ap stat exam prep
The number of tickets purchased by a customer for a musical performance at a certain concert hall can be considered a random variable. The table below shows the relative frequency distribution for the number of tickets purchased by a customer. Suppose each ticket for a certain musical performance cost $12. Based on the distribution shown, what is the mean cost per customer for the performance?
$29.40
Ecologists wanted to estimate the mean biomass (amount of vegetation) of a certain forested region. The ecologists divided the region into plots measuring 1 square meter each, and they selected a random sample of 9 plots. The mean biomass of the 9 plots was 4.3 kilograms per square meter ( kg/m2 ) and the standard deviation was 1.5 kg/m2 . Assuming all conditions for inference are met, which of the following is a 95 percent confidence interval for the population mean biomass, in kg/m2 ?
4.3±2.306(1.53)
Based on the histogram, which of the following is closest to the interquartile range, in inches, of the distribution?
5
The distribution of assembly times required to assemble a certain smartphone is approximately normal with mean 4.6 minutes and standard deviation 0.6 minute. Of the following, which is closest to the percentage of assembly times between 4 minutes and 5 minutes?
59%
A polling agency conducted a survey about social media in which each person in random samples of 1,0001,000 men and 1,0001,000 women was asked what factor he or she considers to be the most important when deciding whether to connect on social media with another person. The responses are shown in the table.What is the contribution to the chi-square test statistic for men who selected business networking as the most important factor?
7.5
The normal curve shown represents the sampling distribution of a sample mean for sample size n = 25, selected at random from a population with standard deviation σx��. Which of the following is the best estimate of the standard deviation of the population, σx��?
75
The distribution of weights of female college cross-country runners is approximately normal with mean 122 pounds and standard deviation 8 pounds. Which of the following is closest to the percent of the runners who weigh between 114 pounds and 138 pounds?
82%
A survey of a random sample of 210 male teens and 228 female teens, ages 13 years to 17 years, found that 122 of the male teens and 160 of the female teens brush their teeth at least twice a day. If there is no difference between the proportions in the population of all male and female teens ages 13 years to 17 years who brush their teeth at least twice a day, approximately how many males and females in the sample would be expected to brush their teeth at least twice a day?
135 males and 147 females
A sleep time of 15.9 hours per day for a newborn baby is at the 10th percentile of the distribution of sleep times for all newborn babies. Assuming the distribution is normal with standard deviation 0.5 hour, approximately what is the mean sleep time, in hours per day, for newborn babies?
16.5
A consumer group wanted to investigate the relationship between the number of items purchased at a single visit to the local grocery store and the total cost of the items purchased. The group obtained a random sample of 11 receipts from the store and recorded the total number of items and the total cost from each receipt. The computer output of an analysis of total cost versus number of items purchased is shown in the table. Assume all conditions for inference were met. Based on the results shown in the table, which of the following is a 95 percent confidence interval for the average change in total cost for each increase of 1 item purchased?
2.784 ± 2.262(0.2265)
At a certain store, the distribution of weights of cartons of large eggs is approximately normal with mean 26 ounces (oz). Based on the distribution, which of the following intervals will contain the greatest proportion of cartons of large eggs at the store?
24 oz to 28 oz
For a recent season in college football, the total number of rushing yards for that season is recorded for each running back. The mean number of rushing yards for the running backs that season is 790 yards. One running back had 1,637 rushing yards for the season, which is 2.42 standard deviations above the mean number of rushing yards. What is the standard deviation of the number of rushing yards for the running backs that season?
350
A scientist recorded the duration of the eruptions of the Old Faithful geyser in Yellowstone National Park that occurred during a one-month time period. The histogram below shows the distribution of the duration, in seconds, of the eruptions. Based on the histogram, which of the following is the best description of the distribution?
The distribution displays two clusters, with one cluster centered at about 125 seconds and the other centered at about 260 seconds, and has a range of at most 250 seconds.
A manufacturer of cell phone batteries claims that the average number of recharge cycles for its batteries is 400. A consumer group will obtain a random sample of 100 of the manufacturer's batteries and will calculate the mean number of recharge cycles. Which of the following statements is justified by the central limit theorem?
The distribution of the sample means of the number of recharge cycles is approximately normal because the sample size of 100 is greater than 30.
Based on records kept at a gas station, the distribution of gallons of gas purchased by customers is skewed to the right with mean 10 gallons and standard deviation 4 gallons. A random sample of 64 customer receipts was selected, and the sample mean number of gallons was recorded. Suppose the process of selecting a random sample of 64 receipts and recording the sample mean number of gallons was repeated for a total of 100 samples. Which of the following is the best description of a dotplot created from the 100 sample means?
The dotplot is approximately normal with mean 10 gallons and standard deviation 0.5 gallon.
n a certain computer card game, the player is awarded 5 points for each card that is moved to a correct position. The player is penalized 10 points for each minute the game is played. Let the random variable X represent the number of cards moved to a correct position, and let the random variable Y represent the number of minutes the game is played. The means and standard deviations of the random variables for a particular player are shown in the table below. Assume that X and Y are independent. What are the expected value and the standard deviation of the points per game for the player?
The expected value is -6.5, and the standard deviation is 65.4.
An agriculturalist working with Australian pine trees wanted to investigate the relationship between the age and the height of the Australian pine. A random sample of Australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. Based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the Australian pine based on the age, in years, of the tree. predicted height = 0.29 + 0.48(age) Which of the following is the best interpretation of the slope of the regression line?
The height increases, on average, by 0.48 meter each year.
A 99 percent one-sample z-interval for a proportion will be created from the point estimate obtained from each of two random samples selected from the same population: sample R and sample S. Let R represent a random sample of size 1,000, and let S represent a random sample of size 4,000. If the point estimate obtained from R is equal to the point estimate obtained from S, which of the following must be true about the respective margins of error constructed from those samples?
The margin of error for R will be 2 times the margin of error for S.
In a physics experiment, two different methods were used to measure the angle of deflection when a subatomic particle collides with a certain material. Ten specimens of the material were used to compare the two methods. For each specimen, the angle of deflection was measured using both methods. For each specimen, the method used first was determined by the flip of a fair coin. The difference between the measured angles was calculated for each specimen. A test of the hypothesis that the population mean difference is zero had a p-value of 0.082. The hypothesis test described had three components: the number of specimens, the sample standard deviation of the differences, and the magnitude of the sample mean difference. Compared to the test described, which of the following would have resulted in a smaller p-value?
The number of specimens remained the same, but the magnitude of the sample mean difference was larger and the sample standard deviation of the difference was smaller.
A two-sided t-test for a population mean is conducted of the null hypothesis H0 : μ = 100. If a 90 percent t-interval constructed from the same sample data contains the value of 100, which of the following can be concluded about the test at a significance level of a = 0.10 ?
The p-value is greater than 0.10, and H0 should not be rejected.
A police officer uses a motion detector to indicate whether a car is traveling faster than the speed limit (speeding). A speeding ticket will be issued to the driver of the car if the officer believes the driver is speeding, as indicated by the detector. The situation is similar to using a null and an alternative hypothesis to decide whether to issue a ticket. The hypotheses can be stated as follows. H0 : The driver is not speeding. Ha : The driver is speeding. Which of the following best describes the power of the test?
The probability of issuing a ticket to a driver who is speeding
The height and age of each child in a random sample of children was recorded. The value of the correlation coefficient between height and age for the children in the sample was 0.80.8. Based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?
The proportion of the variation in height that is explained by a regression on age is 0.640.64.
Grain moisture is a characteristic of grain that affects the price paid for the grain. A random sample of 28 loads of corn was evaluated for moisture as a percent of the total weight. A different random sample of 28 loads of soybeans was also evaluated for moisture. The data are displayed in the dotplots below. Based on the dotplots, which of the following is greater for the percent moisture of corn than for the percent moisture of soybeans?
The range
According to a report for veterinarians in the United States, 36.536.5 percent of households in the United States own dogs and 30.430.4 percent of households in the United States own cats. If one household in the United States is selected at random, what is the probability that the selected household will own a dog or a cat?
not enough info
A veterinarian collected data on the weights of 1,000 cats and dogs treated at a veterinary clinic. The weight of each animal was classified as either healthy, underweight, or overweight. The data are summarized in the table. Based on the data in the table, which of the following is the most appropriate type of graph to visually show whether a relationship exists between the type of animal and the weight classification?
segmented bar chart
A company that makes fleece clothing uses fleece produced from two farms, Northern Farm and Western Farm. Let the random variable X represent the weight of fleece produced by a sheep from Northern Farm. The distribution of X has mean 14.114.1 pounds and standard deviation 1.31.3 pounds. Let the random variable Y represent the weight of fleece produced by a sheep from Western Farm. The distribution of Y has mean 6.76.7 pounds and standard deviation 0.50.5 pound. Assume X and Y are independent. Let W equal the total weight of fleece from 10 randomly selected sheep from Northern Farm and 15 randomly selected sheep from Western Farm. Which of the following is the standard deviation, in pounds, of W ?
sqroot 10(1.3)^2+ 15(.5)^2
At a local ice-cream store, 210 people were surveyed on whether they preferred eating ice cream from a cone or a cup. Of the 210 people surveyed, 70 were adults and 140 were children. Of the responses, 150 indicated the cone as the preferred method of eating ice cream. For those surveyed, there was no association between age and preferred method of eating ice cream. Which of the following tables shows the distribution of responses?
that
Data were collected on the fiber diameter and the fleece weight of wool taken from a sample of 2020 sheep. The data are shown in the following graphs. Graph 11 is a scatterplot of fleece weight versus fiber diameter with the respective least-squares regression line shown. Graph 22 is the associated plot of the residuals versus the predicted values.
C
In 1960 sociologists studied a random sample of 1,018 families that consisted of a husband, a wife, and at least one child. Of those families, 5.8 percent reported that the wife was the primary wage earner of the family. In 2011 the study was replicated with a random sample of 1,013 families that consisted of a husband, a wife, and at least one child. Of those families, 22.3 percent reported that the wife was the primary wage earner of the family. Which of the following represents a 99 percent confidence interval for the difference between the proportions of families that consisted of a husband, a wife, and at least one child from 1960 to 2011 that would have reported the wife as the primary wage earner?
(0.223−0.058)±2.576(0.223)(0.777)1,013+(0.058)(0.942)1,018−−−−−−−−−−−−−−−−−−−√
Measuring the height of a tree is usually more difficult than measuring the diameter of the tree. Therefore, many researchers use regression models to predict the height of a tree from its diameter measured at 44 feet 66 inches from the ground. The following computer output shows the results of a linear regression based on the heights, in feet, and the diameters, in inches, recorded from 3131 felled trees. EstimateStd Errort� valuePr(>|t|>|�|)Intercept62.03162.0314.3834.38314.1514.150.00000.0000Diameter1.0541.0540.3220.3223.273.270.00280.0028 Which of the following is a 9595 percent confidence interval for the slope of the population regression line?
(0.396,1.712)
A medical center conducted a study to investigate cholesterol levels in people who have had heart attacks. A random sample of 16 people was obtained from the names of all patients of the medical center who had a heart attack in the previous year. Of the people in the sample, the mean cholesterol level was 264.70 milligrams per deciliter (mg/dL) with standard deviation 42.12 mg/dL42.12 mg/dL. Assuming all conditions for inference were met, which of the following is a 90 percent confidence interval for the mean cholesterol level, in mg/dLmg/dL, of all patients of the medical center who had a heart attack in the previous year?
(246.24, 283.16)
Research indicates that the standard deviation of typical human body temperature is 0.4 degree Celsius (C). Which of the following represents the standard deviation of typical human body temperature in degrees Fahrenheit (F), where F=95C+32�=95�+32?
(9/5)(.4)
.The marketing director for an ice cream company investigated whether there was a difference in preference for two new ice cream flavors—cotton candy and mango. Each participant from a large group of people was randomly assigned to taste one of the two flavors. After tasting, each person rated the flavor on a numerical scale from 11 to 55, where 11 represented strongly dislike and 55 represented strongly like. A two-sample t�-interval for a difference between means (cotton candy minus mango) was constructed. Based on the interval, there was convincing statistical evidence of a difference in population mean flavor ratings, with mango having the greater sample mean rating. Which of the following could be the constructed interval?
(−2.1,−1.3)
die used in a certain board game has eight faces, of which 33 are red, 33 are yellow, and 22 are blue. Each face is equally likely to land faceup when the die is tossed. In the game, a player tosses the die until blue lands faceup, and the number of tosses before blue lands faceup is counted. For example, a player who tosses the sequence shown in the following table has tossed the die 33 times before blue lands faceup. Toss number11223344Face coloryellowyellowredblue What is the probability that a player will toss the die at least 22 times before blue lands faceup?
.5625
The distribution of number of hours worked by volunteers last year at a large hospital is approximately normal with mean 8080 and standard deviation 77. Volunteers in the top 2020 percent of hours worked will receive a certificate of merit. If a volunteer from last year is selected at random, which of the following is closest to the probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 9090 ?
0.134
To investigate the relationship between age and preference for two mayoral candidates in an upcoming election, a random sample of city residents was surveyed. The residents were asked which candidate they preferred, and each resident was classified into one of three age-groups. The test statistic for the appropriate hypothesis test was 3.7408. Approximately what is the probability that the observed responses would be as far or farther from the expected responses if there is no association between age-group and preference?
0.1541
Data were collected from a longitudinal study designed to investigate the relationship between blood sugar levels and brain shrinkage. The results of an analysis of the data for 22 observations are shown in the table below. Which of the following represents a 98 percent confidence interval for the slope of the least-squares regression line for brain shrinkage on blood sugar levels? Assume the conditions for inference are met.
0.161 ± 2.528(0.073)
A tropical storm is classified as major if it has sustained winds greater than 110 miles per hour. Based on data from the past two decades, a meteorologist estimated the following percentages about future storms. 20% of all tropical storms will originate in the Atlantic Ocean, of which 20% will be classified as major. 30% of all tropical storms will originate in the eastern Pacific Ocean, of which 15% will be classified as major. 50% of all tropical storms will originate in the western Pacific Ocean, of which 25% will be classified as major. Based on the meteorologist's estimates, approximately what is the probability that a future tropical storm will originate in the Pacific Ocean and be classified as major?
0.170
An international polling agency estimates that 36 percent of adults from Country X were first married between the ages of 18 and 32, and 26 percent of adults from Country Y were first married between the ages of 18 and 32. Based on the estimates, which of the following is closest to the probability that the difference in proportions between a random sample of 60 adults from Country X and a random sample of 50 adults from Country Y (Country X minus Country Y) who were first married between the ages of 18 and 32 is greater than 0.15 ?
0.2843
Scientists working for a water district measure the water level in a lake each day. The daily water level in the lake varies due to weather conditions and other factors. The daily water level has a distribution that is approximately normal with mean water level of 84.07 feet. The probability that the daily water level in the lake is at least 100 feet is 0.064. Which of the following is closest to the probability that on a randomly selected day the water level in the lake will be at least 90 feet?
0.29
Sean and Evan are college roommates who have part-time jobs as servers in restaurants. The distribution of Sean's weekly income is approximately normal with mean $225$225 and standard deviation $25$25. The distribution of Evan's weekly income is approximately normal with mean $240$240 and standard deviation $15$15. Assuming their weekly incomes are independent of each other, which of the following is closest to the probability that Sean will have a greater income than Evan in a randomly selected week?
0.303
Based on his past record, Luke, an archer for a college archery team, has a probability of 0.90 of hitting the inner ring of the target with a shot of the arrow. Assume that in one practice Luke will attempt 5 shots of the arrow and that each shot is independent from the others. Let the random variable X represent the number of times he hits the inner ring of the target in 5 attempts. The probability distribution of X is given in the table. What is the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X ?
0.40951
A survey of a random sample of 1,045 young adults found that 60 percent do not have a landline telephone number. A hypothesis test will be used to determine whether the data provide convincing statistical evidence that more than 50 percent of all young adults do not have a landline telephone number. Which of the following is the test statistic for the appropriate test?
0.60−0.50/ √(0.50)(0.50)/1,045
Based on the responses, which of the following is a 95 percent confidence interval for the proportion of all city residents who would respond very supportive or somewhat supportive of the proposal?
0.71 ± 0.028
Suppose a certain scale is not calibrated correctly, and as a result, the mass of any object is displayed as 0.75 kilogram less than its actual mass. What is the correlation between the actual masses of a set of objects and the respective masses of the same set of objects displayed by the scale?
1
A large store has a customer service department where customers can go to ask for help with store-related issues. According to store records, approximately ¼ of all customers who go to the service department ask for help finding an item. Assume the reason each customer goes to the service department is independent from customer to customer. Based on the approximation, what is the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item?
1-(3/4)^4
A grocery store receives deliveries of corn from two farms, one in Iowa and the other in Ohio. Both farms produce ears of corn with mean weight 1.261.26 pounds. The standard deviation of the weights of the ears of corn from the farm in Ohio is 0.010.01 pound greater than that from the farm in Iowa. A randomly selected ear of corn from the farm in Iowa weighed 1.391.39 pounds, which has a standardized score of 1.6451.645 for the distribution of weights for the Iowa corn. If an ear of corn from the farm in Ohio weighs 1.391.39 pounds, how many standard deviations from the mean is the weight with respect to the Ohio distribution?
1.46 standard deviations above the mean
Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is approximately normal with mean 100100 years and standard deviation 1515 years. Based on the estimate, which of the following is closest to the age of a Galápagos Islands giant tortoise at the 90th90th percentile of the distribution?
120
A fitness center offers a one-month program designed to reduce body fat through exercise. The table shows the body fat percentage before and after completing the program for 10 randomly selected participants. The director of the program wants to investigate whether knowing the body fat percentage before beginning the program can help to predict body fat percentage for someone who completes the program. Which of the following procedures is the most appropriate for such an investigation?
A linear regression t-test for slope
Researchers used two footballs of the same size to examine the effect of helium on kicking distance. One football was filled with air, and the other was filled with helium. Eleven people participated in the study. Each person kicked the football filled with air and the football filled with helium, and the kicking distances, in yards, were recorded. The football that was kicked first was determined by the flip of a fair coin, and the people did not know which football was filled with air and which was filled with helium. What type of study was conducted by the researchers and, of the following, which is the appropriate t-interval for inference?
A matched-pairs design and a t-interval for a mean difference
A study will be conducted to examine a new medicine intended to reduce high blood pressure in adult men who have high blood pressure. As part of the study, a random sample of 40 men with high blood pressure will have their blood pressure measured, and then they will take the new medicine every day for one month. At the end of the month, their blood pressure will be measured again. Of the following, which is the best procedure to investigate whether there will be convincing statistical evidence of a change, on average, in blood pressure for men with high blood pressure who take the new medicine?
A matched-pairs t-test for a mean difference
Two high schools have a similar number of students and parking lots of similar size. The safety officers at both schools want to investigate whether there is an average difference in the number of cars parked per day in the student parking lots for the school year. A random sample of 1515 school days will be selected. For each selected day, the number of cars parked in the student parking lots will be counted at both schools and the difference will be recorded. Assuming all conditions for inference are met, which of the following is the appropriate test for the investigation?
A matched-pairs t�-test for a mean difference D
A study was conducted to evaluate the impact of taking a nutritional supplement on a person's reaction time. One hundred volunteers were placed into one of three groups according to their athletic ability: low, moderate, or high. Participants in each group were randomly assigned to take either the nutritional supplement or a placebo for six weeks. At the end of the six weeks, participants were given a coordination task. The reaction time in completing the task was recorded for each participant. The study compared the reaction times between those taking the supplement and those taking the placebo within each athletic ability level. Which of the following is the best description of the study?
A randomized block design
Researchers conducted a telephone survey of 427 adults living in a large city. The adults were asked whether they planned to purchase a smart watch in the next year. The table shows the responses categorized by the region of the city in which the residents live. Which of the following graphical displays is most appropriate for comparing the proportions of those surveyed who plan to purchase a smart watch within the four regions?
A segmented bar chart
A pharmaceutical company manufactures medicine to reduce pain caused by migraine headaches. The company is investigating whether a new medicine is more effective in reducing pain than the current medicine. A random sample of 500 participants who experience migraines was selected, and the participants were randomly assigned to one of two groups of equal size. The first group received the current medicine and the second group received the new medicine. When a participant experienced a migraine, he or she was instructed to take the medicine and, 15 minutes after taking the medicine, to rate the pain relief on a scale from 1 to 10, with 1 being no relief to 10 being complete relief. At the end of six months, the average pain relief for each participant was calculated. Which of the following is the best description of the study?
An experiment using a completely randomized design
Measurements of water quality were taken from a river downstream from an abandoned chemical dumpsite. Concentrations of a certain chemical were obtained from 9 measurements taken at the surface of the water, 9 measurements taken at mid-depth of the water, and 9 measurements taken at the bottom of the water. What type of study was conducted, and what is the response variable of the study?
An observational study was conducted, and the response variable is the concentration of the chemical.
A polling agency reported that 66 percent of adults living in the United States were satisfied with their health care plans. The estimate was taken from a random sample of 1,542 adults living in the United States, and the 95 percent confidence interval for the population proportion was calculated as (0.636, 0.684). Which of the following statements is a correct interpretation of the 95 percent confidence level?
Approximately 95% of random samples of the same size from the population will result in a confidence interval that includes the proportion of all adults living in the United States who are satisfied with their health care plans.
At a certain restaurant, the distribution of wait times between ordering a meal and receiving the meal has mean 11.411.4 minutes and standard deviation 2.62.6 minutes. The restaurant manager wants to find the probability that the mean wait time will be greater than 12.012.0 minutes for a random sample of 8484 customers. Assuming the wait times among customers are independent, which of the following describes the sampling distribution of the sample mean wait time for random samples of size 8484 ?
Approximately normal with mean 11.411.4 minutes and standard deviation 2.684√2.684 minute
A program that was intended to cure a person's fear of spiders was offered at a local zoo. Volunteers with a fear of spiders participated in the program, which included holding a spider for 15 minutes. One month after they completed the program, the participants were contacted and surveyed about the program. Over 90 percent of the participants claimed they were cured of their fear of spiders. Based on the description of the program, which of the following statements is true?
Because the participants were self-selected, a person's desire to be cured could be a confounding variable.
Researchers investigated whether a new process for producing yarn could reduce the mean amount of volatile organic compounds (VOCs) emitted by carpet. From random samples of carpets, the researchers found the mean reduction of VOCs emitted by carpets made with yarn produced by the new process compared with that of carpets made with yarn produced by the traditional process was 13 parts per million (ppm). All conditions for inference were met, and the p-value for the appropriate hypothesis test was 0.095. Which of the following statements is the best interpretation of the p-value?
If the null hypothesis is true, the probability of observing a mean reduction of at least 13 ppm is 0.095.
In a standard golf tournament, golfers play 18 holes of golf on each of 4 consecutive days. For each hole, golfers keep track of the number of times they hit the ball (strokes) before the ball goes into the cup. A golfer's score for the tournament is the total number of strokes needed to complete the tournament. The boxplots below summarize the scores for golfers who competed in tournament 1 and golfers who competed in tournament 2. Based on the boxplots, which of the following statements must be true?
In both tournaments, at least half the golfers completed the tournament with a score less than 288.
A recent survey estimated that 19 percent of all people living in a certain region regularly use sunscreen when going outdoors. The margin of error for the estimate was 1 percentage point. Based on the estimate and the margin of error, which of the following is an appropriate conclusion?
It is plausible that the percent of all people living in the region who regularly use sunscreen is 18.5%.
A survey was conducted in a large city to investigate public opinion on banning the use of trans fats in restaurant cooking. A random sample of 230 city residents with school-age children was selected, and another random sample of 341 city residents without school-age children was also selected. Of those with school-age children, 94 opposed the banning of trans fats, and of those without school-age children, 147 opposed the banning of trans fats. An appropriate hypothesis test was conducted to investigate whether there was a difference between the two groups of residents in their opposition to the banning of trans fats. Is there convincing statistical evidence of a difference between the two population proportions at the significance level of 0.05 ?
No, because the probability of observing a difference at least as large as the sample difference, if the two population proportions are the same, is greater than 0.05.
A research organization reported that 4141 percent of adults who were asked to describe their day responded that they were having a good day rather than a typical day or a bad day. To investigate whether the percent would be different for high school students, 600600 high school students were randomly selected. When asked to describe their day, 245245 students reported that they were having a good day rather than a typical day or a bad day. Do the data provide convincing statistical evidence that the proportion of all high school students who would respond that they were having a good day is different from 0.410.41 ?
No, because the p�-value is greater than any reasonable significance level.
A state study on labor reported that one-third of full-time teachers in the state also worked part time at another job. For those teachers, the average number of hours worked per week at the part-time job was 1313. After an increase in state teacher salaries, a random sample of 400400 teachers who worked part time at another job was selected. The average number of hours worked per week at the part-time job for the teachers in the sample was 12.512.5 with standard deviation 6.56.5 hours. Is there convincing statistical evidence, at the level of α=0.05�=0.05, that the average number of hours worked per week at part-time jobs decreased after the salary increase?\
No. The p�-value of the appropriate test is greater than 0.05 \
The values 6060, 6262, and 8484 were common to both samples. The three values are identified as outliers with respect to the age-group 2020 years to 3030 years because they are either 1.51.5 times the interquartile range (IQR)(IQR) greater than the upper quartile or 1.51.5 times the IQRIQR less than the lower quartile. Using the same method for identifying outliers, which of the three values are identified as outliers for the age-group 4040 years to 5050 years?
Only 6060 is identified as an outlier.
Events D and E are independent, with P( D ) = 0.6 and P( D and E ) = 0.18. Which of the following is true?
P( D or E ) = 0.72
A program exists to encourage more middle school students to major in math and science when they go to college. The organizers of the program want to estimate the proportion of students who, after completing the program, go on to major in math or science in college. The organizers will select a sample of students from a list of all students who completed the program. Which of the following sampling methods describes a stratified random sample?
Randomly select 25 names from the female students on the list and randomly select 25 names from the male students on the list.
As part of a demographic study, a college administrator needed to survey a sample of students from the college. From each major offered at the college, the administrator randomly selected 55 percent of the students with that major to participate in the survey. Which of the following is the best description of the type of sample selected by the administrator? A
Stratified random sample
Researchers working for a certain airline are investigating the weight of carry-on bags. The researchers will use the mean weight of a random sample of 800 carry-on bags to estimate the mean weight of all carry-on bags for the airline. Which of the following best describes the effect on the bias and the variance of the estimator if the researchers increase the sample size to 1,300 ?
The bias will remain the same and the variance will decrease.
An airline recorded the number of on-time arrivals for a sample of 100 flights each day. The boxplot below summarizes the recorded data for one year. Based on the boxplot, which of the following statements must be true?
The difference between the median and the lower quartile for the number of on-time arrivals is less than 2.
A biologist studying trees constructed the confidence interval (0.14,0.20)(0.14,0.20) to estimate the proportion of trees in a large forest that are dead but still standing. Using the same confidence level, the interval was later revised because the sample proportion had been miscalculated. The correct sample proportion was 0.270.27. Which of the following statements about the revised interval based on the correct sample proportion is true?
The revised interval is wider than the original interval because the correct sample proportion is closer to 0.50.5 than the miscalculated proportion is.
Staff members of a high school newspaper want to obtain an estimate of the average number of years teachers in the state have been teaching. At an educational conference attended by many teachers in the state, the staff members randomly selected 50 conference attendees and asked the attendees how long they have been teaching. Which of the following describes the sample and the population to which it would be most reasonable for the staff members to generalize the results?
The sample is the 50 conference attendees, and the population is all conference attendees.
Which of the following could explain why the margin of error of sample A is greater than the margin of error of sample B?
The sample size of A is less than the sample size of B.
According to data from the United States Elections Project, only 3636 percent of eligible voters voted in the 20142014 elections. For random samples of size 4040, which of the following best describes the sampling distribution of pˆ�^, the sample proportion of people who voted in the 20142014 elections?
The sampling distribution is approximately normal, with mean 0.360.36 and standard deviation 0.0760.076.
As part of a science experiment, a student recorded 10 measurements of the temperature of a liquid. One of the measurements was an outlier when compared with the other 9 measurements. Which of the following must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements? (Note: An outlier is any number that is greater than the upper quartile or less than the lower quartile by at least 1.5 times the interquartile range.)
The standard deviation of the 9 measurements is less than the standard deviation of the 10 measurements.
Nyasha's financial literacy project involved comparing the annual sales of companies in Canada and companies in the United States that produce software. Using the ratio of 1 Canadian dollar to 0.75 United States dollar, she converted all annual sales from the Canadian companies into United States dollars. For which of the following will the value of the statistic for the annual sales in Canadian dollars be equal to the value of the corresponding statistic in United States dollars?
The standardized score of the minimum annual sales
Researchers believed that an increase in lean body mass is associated with an increase in maximal oxygen uptake. A scatterplot of the measurements taken from 18 randomly selected college athletes displayed a strong positive linear relationship between the two variables. A significance test for the null hypothesis that the slope of the regression line is 0 versus the alternative that the slope is greater than 0 yielded a p-value of 0.04. Which statement is an appropriate conclusion for the test?
The strong positive linear relationship displayed in the scatterplot along with a p-value less than 0.05 indicates that college athletes with higher lean body mass tend to have higher maximal oxygen uptake.
An environmental group wanted to estimate the proportion of fresh produce sales identified as organic in a local grocery store. In the winter, the group obtained a random sample of sales from the store and used the data to construct the 95 percent z-interval for a proportion (0.087, 0.133 ). Six months later in the summer, the group obtained a second random sample of sales from the store. The second sample was the same size as the first, and the proportion of sales identified as organic was 0.4. How does the 95 percent z-interval for a proportion constructed from the summer sample compare to the winter interval?
The summer interval is wider and has a greater point estimate.
High school students from track teams in the state participated in a training program to improve running times. Before the training, the mean running time for the students to run a mile was 402402 seconds with standard deviation 4040 seconds. After completing the program, the mean running time for the students to run a mile was 368368 seconds with standard deviation 3030 seconds. Let X� represent the running time of a randomly selected student before training, and let Y� represent the running time of the same student after training. Which of the following is true about the distribution of X−Y�−� ?
The variables X� and Y� are not independent; therefore, the mean is 3434 seconds and the standard deviation cannot be determined with the information given.
A student working on a physics project investigated the relationship between the speed and the height of roller coasters. The student collected data on the maximum speed, in miles per hour, and the maximum height, in feet, for a random sample of 2121 roller coasters, with the intent of testing the slope of the linear relationship between maximum speed and maximum height. However, based on the residual plot shown, the conditions for such a test might not be met.
The variance of the response variable is constant for all values of the explanatory variable.
An experiment was conducted to investigate the relationship between the dose of a pain medication and the number of hours of pain relief. Twenty individuals with chronic pain were randomly assigned to one of five doses—0.0, 0.5, 1.0, 1.5, 2.0—in milligrams (mg) of medication. The results are shown in the scatterplot below. The data were used to fit a least-squares regression line to predict the number of hours of pain relief for a given dose. Which of the following would be revealed by a plot of the residuals of the regression versus the dose?
The variation in the hours of pain relief is not the same across the doses.
Researchers conducted a study to investigate the effects of soft drink consumption on fat stored in muscle tissue. From a sample of 80 adult volunteers, 40 were randomly assigned to consume one liter of a soft drink each day. The remaining 40 were asked to drink one liter of water each day and not to consume any soft drinks. At the end of six months, the amount of fat stored in each person's muscle tissue was recorded. The people in the group who drank the soft drink had, on average, a higher percentage of fat stored in the tissue than the people who drank only water. Which of the following is the most appropriate conclusion?
There is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only water, and the conclusion can be generalized to adults similar to those in the study.
people in the placebo group had normal blood glucose levels. For people similar to those in the study, do the data provide convincing statistical evidence that the proportion who would be classified as normal after one month of taking cinnamon is greater than the proportion who would be classified as normal after one month of not taking cinnamon?\
There is not convincing statistical evidence at any reasonable significance level.
According to a recent report, customers who shop at a certain online store spend, on average, $1,500 a year at the store. To investigate whether the mean amount spent was greater than the reported average, an economist obtained the mean and standard deviation of the amount spent in the past year by a random sample of 120 customers who shop at the store. With all conditions for inference met, the economist conducted the appropriate hypothesis test and obtained a p-value of 0.25. Which of the following statements is the most appropriate conclusion for the investigation?
There is not convincing statistical evidence that the mean amount of money spent each year by all customers who shop at the store is greater than $1,500.
Suppose a roadrunner has a total length of 59.0 cm and tail length of 31.1 cm. Based on the residual, does the regression model overestimate or underestimate the tail length of the roadrunner?
Underestimate, because the residual is positive.
A company produces millions of 1-pound packages of bacon every week. Company specifications allow for no more than 3 percent of the 1-pound packages to be underweight. To investigate compliance with the specifications, the company's quality control manager selected a random sample of 1,000 packages produced in one week and found 40 packages, or 4 percent, to be underweight. Assuming all conditions for inference are met, do the data provide convincing statistical evidence at the significance level of α = 0.05� = 0.05 that more than 3 percent of all the packages produced in one week are underweight?
Yes, because the p-value of 0.032 is less than the significance level of 0.05.
The president of a large company recommends that employees perform, on average, 24 hours of community service each year. The president believes that the mean number of hours of community service performed last year was different from the recommended 24 hours. To estimate the mean number of hours of community service performed last year, the president obtained data from a random sample of employees and used the data to construct the 95 percent confidence interval (20.37, 23.49). If all conditions for inference were met, does the interval provide convincing statistical evidence, at a level of significance of α = 0.05� = 0.05, to support the president's belief that the mean number of hours of community service performed last year is different from what is recommended?
Yes, the interval supports the president's belief because 24 is not contained in the interval.
