear trend, it weakens the correlation.

A tennis court official selects a random sample of 50 tennis balls that were slated for use in a highly contested match. He randomly assigns half of them to be subjected to 90 degree heat to replicate the presumed temperature at match time. The other half are run through a machine that replicates the action of hitting the ball 500 times. After the treatments, he inspects the balls for wear and tear. Which of the following conclusions can we draw from this study? A: We can make inferences based on the results of this study for the population of all tennis balls slated for use in the match. B: We can draw conclusions about cause and effect for the population of tennis balls slated for use in the match.

Both A and B

A sunscreen manufacturer tests a new water-resistant sunscreen by finding 120 volunteers at a community pool. The subjects are randomly assigned to one of two groups by drawing either a 1 or 2 marked on slips of equal-sized paper from a bag. Half of the subjects use an old formulation, and half use the new formulation over an 8-hour time frame on the same sunny day. Test administrators apply a measured amount of sunscreen to each subject at the beginning of the day and reapply it at regular intervals throughout the day. Test subjects are asked to remain in unshaded areas as much as possible during the test. The levels of sunburn are compared at the end of the day. Which of the following accurately describes the benefit, if any, of control in the experiment?

By controlling variables that may influence the response variable, we reduce variability in the response variable.

A computer company wants to determine if the proportion of defective computer chips from a day's production is more than 10%. A quality control specialist randomly selects 200 chips from a day's production and finds that 24 chips are defective. Which hypotheses would test if the proportion of defective chips is more than 10%?

A local school board believes there is a difference in the proportion of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school-aged children that would support starting the school year a week earlier. They survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 38 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 25 respond yes. Let ps = the true proportion of households with school-aged children that would support starting the school year a week early and pW = the true proportion of households without school-aged children that would support starting the school year a week earlier. Which of the following are the correct hypotheses to test the school board's claim?

A local school board wants to determine the proportion of households in the district that would support a proposal to start the school year a week earlier. They ask a random sample of 100 households whether they would support the proposal, and 62 households stated that they would. Assuming that conditions have been met, what is the 90% confidence interval for the true proportion of households that would support the proposal

A local school board wants to estimate the difference in the proportion of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school-aged children that would support starting the school year a week earlier. They survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 30 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 25 respond yes. Assuming the conditions for inference have been met, what is the 90% confidence interval for the difference in proportions of households that would support starting the school year a week earlier?

A political pollster claims that 55% of voters prefer candidate A. To investigate this claim, a random sample of 75 voters is polled. The pollster finds that 39 of those polled prefer candidate A. He would like to know if the data provide convincing evidence that the true proportion of all voters who prefer candidate A is less than 55%. What are the values of the test statistic and P-value for this test?

A school guidance counselor is concerned that a greater proportion of high school students are working part-time jobs during the school year than a decade ago. A decade ago, 28% of high school students worked a part-time job during the school year. To investigate whether the proportion is greater today, a random sample of 80 high school students is selected. It is discovered that 37.5% of them work part-time jobs during the school year. The guidance counselor would like to know if the data provide convincing evidence that the true proportion of all high school students that work a part-time job during the school year is greater than 0.28. The conditions for inference are met. What is the value of the test statistic and P-value for this test?

A student wants to survey the sophomore class of 200 students about whether the school should require uniforms. A random sample of 50 sophomores is surveyed and asked whether they support the school adopting uniforms. Of the 50 sophomores, 12 say they would favor school uniforms. Assuming the conditions for inference have been met, what is the 90% confidence interval for the true proportion of sophomores who favor the adoption of uniforms?

A study seeks to estimate the difference in the mean fuel economy (measured in miles per gallon) for vehicles under two treatments: driving with underinflated tires versus driving with properly inflated tires. To quantify this difference, the manufacturer randomly selects 12 cars of the same make and model from the assembly line and then randomly assigns six of the cars to be driven 500 miles with underinflated tires and the other six cars to be driven 500 miles with properly inflated tires. Here are summary statistics and dotplots of the results: What is the correct 90% confidence interval for the true difference in the population means (underinflated - properly inflated)? Use the conservative df.

A teacher has two large containers filled with blue, red, and green beads, and claims the proportion of red beads is the same for both containers. The students believe the proportions are different. Each student shakes the first container, selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container. One student's samples contained 10 red beads from the first container and 16 red beads from the second container. Let p1= the true proportion of red beads in container 1 and p2= the true proportion of red beads in container 2. Which of the following is the correct standardized test statistic and P-value for the hypotheses,

A teacher has two large containers filled with blue, red, and green beads, and claims the proportion of red beads is the same in each container. The students believe the proportions are different. Each student shakes the first container, selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container. One student's samples contained 10 red beads from the first container and 16 red beads from the second container. Let p1 = the true proportion of red beads in container 1 and p2 = the true proportion of red beads in container 2. Which of the following are the correct hypotheses to test the students' claim?

In a statistics activity, students are asked to determine if there is a difference in the proportion of times that a spinning penny will land with tails up, and the proportion of times a spinning dime will land tails up. The students are instructed to spin the penny and the dime 30 times and record the number of times they land tails up. For one student, the penny lands tails side up 18 times, and the dime lands tails side up 20 times. Assuming the conditions for inference are met, what is the 98% confidence interval for the difference in proportions of tails side up for a penny and a dime?

The distribution of the heights of five-year-old children has a mean of 42.5 inches. A pediatrician believes the five-year-old children in a city are taller on average. The pediatrician selects a random sample of 40 five-year-old children and measures their heights. The mean height of the sample is 44.1 inches with a standard deviation of 3.5 inches. Do the data provide convincing evidence at the level that the mean height of five-year-old children in this city is greater than 42.5 inches? What hypotheses should the pediatrician use to conduct a significance test?

The nutrition supervisor for a school district is considering adding a baked potato bar to the lunch menu for all the high school cafeterias. He wants to determine if there is a difference in the proportion of students who would purchase from the potato bar for two high schools, East and West. The cafeteria manager at each high school randomly surveys 90 students. At East High School, 63 of the students say they would purchase from the potato bar. At West High School, 58 students say they would. Assuming the conditions for inference have been met, what is the 99% confidence interval for the difference in proportion of students from the two schools who would purchase from the potato bar?

The owner of a computer company claims that the proportion of defective computer chips produced at plant A is higher than the proportion of defective chips produced by plant B. A quality control specialist takes a random sample of 80 chips from production at plant A and determines that there are 12 defective chips. The specialist then takes a random sample of 90 chips from production at plant B and determines that there are 10 defective chips. Let pA = the true proportion of defective chips from plant A and pB = the true proportion of defective chips from plant B. Which of the following is the correct standardized test statistic for the hypotheses,

The owner of a computer company claims that the proportion of defective computer chips produced at plant A is higher than the proportion of defective chips produced by plant B. A quality control specialist takes a random sample of 80 chips from production at plant A and determines that there are 12 defective chips. The specialist then takes a random sample of 90 chips from production at plant B and determines that there are 10 defective chips. Let pA = the true proportion of defective chips from plant A and pB = the true proportion of defective chips from plant B. Which of the following is the correct standardized test statistic for the hypotheses, ?

The owner of a local movie theater keeps track of the number of tickets sold in each purchase. The owner determines the probabilities based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table. Which of the following histograms correctly displays the distribution?

Two students want to determine whose paper airplane model can fly the farthest. To put their models to the test, they recruit five friends to participate in a study. Because the friends have varying throwing abilities, the students decide to have each friend throw each model of airplane. To determine which paper airplane each friend throws first, a coin is tossed. The data are displayed in the table, which shows how far each airplane flies to the nearest inch. What is the mean difference (B - A) and the standard deviation of the differences?

When spinning a penny, Claire believes the proportion of times the penny lands on heads is not 0.5. She spins a penny 50 times and it lands on heads 30 times. Which hypotheses would test Claire's claim?

Which scatterplot corresponds to the residual plot?

The graph displays people's favorite holidays in relation to their housing arrangement. Which statement is true?

Holiday preference and housing status are associated because the percentage of people who favor each holiday differs by housing status.

A company makes a product and has no way to determine which ones are faulty until an unhappy customer returns it. Three percent of the products are faulty and will cost the company $200 each in customer service and repairs. If the company does not refund the customer when repairing the item, how much should the company charge to make a profit of $2.00 per item?

C- $8

The power of a significance test to reject the null hypothesis when a particular value of the alternative is true is 0.8. What is the probability that this test results in a Type II error?

C- 0.20

The manager of a movie theater is standing outside the theater complex one evening. He will be asking the moviegoers questions.

How much did you spend at the movies today?

The distribution of tips given by customers who buy only a cup of coffee is bimodal with a mean of $0.29 and a standard deviation of $0.116. The distribution of tips given by customers who buy only a salad is approximately Normally distributed with a mean of $2.89 and a standard deviation of $1.18. If a random sample of 35 tips from customers who buy only a cup of coffee is selected and a random sample of 20 customers who buy only a salad is selected, what is the probability of a sample mean being at least $2.50 more for customers who buy only a salad than for those who buy only a cup of coffee?

C- 0.6781

C- 4.8

A student believes that a certain 6-sided number cube, with the numbers 1 to 6, is unfair and is more likely to land with a 6 facing up. The student rolls the cube 100 times and lands with 6 facing up 20 times. The P-value for the test of the hypotheses, H0:p=0.17 and Ha:p>0.17, is 0.19. What is the correct interpretation of this value?

C- Assuming 0.17 is the true proportion of the cube landing with a 6 facing up, this sample proportion can be expected by chance 19% of the time.

C- Because the P-value > α = 0.05, the correct decision is to fail to reject H0.

An emergency fund is defined as a savings account that has a balance equal to at least two months' living expenses. An article in a financial magazine claims that 80% of American adults do not have an emergency fund. To investigate this claim, a financial advisor selects a random sample of 150 Americans and finds that 112 do not have an emergency fund. The financial advisor would like to know if the data provide convincing evidence that the true proportion of American adults who do not have an emergency fund is less than 80%. The financial advisor tests the hypotheses H0: p = 0.80 versus Ha: p < 0.80, where p = the true proportion of all American adults that do not have an emergency fund. The conditions for inference are met. The standardized test statistic is z = -1.62 and the P-value is 0.0526. What conclusion should the financial advisor make using the α = 0.05 significance level?

C- Because the P-value is greater than α = 0.05, there is not convincing evidence that the true proportion of American adults who do not have an emergency fund is less than 80%.

It is common knowledge that a fair penny will land heads up 50% of the time and tails up 50% of the time. It is very unlikely for a penny to land on its edge when flipped, so a probability of 0 is assigned to this outcome. A curious student suspects that 5 pennies glued together will land on their edge 50% of the time. To investigate this claim, the student securely glues together 5 pennies and flips the penny stack 100 times. Of the 100 flips, the penny stack lands on its edge 46 times. The student would like to know if the data provide convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5. The student tests the hypotheses H0: p = 0.50 versus Ha: p ≠ 0.50, where p = the true proportion of all flips for which the penny stack will land on its edge. The conditions for inference are met. The standardized test statistic is z = -0.80 and the P-value is 0.2119. What conclusion should the student make using the α = 0.10 significance level?

C- Because the P-value is greater than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.

A nutritionist believes that 10% of teenagers eat cereal for breakfast. To investigate this claim, she selects a random sample of 150 teenagers and finds that 25 eat cereal for breakfast. She would like to know if the data provide convincing evidence that the true proportion of teenagers who eat cereal for breakfast differs from 10%. The standardized test statistic is z = 2.72 and the P-value is 0.0066. What conclusion should be made using the = 0.05 significance level?

C- Because the P-value is less than = 0.05, there is convincing evidence that the true proportion of teenagers who eat cereal for breakfast differs from 10%.

According to historical data, it is believed that 12% of American adults work more than one job. To investigate if this claim is still accurate today, a random sample of 100 American adults is selected. It is discovered that 18 of them work more than one job. A researcher would like to know if the data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12%. The standardized test statistic is z = 1.85 and the P-value is 0.0644. What decision should the researcher make using the = 0.05 significance level?

C- Fail to reject H0 because the P-value is greater than = 0.05.

Timmy could follow two main routes to get to school. Timmy believes that route 1 is faster than route 2. To investigate, he decides to keep track for the next 4 weeks. Each morning, he flips a coin to determine which route he takes. Of the 20 school days, 12 days were randomly assigned to route 1, and 8 days were randomly assigned to route 2. The mean travel time for days assigned to route 1 was 20 minutes with a standard deviation of 3 minutes. The mean travel time for the days assigned to route 2 was 22 minutes with a standard deviation of 2 minutes. Timmy would like to know if the data provide convincing evidence of a difference in travel time for the 2 routes, so he tests H0: μ1 - μ2 = 0, Ha: μ1 - μ2 ≠ 0. Let μ1 = the true mean travel time to school along route 1 and μ2 = the true mean travel time to school along route 2. Dotplots of the distribution of travel time for route 1 and route 2 show no strong skewness or outliers. The conditions for inference have been met. The standardized test statistic is t = -1.79, and the P-value is between 0.05 and 0.10. What conclusion should be made using the significance level, = 0.05?

C- Fail to reject H0. There is not convincing evidence that the true mean travel time for route 1 differs from the true mean travel time for route 2.

A researcher is 95% confident that the interval from 5.09 to 10.13 captures the true mean amount of times models change clothes during a fashion shoot. Is it plausible that the true mean number of times for all models to change clothes during a fashion shoot may be 10?

C- Yes, this is a plausible value for the population mean, because 10 is within the 95% confidence interval.

C- H0: p = 0.5 versus Ha: p ≠ 0.5, where p = the true proportion of flips for which the penny stack will land on its edge.

A chiropractor would like to estimate the mean length of time needed for patients to recover from straining a back muscle. He selects a random sample of 15 patients from the large number of patients with this type of injury. He records the length of time it takes for each of these patients to fully recover. The distribution of recovery times for these patients is unimodal, fairly symmetric, and has no outliers. The standard error of the mean is 3.25 days. What is the interpretation of the standard error of the mean?

C- If we select many random samples of patients recovering from straining a back muscle, the sample mean length of time needed to recover will typically vary by about 3.25 days from the population mean.

Kat is interested in getting chickens so she can have fresh eggs. Before she buys her chickens, she wants to find the mean number of eggs each one will lay. She begins by randomly selecting 40 chickens from a large poultry farm and counts how many eggs each one lays within one month. She finds the mean to be 24.8 eggs with a standard deviation of 6.9 eggs. The resulting interval is (22.96, 26.64). Which of the following correctly interprets the 90% confidence interval for the true mean number of eggs chickens from this poultry farm lay within one month?

C- Kat can be 90% confident that the constructed interval (22.96, 26.64) captures the true mean number of eggs chickens from this farm lay.

The distribution of professional baseball player salaries has a mean of $3.2 million. An analyst believes that the mean salary for teams on the East Coast is different. The analyst randomly selects 15 baseball players from teams on the East Coast and records their annual salaries. The mean salary for the players in the sample is $3.9 million with a standard deviation of $2.1 million. Do the data provide convincing evidence at the level that the mean salary for the baseball players on the East Coast is different from $3.2 million? Are the conditions for inference met?

C- No, since it is not known that the population of all players' salaries is approximately Normal, the Normal/large sample condition is not met.

A reporter claims that 90% of American adults cannot name the current vice president of the United States. To investigate this claim, the reporter selects a random sample of 50 American adults and finds that 28 are unable to name the current vice president. The reporter would like to know if the data provide convincing evidence that fewer than 90% of American adults are unable to name the current vice president. Are the conditions for inference met?

C- No, the Large Counts Condition is not met.

A food delivery service manager would like to estimate the mean amount of time it takes employees of his company to deliver food to the customers. To do so, he selects a random sample of 10 deliveries from the large number of deliveries made and records the amount of time each of those deliveries took. Are the conditions for constructing a t confidence interval met?

C- No, the Normal/large sample condition is not met.

To estimate the amount of carbon emissions released by cars, the mean weight of cars must be estimated. To do this, a random sample of 20 cars is selected and their mean weight is calculated. Are the conditions for constructing a t confidence interval met?

C- No, the Normal/large sample condition is not met.

On average, a person's body temperature should be approximately 98.6°F. A doctor would like to test the hypotheses versus where μ = the true mean body temperature of all adults. A 99% confidence interval based upon a random sample of 100 adults is (97.5, 99.2). Using the interval, can the researcher reject the null hypothesis?

C- No, the null hypothesis cannot be rejected at the significance level α = 0.01, because 98.6 is contained in the 99% confidence interval.

A claw machine game displays a sign that claims 90% of plays result in a win. A suspicious customer watches 40 consecutive plays of this game and observes that there is a winner in 30 of the games. The customer would like to know if the data provide convincing evidence that the true proportion of winners is less than 0.9. Are the conditions for inference met?

C- No, two conditions are not met.

An equestrian enthusiast is interested in the racing times of horses. She believes an older horse will have a faster race time than a younger horse. She selects a random sample of 17 sibling pairs of adult horses and records their times for running on the same track. The mean difference (older - younger) in the times to run the track is -15.7 seconds with a standard deviation of 8.3 seconds. Are the conditions for inference met?

C- No. The Normal/Large Sample condition is not met because the sample size is too small and the shape of the distribution of differences is not known.

Based upon historical data, it is known that 8% of 12-egg cartons contain at least one broken egg. A grocery store manager would like to carry out a simulation to estimate the number of cartons, in a sample of 10, that would contain at least one broken egg. She assigns the digits to the outcomes. 01-08 = carton contains a broken egg 09-99, 00 = carton does not contain a broken egg How can a random number table be used to simulate one trial of this situation?

C- Read 10 two-digit numbers. Count the number of two-digit pairs that represent cartons containing at least one broken egg.

A researcher is 95% confident that the interval from 19.8 to 31.5 captures the true mean number of unbroken crackers in a certain-sized bag. Is it plausible that the true mean number of unbroken crackers for all bags of this size may be 30?

C- Yes, this is a plausible value for the population mean, because 30 is within the 95% confidence interval.

A local school board believes there is a difference in the proportion of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school-aged children that would support starting the school year a week earlier. They survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 38 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 35 respond yes. Let ps= the true proportion of households with school-aged children that would support starting the school year a week early and pw= the true proportion of households without school-aged children that would support starting the school year a week earlier. Which of the following is a correct statement about the conditions for this test?

C- The Large Counts Condition is not met.

A doctor would like to estimate the mean difference in height of pairs of identical twins. The doctor randomly selects 8 pairs of identical twins and determines the current height, in inches, of each twin. The data are displayed in the table. The conditions for inference are met. The 95% confidence interval for the mean difference (twin 1 - twin 2) in height is (-0.823, 0.573). What is the correct interpretation of this interval?

C- The doctor can be 95% confident that the interval from -0.823 inches to 0.573 inches captures the true mean difference in the height of twins.

Two different furniture manufacturers produce chairs. Let X represent the number of chairs produced daily at plant X, and let Y represent the number of chairs produced daily at plant Y. Assume that X and Y are independent random variables. Which of the following choices explains the meaning of independent random variables in context?

C- The independence of the two manufacturers means that knowing how much one furniture plant produces does not help us predict how much the other produces.

Animal shelters in a county need at least 15% of their animals to be adopted weekly to have room for the new animals that are brought into the various shelters. The county manager takes a random sample of shelters each week to estimate the overall proportion of animals that are adopted. If he concludes that the proportion has dropped below 15%, he will not accept any new animals into the shelters that week. He tests the hypotheses: H0: The adoption rate is 15%, and Ha: The adoption rate is less than 15%. What is a Type I error, and what is its consequence in this context?

C- The manager believes the adoption rate has dropped below 15%, when it actually has not. The manager will not accept more animals into the shelters, when there actually is room to care for those animals.

The manager of an aquatic center is interested in the average number of fish people keep in their saltwater tanks. She randomly selects 38 people who own saltwater fish tanks and asks how many fish they have. The mean amount is 48.2 fish with a standard deviation of 22.1 fish. Which of the following correctly interprets the 99% confidence interval for the true mean number of fish in saltwater tanks?

C- The manager can be 99% confident that the constructed interval captures the true mean number of fish in saltwater tanks.

From previous experience, the owner of an apple orchard knows that the mean weight of Gala apples is 140 grams. There has been more precipitation than usual this year. The owner believes the weights of the apples will be heavier than usual and therefore the crop will be more profitable. This will allow the owner to expand the orchard. The owner takes a random sample of 30 apples and records their mean weight. What is the consequence of a Type I error in this situation?

C- The owner believes the crop will be more profitable and expands the orchard when the true mean weight of the apples is actually not greater than 140 grams.

Two students want to determine whose paper airplane model can fly the farthest. To put their models to the test, they recruit five friends to participate in a study. Because the friends have varying throwing abilities, the students decide to have each friend throw each model of airplane. To determine which paper airplane each friend throws first, a coin is tossed. The data are displayed in the table, which shows how far each airplane flies to the nearest inch. The mean of the differences is 40 inches, and the standard deviation of the differences is 53.57 inches. The conditions for inference are met. A 90% confidence interval for the mean difference (B - A) in flight distance is -11.08 inches to 91.08 inches. What is the correct interpretation of this interval?

C- The students can be 90% confident that, on average, the model A plane flies between 91.08 inches farther than and 11.08 inches less than the model B plane.

A statistics class weighed 20 bags of grapes purchased from the store. The bags are advertised to contain 16 ounces, on average. The class calculated the 90% confidence interval for the true mean weight of bags of grapes from this store to be (15.875, 16.595) ounces. What is the correct interpretation of the 90 percent confidence interval?

C- We are 90% confident that the interval from 15.875 ounces to 16.595 ounces captures the true mean weight of bags of grapes.

A random sample of 30 students is selected. Each student is asked to report how much time they spent the previous night on math homework and how much time they spent on science homework. A 95% confidence interval for the true mean difference (math - science) in the amount of time spent on homework is 30 minutes to 75 minutes. A science teacher claims that students tend to spend more time working on math homework than on science homework. Is this claim supported by the 95% confidence interval?

C- Yes, the confidence interval consists entirely of positive numbers.

A random sample of 50 pairs of parents and children is selected. The parent is asked to estimate how many hours their child spent watching TV yesterday. The child is asked many hours they spent watching TV yesterday. A 90% confidence interval for the mean difference (parent's response - child's response) in the amount of time spent watching TV is 0.25 hours to 2.5 hours. A newspaper columnist writes the headline "Parents overestimate how much time children spend watching TV." Is this headline supported by the 90% confidence interval?

C- Yes, the confidence interval consists entirely of positive numbers.

A researcher is 95% confident that the interval from 2.8 hours to 6.5 hours captures the true mean amount of time it takes for 1 square foot of fresh paint to dry. Is there evidence that the true mean number of hours for 1 square foot of this type of paint to dry is greater than 5?

C- Yes, there is evidence for the population mean to be greater than 5, because 5 is within the 95% confidence interval.

The prices of pants at a large clothing store chain are skewed left with a mean of $32 and a standard deviation of $20. The manager at one of the stores randomly selects 30 pairs of pants. What is the shape of the distribution of the sample mean for all possible random samples of size 30 from this population?

C- approximately Normal

The prices of houses in the US is strongly skewed to the right with a mean of $383,500 and a standard deviation of $289,321. A real estate agent takes a random sample of 30 houses and records the mean price. What is the best description for the sampling distribution?

C- approximately Normal with a mean of 383,500 and a standard deviation of 52,823

A junior at a large high school wants to estimate the amount of time it takes to log in to a school computer. He randomly selects 35 students and records the amount of time it takes to log in. The junior constructs a 95% confidence interval for the true mean amount of time it takes to log in to a school computer. Which of the following would decrease the margin of error?

C- constructing a 90% confidence interval

A social worker at a large high school wants to estimate the number of days students are absent. He randomly selects 45 students and records the number of days each one is absent. The social worker constructs a 95% confidence interval for the true mean number of days students at this school are absent. Which of the following would decrease the margin of error?

C- constructing a 90% confidence interval

The volleyball coach at a large high school wants to estimate the number of times players spike the ball during any given game. She randomly selects 30 games and records the number of spikes. The coach constructs a 95% confidence interval for the true mean number of spikes players make in a game. Which of the following would decrease the margin of error?

C- constructing a 90% confidence interval

A company that sells hair-care products claims that a product that combines shampoo and conditioner works better than a shampoo and conditioner used separately. A researcher recruits 60 volunteers and pairs them according to age, hair color, and hair type. For each pair, the researcher flips a coin to determine which volunteers will use the shampoo/conditioner combination and which ones will use the separate shampoo and conditioner. After using the products for one month, the subjects are asked to rate their satisfaction with the hair products on a scale of 1-10 (1 = highly dissatisfied and 10 = highly satisfied). The mean difference in satisfaction ratings (Combined - Separate) is calculated. What is the appropriate procedure for testing the company's claim?

C- one-sample t-test for U diff

A pool supply company sells 50-pound buckets of chlorine tablets. A customer believes that the company may be underfilling the buckets. To investigate, an inspector is hired. The inspector randomly selects 30 of these buckets of chlorine tablets and weighs the contents of each bucket. The sample mean is 49.4 pounds with a standard deviation of 1.2 pounds. The inspector would like to know if this provides convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds, so he plans to test the hypotheses H0: μ = 50 versus Ha: μ < 50, where μ = the true mean weight of all 50-pound buckets of chlorine tablets. The conditions for inference are met. What are the appropriate test statistic and P-value?

C- t = -2.74. The P-value is between 0.005 and 0.01.

The mean price of houses in the US is $383,500. A real estate agent believes the mean price of houses in a local neighborhood is less than the national mean. The agent takes a random sample of 30 houses and finds the mean price to be $295,089 with a standard deviation of $156,321. Do the data provide convincing evidence at the level that the mean price of the houses in the area is less than $383,500? What are the test statistic and P-value for this significance test?

C- t = -3.10 and 0.001 < P-value < 0.0025

A student claims that professional male basketball players are taller, on average, than college male basketball players. To investigate this claim, the student selects a random sample of 30 professional basketball players and 30 college basketball players. The mean height of the sample of professional male basketball players is 76 inches with a standard deviation of 3.5 inches. The mean height of the sample of college male basketball players is 74.5 inches with a standard deviation of 5.5 inches. The student would like to determine if there is convincing evidence that the true mean height of all professional male basketball players is greater than the true mean height of all college male basketball players. The hypotheses H0: μ1 - μ2 = 0, Ha: μ1 - μ2 > 0 are tested where μ1 = the true mean height of all professional male basketball players, and μ2 = the true mean height of all college male basketball players. The conditions for inference have been met. What are the values of the test statistic and P-value for a t-test about a difference in means?

C- t = 1.26. The P-value is between 0.10 and 0.15.

An engineer would like to design a parking garage in the most cost-effective manner. He reads that the average height of pickup trucks, which is the largest type of vehicle that should be expected to fit into the parking garage is 76.4 inches. To double-check this figure, the engineer employs a statistician. The statistician selects a random sample of 100 trucks and finds the mean height of the sample to be 77.1 inches with a standard deviation of 5.2 inches. The statistician will determine if these data provide convincing evidence that the true mean height of all trucks is greater than 76.4 inches. The statistician plans to test the hypotheses, H0: μ = 76.4 versus Ha: μ > 76.4, where μ = the true mean height of all trucks. The conditions for inference are met. What are the appropriate test statistic and P-value?

C- t = 1.35. The P-value is between 0.05 and 0.10.

Timmy could follow two main routes to get to school. Timmy believes that route 1 is faster than route 2. To investigate, he decides to keep track for the next 4 weeks. Each morning, he flips a coin to determine which route he takes. Of the 20 school days, 12 days were randomly assigned to route 1, and 8 days were randomly assigned to route 2. The mean travel time for days assigned to route 1 was 20 minutes with a standard deviation of 3 minutes. The mean travel time for the days assigned to route 2 was 22 minutes with a standard deviation of 2 minutes. Timmy would like to know if the data provide convincing evidence of a difference in travel time for the 2 routes, so he tests H0: μ1 - μ2 = 0, Ha: μ1 - μ2 ≠ 0. Let μ1 = the true mean travel time to school along route 1 and μ2 = the true mean travel time to school along route 2. Dotplots of the distribution of travel time for route 1 and route 2 show no strong skewness or outliers. The conditions for inference have been met. What are the values of the test statistic and P-value for a t-test about a difference in means?

C- t = 1.79. The P-value is between 0.025 and 0.05.

A manufacturer of cell phones would like to estimate how much longer the battery lasts in their model 10 phone than in their model 9 phone. To estimate this difference, they randomly select 40 cell phones of each model from the production line. They subject each phone to a standard battery life test. The 40 model 10 phones have a mean battery life of 14.4 hours with a standard deviation of 2.1 hours. The 40 model 9 phones have a mean battery life of 12.8 hours with a standard deviation of 2.3 hours. What is the appropriate inference procedure to be used to estimate how much longer the battery lasts in their model 10 phone than in their model 9 phone?

C- t confidence interval for a difference in means

The maintenance crew of a hotel must monitor the temperature of the hotel pool and hot tub. To enhance comfort, the management team requests that the mean pool temperature and the mean hot tub temperatures not differ by more than 15 degrees. To estimate the difference in these mean temperatures the maintenance crew selects a random sample of 8 times to check the hot tub temperature and a random sample of 10 times to check the pool temperature. Although the sample sizes are small, the distribution of temperature for the pool and for the hot tub does not show strong skewness or any outliers. What is the appropriate inference procedure?

C- t confidence interval for a difference in means

A real-estate agent conducted an experiment to test the effect of selling a staged home vs. selling an empty home. To do so, the agent obtained a list of 10 comparable homes just listed for sale that were currently empty. He randomly assigned 5 of the homes to be "staged," meaning they were filled with nice furniture and decorated. The owners of the 5 homes all agreed to have their homes staged by professional decorators. The other 5 homes remained empty. The hypothesis is that empty homes are not as appealing to buyers as staged homes and, therefore, sell for lower prices than staged homes. The mean selling price of the 5 empty homes was $150,000 with a standard deviation of $22,000. The mean selling price of the 5 staged homes was $175,000 with a standard deviation of 35,000. A dotplot of each sample shows no strong skewness and no outliers. The agent tests H0: μ1 - μ2 = 0, Ha: μ1 - μ2 < 0, where μ1 = the true mean selling price of all comparable empty homes and μ2 = the true mean selling price of all comparable staged homes. What is the name of the appropriate inference procedure?

C- t-test for a difference in means

A teacher has two large containers (A and B) filled with blue, red, and green beads, and claims the proportion of red beads is the same in each container. The students believe the proportions are different. Each student shakes the first container, selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container. One student's samples contained 10 red beads from the first container and 16 red beads from the second container. The student then calculated the difference in the proportions of red beads. What is the appropriate inference procedure?

C- two-sample z-test for PA-PB

The owner of a computer company claims that the proportion of defective computer chips produced at plant A is higher than the proportion of defective chips produced by plant B. A random sample of 100 chips is collected from each plant and the difference (A - B) in the proportion of defective chips is calculated. What is the appropriate inference procedure?

C- two-sample z-test for PA-PB

Sisters Amilia and Bianca play games together often. Let A represent the number of games Amilia wins monthly, and let B represent the number of games Bianca wins monthly. A and B are independent events. The mean of A is 35.7 games with a standard deviation of 5.1 games, and the mean of B is 37.3 games with a standard deviation of 6.8 games. What is the mean and standard deviation of the total number of games won, S = A + B?

C- us= 73.0 games and as= 8.5 games

Devon's tennis coach says that 72% of Devon's serves are good serves. Devon thinks he has a higher proportion of good serves. To test this, 50 of his serves are randomly selected and 40 of them are good. To determine if these data provide convincing evidence that the proportion of Devon's serves that are good is greater than 72%, 100 trials of a simulation are conducted. Devon's hypotheses are: H0: p = 72% and Ha: p > 72%, where p = the true proportion of Devon's serves that are good. Based on the results of the simulation, what is the estimate of the P-value of the test?

C-0.14

A restaurant wants to determine how much their customers like the dinner specials prepared by the new restaurant chef. Which survey method is most likely to lead to response bias?

Create a survey that is administered by the waitstaff prior to the customer leaving the restaurant.

A director of a company notices that there is a declining relationship between the company's sales revenue and customer satisfaction. Here is a scatterplot of the data for the past six months. Which statement is true?

Customer satisfaction is declining ever more rapidly as the company's sales revenue increases.

Consider the given probability histogram of a binomial random variable. What are the center and shape of the distribution?

Center: 5.4Shape: skewed left

Consider the given probability histogram of a binomial random variable. What are the center and shape of the distribution?

Center: 8 Shape: skewed left

A newspaper collected information on schools in its circulation area in order to compare their quality. Two measures the newspaper collected for each school, mean class size and mean score on a statewide reading exam, are shown in the scatterplot. Which statement regarding the association shown could explain the relationship?

Class size appears to have little effect on test scores. Schools in more affluent areas have larger class sizes, which is associated with higher test scores. -Schools in more affluent areas have smaller class sizes, which is associated with higher test scores. Schools in less affluent areas tend to have smaller class sizes, which is associated with lower test scores.

Which of the following is not true about cluster sampling?

Cluster sampling has the advantage of reducing sampling variability.

Residents were asked to identify the type of car they drive and the average miles per gallon (mpg) the car receives on the highway.

Complete the statements based on the information. The categorical variable is names of residents✔ types of carsnumbers of miles per gallon. The continuous quantitative variable is names of residentstypes of cars✔ numbers of miles per gallon.

A veterinarian knows that the supplement glucosamine is beneficial for dogs' joints. He wants to determine if a supplement with both glucosamine and chondroitin would be more beneficial than glucosamine alone for dogs' joint health. The veterinarian asks the owners of dogs with known joint issues if they would be willing to have their dog participate in his study, and 32 owners agree to the study. The veterinarian also knows that breed and age may affect the results of the experiment. Which of the following designs would be most appropriate for this experiment?

Completely randomized design: Randomly assign the treatments to the dogs. -Matched pairs design: Block the dogs based on breed. Then, within each block, pair the dogs based on age. Randomly assign the treatments to each dog in the pairs. Randomized block design: Block the dogs based on breed. Then, randomly assign half of the dogs in each block to receive glucosamine only and the other half to receive glucosamine with chondroitin. Observational study: The veterinarian should randomly select patient records. Then, use the joint health of dogs that use glucosamine only and those that use glucosamine with chondroitin.

A company that makes robotic vacuums claims their newest model of vacuum lasts, on average, 2 hours when starting on a full charge. To investigate this claim, a consumer group purchases a random sample of 5 vacuums of this model. They charge each unit fully and then measure the amount of time each unit runs. They would like to know if there is convincing evidence that the true mean run time differs from 2 hours. The consumer group plans to test the hypotheses = 2 versus < 2, where μ = the true mean run time for all vacuums of this model. The power of this test to reject = 2 when μ = 1.75 is 0.0865 using a significance level of 0.05. Which combination of sample size and significance level would increase the power of this test the most?

A computer company wants to determine the proportion of defective computer chips from a day's production. A quality control specialist takes a random sample of 100 chips from the day's production and determines that there are 12 defective chips. Assuming all conditions are met, he constructs a 95% confidence interval for the true proportion of defective chips from a day's production. What are the calculations for this interval?

A local candidate believes more than half of the constituents in their district would favor them for political office. A random sample of 120 voters was polled, and 65 stated they would likely vote for the candidate. Which hypotheses would test the candidate's claim?

A local school board believes there is a difference in the proportion of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school-aged children that would support starting the school year a week earlier. They survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 38 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 25 respond yes. Let ps= the true proportion of households with school-aged children that would support starting the school year a week early and pw= the true proportion of households without school-aged children that would support starting the school year a week earlier. Which of the following is the correct standardized test statistic and P-value for the hypotheses, ?

A popular restaurant chain will open a new franchise if a study shows that more than 60% of residents in an area would purchase food from the restaurant. An analyst of a particular area randomly selects 500 residents and surveys them about their interest in the restaurant. Of the 500 residents, 320 stated they would purchase food from the restaurant. Which hypotheses test the proportion of residents who would purchase food from the restaurant in this area?

A statistics student wants to survey a high school of 910 students concerning support for increasing the number of student parking spots. The student randomly selects 90 students, and finds that 63 support increasing the number of student parking spots. Assuming the conditions for inference have been met, what is the 95% confidence interval for the true proportion of students who would support the increase in the number of parking spots?

A study found that 15% of teenagers get the recommended 8 to10 hours of sleep each night. A guidance counselor at a large high school takes a random sample of 80 students and asks them if they get 8 to 10 hours of sleep each night of the school week. Of the 80 students, 15 state they get 8-10 hours of sleep each school night. Which hypotheses would test if the proportion of students at this high school is different from the proportion in the study?

A therapist wanted to determine if yoga or meditation is better for relieving stress. The therapist recruited 100 of her high-stress patients. Fifty of them were randomly assigned to take weekly yoga classes, and the other 50 were assigned weekly meditation classes. After one month, 30 of the 50 patients in the yoga group reported less stress, and 35 of the 50 patients in the meditation group reported less stress. Assuming the conditions for inference are met, what is the 95% confidence interval for the difference in proportions of patients experiencing stress relief from the yoga and meditation groups?

Chuck wants to know which brand of tire, A or B, lasts longer on cars. He chooses 32 cars and puts brand A on one side of the car and brand B on the other side. The side that receives brand A is determined by a coin toss. After three months, Chuck measures the amount of tread on all tires to determine if, on average, there is a difference (brand A - brand B) in tread wear. What are the hypotheses Chuck should use?

In a small town of 5,832 people, the mayor wants to determine if there is a difference in the proportion of voters ages 18-30 who would support an increase in the food tax, and the proportion of voters ages 31-40 who would support an increase in the food tax. An assistant to the mayor surveys 85 randomly chosen voters ages 18-30, and finds that 62 support the increase. A random sample of 70 voters ages 31-40 is also surveyed, and 56 support the increase. Assuming the conditions for inference have been met, what is the 99% confidence interval for the difference in proportions of voters who would support the increase in the food tax for the different age groups?

On average, a person's body temperature should be approximately 98.6°F. A doctor would like to test the hypotheses = 98.6 versus 98.6 where μ = the true mean body temperature of all adults. Before conducting the test, the doctor determines that the power of the test to reject the null hypothesis when μ = 98 using α = 0.01 and n = 10 is 0.2474. What combination of sample size and significance level would increase the power of this test the most?

The owner of a popular coffee shop believes that customers who drink coffee are more likely to use their own cup than customers who drink espresso. Customers using their own cups get a 5% discount, which is displayed on the receipt. The owner randomly selects 50 receipts from all coffee purchases and 50 receipts from all espresso purchases. For coffee purchases, 24 receipts showed that the customer used their own cup. For espresso purchases, 18 receipts showed the customer used their own cup.

The owner of a popular coffee shop believes that customers who drink espresso are less likely to use their own cup compared to customers who drink coffee. Customers using their own cups get a 5% discount, which is displayed on the receipt. The owner randomly selects 50 receipts from all espresso purchases and 50 receipts from all coffee purchases. For espresso purchases, 15 receipts showed that the customer used their own cup. For coffee purchases, 24 receipts showed the customer used their own cup. Let pEspresso = the true proportion of customers who drink espresso and use their own cup and pCoffee = the true proportion of customers who drink coffee and use their own cup. Which of the following are the correct hypotheses to test the owner's claim?

The proportion of students at a large high school who live within five miles of the school is p = 0.19. The principal takes a random sample of 17 students from this school. Which is the best description of the shape for the sampling distribution of p?

To estimate the benefits of an SAT prep course, a random sample of 10 students enrolled in the course is selected. For each of these students, their entrance score on the exam taken at the beginning of the course is recorded. Their exit score on the exam they take at the end of the course is recorded as well. The table displays the scores. The mean of the differences is 193 points, and the standard deviation of the differences is 62.73 points. The conditions for inference are met. What is the correct 98% confidence interval for the mean difference (after - before) in score?

A grocery store shopper wants to estimate the mean weight of the eggs in a particular carton of extra-large eggs. She opens the carton of eggs, randomly selects three eggs, and weighs them on a food scale. Are the conditions for constructing a t confidence interval met?

D- No, the 10% condition is not met, the Normal/large sample condition is not met, but the random condition is met

A cell phone provider has 85% of its customers rank their service as "satisfactory." Nico takes a random sample of 75 customers from this cell phone provider. What is the probability that 83% or more of this sample ranks the provider's service as "satisfactory"?

D- 0.686

The distribution of the number of items washed in a standard load of laundry is skewed left with a mean of 41 items and a standard deviation of 7.7 items. What is the probability that 50 randomly selected loads of laundry have a mean of more than 39.5 items?

D- 0.9158

There are 4 blood types, and not all are equally likely to be in blood banks. In a certain blood bank, 49% of donations are Type O blood, 27% of donations are Type A blood, 20% of donations are Type B blood, and 4% of donations are Type AB blood. What is the expected number of donations until the first Type AB donation is received?

D- 25

A conference consists of 5 sessions: A, B, C, D, and E. Here are the costs of the sessions. Session A: $50Session B: $50Session C: $100Session D: $150Session E: $200 Here is a graph of the cost of all 5 sessions. A participant plans to attend 3 sessions. Here is a list of all possible samples of size 3 sessions from this population of 5 sessions: ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, and CDE. Here is a graph displaying the minimum session cost for each possible sample of 3 sessions. The participant chooses 3 sessions at random from the list of all 5 sessions. The result of the random selection is sessions B, D, and E. Here is a graph displaying the distribution of session cost for this sample. Which of the following gives the correct order of the graphs of the population distribution, distribution of a single sample, and sampling distribution, respectively?

D- A, C, B

D- All conditions are met.

The owner of a popular coffee shop believes that customers who drink espresso are less likely to use their own cup compared with customers who drink coffee. Customers using their own cups get a 5% discount, which is displayed on the receipt. The owner randomly selects 50 receipts from all espresso purchases and 50 receipts from all coffee purchases. For espresso purchases, 15 receipts showed that the customer used their own cup. For coffee purchases, 24 receipts showed the customer used their own cup. Let pEspresso= the true proportion of customers who drink espresso and use their own cup and pCoffee= the true proportion of customers who drink coffee and use their own cup. Which of the following is a correct statement about the conditions for this test?

D- All conditions for inference are met.

D- Based on the sample mean, the owner concludes that the mean weight of all of the bunches of bananas is not less than 3.54 pounds when the true mean weight is actually less than 3.54 pounds.

A school administrator claims that 85% of the students at his large school plan to attend college after graduation. The statistics teacher selects a random sample of 50 students from this school and finds that 76% of them plan to attend college after graduation. The administrator would like to know if the data provide convincing evidence that the true proportion of all students from this school who plan to attend college after graduation is less than 85%. The standardized test statistic is z = -1.78 and the P-value is 0.0375. What conclusion should be made using the = 0.01 significance level?

D- Because the P-value is greater than = 0.01, there is not convincing evidence that the true proportion of all students from this school who plan to attend college after graduation is less than 85%.

D- Because the P-value is greater than = 0.05, there is not convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old.

A local pet store claims that its puppy training program increases the length of time puppies sit still when commanded to do so. A patron wonders if this claim is true. The patron asks to see the sitting times of 14 randomly chosen puppies. The differences (pretraining - post-training) in times for each puppy are listed. A positive value indicates the puppy's sitting time decreased after the training. -1.2, 3.8, 0.5, 2.1, -0.4, 1.0, 2.5, -5.7, 3.0, 1.0, 2.3, -0.8, 0, 0.4 Assuming the conditions for inference have been met, is there evidence of an increase in sitting times for puppies like the ones in the study? Use a significance level of α = 0.05.

D- Because the P-value is greater than α, there is not sufficient evidence of an increase, on average, in sitting times for puppies like the ones in the study.

The owner of a fitness watch would like to determine if the mean number of steps he takes per day differs from the recommended 10,000 steps per day, using α = 0.05. He selects a random sample of 50 days with the intention of testing the hypotheses = 10,000 steps versus steps where μ = the true mean number of steps taken per day. Rather than test these hypotheses, he computes a 95% confidence interval for the true mean number of steps he takes per day. The 95% confidence interval is (8,250, 10,700). Based on the confidence interval, what conclusion can be made?

D- Fail to reject H0. Since 10,000 does not fall outside the 95% confidence interval, there is not convincing evidence that the true mean number of steps he takes per day differs from 10,000 steps.

On the SAT exam, a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the time allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses H0: μ = 25 versus Ha: μ < 25, where μ = the true mean amount of time needed for students of this school to complete this portion of the exam. The conditions for inference are met. The test statistic is t = -1.85 and the P-value is between 0.025 and 0.05. What conclusion should be made at the significance level, ?

D- Fail to reject H0. There is not convincing evidence that the true mean amount of time needed for students of this school to complete this portion of the exam is less than 25 minutes.

A company that makes robotic vacuums claims that their newest model of vacuum lasts, on average, two hours when starting on a full charge. To investigate this claim, a consumer group purchases a random sample of five vacuums of this model. They charge each unit fully and then measure the amount of time each unit runs. Here are the data (in hours): 2.2, 1.85, 2.15, 1.95, and 1.90. They would like to know if the data provide convincing evidence that the true mean run time differs from two hours. The consumer group plans to test the hypotheses H0: μ = 2 versus Ha: μ ≠ 2, where μ = the true mean run time for all vacuums of this model. The conditions for inference are met. The test statistic is t = 0.14 and the P-value is greater than 0.25. What conclusion should be made at the significance level, ?

D- Fail to reject H0. There is not convincing evidence that the true mean run time for all vacuums of this model is different from 2 hours.

D- H0: p = 0.1 versus Ha: p ≠ 0.1, where p = the proportion of players who win this game.

A school nurse would like to estimate the true mean amount of sleep that students at the high school get per night. To do so, she selects a random sample of 30 students and determines that the 90% confidence interval for the true mean number of hours of sleep that high school students get per night to be 6.5 to 7.5 hours. Which of these statements is a correct interpretation of the confidence level?

D- If many random samples of size 30 are selected from the population of all students, about 90% of the intervals would capture the true mean number of hours of sleep that students of this high school get per night.

A farmer would like to estimate the mean amount of corn produced on the east side of his farm versus the west side of his farm where the soil is different. To do so, he selects a random sample of 20 of the 400 plots of land on the east side of the farm and randomly selects 10 plots of land from the 150 plots on the west side of his farm and measures the amount of corn produced for each plot. Are the conditions for inference met?

D- No, the Normal/large sample condition is not met for both samples.

A veteran math teacher at a large high school claims that 93% of their students pass the state's final exam. A random sample of 120 of the teacher's students was chosen, and 108 passed the state's final exam. Let = the proportion of the random sample who passed the state's final exam. The probability that 90% or fewer of this teacher's students passed the state's final exam is 0.096. Does this result provide convincing evidence against the teacher's claim?

D- No, the difference between the sample result and what is expected is not extreme enough. The probability of it occurring by chance alone is not unlikely.

An air-conditioning repair technician claims to complete 67% of repairs in under an hour. A random sample of 31 repairs was chosen, and 22 of those were completed in under an hour. Let = the proportion of the random sample that were completed in under an hour. The probability that 71% or more of this technician's repairs were completed in under an hour is 0.317. Does this result provide convincing evidence against the technician's claim?

D- No, the difference between the sample result and what is expected is not extreme enough. The probability of it occurring by chance alone is not unlikely.

Ten membersThree juniors and seven seniors from the science club qualify for a national competition, but only five people per school can attend the event. The coach decides to put the 10 members' names on identical slips of paper, put the slips in a hat, and pull out five names, one at a time. Those five students will go to the national competition. Let X represent the number of juniors selected to attend the competition. Have the conditions for a binomial setting been met for this scenario?

D- No, the names were pulled and not replaced in the hat, so the independence condition is not met.

The distribution of professional baseball player salaries has a mean of $3.2 million. An analyst believes that the mean salary for teams on the East Coast is different. The analyst randomly selects 30 baseball players from teams on the East Coast and records their annual salaries. The mean salary for the players in the sample is $3.9 million with a standard deviation of $2.1 million. The analyst conducts a one-sample t-test for and calculates a P-value of 0.078. At the level, what is the correct conclusion for this test?

D- The analyst should fail to reject the null hypothesis since 0.078 > 0.05. There is not convincing evidence that the mean salary of the baseball players on the East Coast is different from $3.2 million.

On a college entrance exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the time allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The counselor would like to know if there is convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses = 25 versus < 25, where μ = the true mean amount of time needed by students at this school to complete this portion of the exam. The power of this test to reject the null hypothesis when μ = 24.5 is 0.735. What could the counselor have done to increase the power of this test?

D- The counselor could have used a sample size of 40 students.

At a university, 34% of undergraduate students love spicy food, while 45% of graduate students love spicy food. Let and be the sample proportions of undergraduate and graduate students at this university, respectively, who love spicy food. Suppose 35 undergraduate students and 28 graduate students from this university are selected at random and asked if they love spicy food. Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of ?

D- The difference (undergraduate students - graduate students) in the sample proportions of those who love spicy food typically varies about 0.123 from the true difference in proportions.

The distribution of the heights of five-year-old children has a mean of 42.5 inches. A pediatrician believes the five-year-old children in a city are taller on average. The pediatrician selects a random sample of 30 five-year-old children and measures their heights. The mean height of the sample is 43.6 inches with a standard deviation of 3.6 inches. The pediatrician conducts a one-sample t-test for and calculates a P-value of 0.052. At the level, what is the correct conclusion for this test?

D- The pediatrician should fail to reject the null hypothesis since 0.052 > 0.01. There is not convincing evidence that the mean height of five-year old children in this city is greater than 42.5 inches.

D- There is not convincing evidence that the true proportion of college soccer players who have had at least one sprained ankle is greater than 75%.

D- Yes, all conditions for inference are met.

The mean price of houses in the US is $383,500. A real estate agent believes the mean price of houses in a local neighborhood is less than the national mean. The agent takes a random sample of 30 houses and finds the mean price to be $295,089 with a standard deviation of $156,321. Do the data provide convincing evidence at the level that the mean price of the houses in the area is less than $383,500? Are the conditions for inference met?

D- Yes, all conditions for inference are met.

A manufacturing company packages shipments in either large or small boxes. A random sample of 40 shipments that are packaged in large boxes is found to have a mean of 15 pounds and a standard deviation of 2.8 pounds. A separate random sample of 50 shipments that are packaged in small boxes is found to have a mean of 10 pounds and a standard deviation of 1.5 pounds. The manager would like to know if the data provide convincing evidence that the true mean weight of all shipments that are packaged in small boxes is less than the true mean weight of all shipments that are packaged in large boxes. Let μL = the true mean weight of all shipments that are packaged in large boxes and μS = the true mean weight of all shipments that are packaged in small boxes. Are the conditions for inference met?

D- Yes, all of the conditions for inference have been met.

Can a person train to become better at holding their breath? An experiment was designed to find out. Twelve volunteers were randomly assigned to 1 of 2 groups. The 6 volunteers assigned to group 1 were given breath-holding exercises to perform for 2 weeks. The other group was not given any information about the experiment. At the end of the 2 weeks, all 12 volunteers were individually tested to determine how long they could hold their breath. Here are the data (in seconds). Group 1: 90, 88, 70, 110, 75, 105 Group 2: 40, 48, 35, 50, 55, 62 The researcher would like to determine if these data provide convincing evidence that the true mean amount of time volunteers who were given training held their breath is greater than the volunteers without training. Let μ1 = the true mean amount of time that volunteers who were given training held their breath and μS = the true mean amount of time that volunteers without training held their breath. Are the conditions for inference met?

D- Yes, all of the conditions for inference have been met.

Timmy could follow two main routes to get to school. Timmy believes that route 1 is faster than route 2. To investigate, he decides to keep track for the next 4 weeks. Each morning, he flips a coin to determine which route he takes. Of the 20 school days, 12 days were randomly assigned to route 1, and 8 days were randomly assigned to route 2. The mean travel time for days assigned to route 1 was 20 minutes with a standard deviation of 3 minutes. The mean travel time for the days assigned to route 2 was 22 minutes with a standard deviation of 2 minutes. Timmy would like to know if the data provide convincing evidence of a difference in travel time for the 2 routes. Let μ1 = the true mean travel time to school along route 1 and μ2 = the true mean travel time to school along route 2. Dotplots of the distribution of travel time for route 1 and route 2 show no strong skewness or outliers. Are the conditions for inference met?

D- Yes, all of the conditions for inference have been met.

A chiropractor would like to estimate the mean length of time needed for patients to recover from straining a back muscle. He selects a random sample of 15 patients from the large number of patients with this type of injury. He records the length of time it takes for each of these patients to fully recover. The distribution of recovery times for these patients is unimodal, fairly symmetric, and has no outliers. Are the conditions for constructing a t confidence interval met?