UNIT TESTS

A random sample of high school seniors was surveyed about whether they drive to school. Of the 75 seniors surveyed, 64 stated they drive to school. Which of the following is the 90% confidence interval for p, the proportion of all high school seniors who drive to school?

(0.79, 0.92)

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 catering company provides packages for weddings and for showers. The cost per person for small groups is approximately Normally distributed for both weddings and showers. The mean cost for weddings is $82.30 with a standard deviation of $18.20, while the mean cost for showers is $65 with a standard deviation of $17.73. If 9 weddings and 6 showers are randomly selected, what is the probability the mean cost of the weddings is more than the mean cost of the showers?

0.9665

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 standard deviation of the distribution?

1.3

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

1.96

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?

Yes, because the entire interval is greater than 0.75.

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?

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

An athletic trainer would like to estimate how many additional calories are burned when completing a high intensity interval training (HIIT) workout for 30 minutes rather than doing yoga for 30 minutes. A group of 30 volunteers are randomly assigned to take a 30-minute HIIT class or a 30-minute yoga class wearing a calorie-counting armband. A 90% confidence interval for the true difference in the population means is 157.23 calories to 210.91 calories. Based upon the confidence interval, is it reasonable to claim that doing 30 minutes of a HIIT workout burns 250 more calories than doing a 30-minute yoga workout?

no because 250 is not in the confidence interval

One professional basketball player typically attempts eight free throws per game. Let X represent the number of free throws made out of eight. The histogram displays the distribution. What is the shape of the distribution?

slightly skewed left

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?

the second one

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 ?

-0.52

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?

0.0042

One of Natalia's professors claims that 13% of the students at their college frequently wear hats. Natalia feels that the actual rate is much lower. She selects a random sample of 100 students at the college and finds that only 9 of them wear hats frequently. To determine if her data provide convincing evidence that the true proportion is less than 13%, she conducts 200 trials of a simulation. Natalia is testing the hypotheses: H0: p = 13% and Ha: p < 13%, where p = the true proportion of students at the college who frequently wear hats. Based on the results of the simulation, what is an estimate of the P-value of the test?

0.005

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?

0.0504

A man owns five bow ties. He chooses one bow tie at random to wear on any given day. The polka-dot bow tie is his favorite, so his random process uses a larger probability for that bow tie. The rest of the bow ties are given equal probabilities of being chosen, as shown in the table. A man owns five bow ties. He chooses one bow tie at random to wear on any given day. The polka-dot bow tie is his favorite, so his random process uses a larger probability for that bow tie. The rest of the bow ties are given equal probabilities of being chosen, as shown in the table.

0.15

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

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 at least 1 of them shows a 2?

0.2297

A survey of 500 college students moving into their dorm revealed that 425 brought a microwave, 380 brought a video game console, and 50 brought neither a microwave nor game console. A survey participant is randomly selected. Let M be the event the participant brought a microwave and let C be the event the participant brought a video game console. Organize these events in a two-way table. What is the probability that the participant did not bring a microwave or did not bring a console, P(MC or CC)?

0.29

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. The tree diagram displays the possible outcomes of orders at this coffee shop. Which probability is represented by label 4 in the tree diagram?

0.30

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?

0.32

A survey of teens suggested that 33% can name at least one professional baseball player, and 90% of those teens can also name at least one professional football player. In the entire population, 64% can name at least one professional football player. What percentage of teens can name at least one player from these sports?

0.33 + 0.64 - (0.90)(0.33) = 0.673

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?

0.359

At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. The probabilities are displayed in the tree diagram. The professor informs the class that there will be a test next week. What is the probability that a randomly selected student passes the test with a B or higher?

0.41

A car wash has three different types of washes: basic, classic, and ultimate. Based on records, 45% of customers get the basic wash, 35% get the classic wash, and 20% get the ultimate wash. Some customers also vacuum out their cars after the wash. The car wash records show that 10% of customers who get the basic wash, 25% of customers who get the classic wash, and 60% of customers who get the ultimate wash also vacuum their cars. The probabilities are displayed in the tree diagram. What is the probability that a randomly selected customer purchases the ultimate car wash if they vacuum their car?

0.48

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?

0.48 - 0.36 +- 2.58

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?

0.60 - 0.70 +- 1.96

For students majoring in Hospitality Management, it was determined that 5% have visited 1-10 states, 16% have visited 11-20 states, 45% have visited 21-30 states, 19% have visited 31-40 states, and 15% have visited 41-50 states. Suppose a Hospitality Management student is randomly picked. What is the probability that the student has visited 30 or fewer states?

0.66

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?

0.6781

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"?

0.686

A recent survey found that 80% of jeans have back pockets, 65% have front pockets, and 48% have both back and front pockets. Suppose a pair of jeans is selected at random and it is determined that it has front pockets. What is the probability that a randomly selected pair of jeans with front pockets also has back pockets?

0.74

A farmer would like to estimate the mean amount of milk produced per day by his 300 cows. He selects a random sample of 15 cows and records the amount of milk produced (in gallons) by those cows. The dotplot shows the data. Given that all of the recorded values are integers, what is the value of the standard error of the mean?

0.765

In a certain board game, a 12-sided number cube showing numbers 1-12 is rolled. If 4 such number cubes are rolled, what is the probability that at least 1 number cube will show a number 8 or larger?

0.8842

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?

0.9158

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 recorded. Which of the following values of the mean of the sample is most likely to occur if the true mean number of ounces is 20.8?

20.9

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? 2.127

25

At a certain pizzeria, it is known that 25% of orders are for small pizzas. What is the probability that the 5th pizza ordered is the first small pizza?

81/1024

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

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. 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

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 pCoffeee= the true proportion of customers who drink coffee and use their own cup. Which of the following is the correct standardized test statistic and P-value for the hypotheses,

A.

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 < , 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 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 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. Which of the following gives a complete list of all possible samples of size 3 from this population of 5 sessions, selected without replacement?

ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE

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?

All conditions for inference are met.

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 ?

B

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?

B

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?

B

Can you train yourself to become better at holding your 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 and the P-value is approximately 0. What conclusion should be made using the significance level = 0.01?

B

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?

B

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.

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. What are the appropriate hypotheses for this test?

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.

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.

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 a Type II error in this situation?

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.

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 ?

Because , np = 17(0.19) = 3.23 < 10 the sampling distribution of is not approximately Normal. Because p = 0.19 is closer to 0 than 1, the sampling distribution of is skewed to the right.

An economics major believes that in married couples, the taller spouse has the higher income. To test this theory, she randomly selects 26 married couples and records their yearly incomes. The mean difference (taller - shorter) in incomes is $1,668 with a standard deviation of $1,290. Assuming the conditions have been met, is there evidence that, on average, the taller member of a married couple has a higher income? Use a significance level of α = 0.05. Find the t-table here.

Because the P-value is less than α, there is evidence that in married couples, the taller of the two has a higher income on average.

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?

C.

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 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.

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.

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

Center: 2.4Shape: skewed right

A company claims that its brand of dish detergent, A, is more effective than a competitor's brand, B. 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 = least clean to 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?

D

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?

D

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?

D.

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 the consequence of a Type II error in this context?

D. The company believes the humidity absorbed is not more than 3%, when in fact it is more than 3%. The company will sell components that absorb a dangerous level of humidity.

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. Let μ1 = the true mean travel time to school along route 1 and μ2 = the true mean travel time to school along route 2. Timmy would like to know if the data provide convincing evidence of a difference in travel time for the 2 routes. Dotplots of the distribution of travel time for route 1 and route 2 show no strong skewness or outliers. What are the appropriate hypotheses?

H0: μ1 - μ2 = 0, Ha: μ1 - μ2 ≠ 0

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?

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 teacher would like to estimate the mean number of steps students take during the school day. To do so, she selects a random sample of 50 students and gives each one a pedometer at the beginning of the school day. They wear the pedometers all day and then return them to her at the end of the school day. From this, she computes the 98% confidence interval for the true mean number of steps students take during the school day to be 8,500 to 10,200 steps. Which of these statements is a correct interpretation of the confidence level?

If many random samples of size 50 are selected from all students at this school, approximately 98% of the intervals would capture the true mean number of steps taken during the school day.

A teacher would like to estimate the mean amount of time it takes for students taking this statistics class to complete this multiple-choice assessment item. To do so, she selects a random sample of 50 students enrolled in this statistics class and records the amount of time (in minutes) it takes them to complete this question. The standard error of the mean is 0.27 minutes. What is the interpretation of the standard error of the mean?

If we select many random samples of students enrolled in this statistics class, the sample mean amount of time needed to complete this question would typically vary by about 0.27 minutes from the population mean.

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 in order to find a package that was not delivered on time. What is an appropriate assignment of digits to carry out this simulation?

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

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. What is an appropriate assignment of digits for this simulation?

Let 01-08 = the carton contains a broken egg. Let 09-99 and 00 = the carton does not contain a broken egg.

The following two-way table shows the distribution of weekend work hours and how long employees have been at the company. Suppose an employee is selected from this company at random. Let event A = work weekends and event B = worked less than 5 years. Are events A and B independent?

No, P(A) ≠ P(A|B)

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?

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?

No, the 10% condition is not met.

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?

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

The owner of an apple orchard would like to estimate the mean number of usable apples produced per tree in his large orchard. He selects a random sample of 10 trees from his large orchard. This dotplot displays the number of usable apples produced for each of these trees. Are the conditions for constructing a t confidence interval met?

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

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?

No, the confidence interval does not consist entirely of negative numbers.

The ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The minimum of the ages of the officers is 15. The table displays all possible samples of size 2 and the corresponding minimum for each sample. Using the minimums in the table, is the sample minimum an unbiased estimator?

No, the mean of the sampling distribution of the sample minimums is 16, which is not 15.

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?

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

A varsity swimmer at a large high school wants to estimate the amount of time (in hours), on average, athletes at this school train or practice each day. This swimmer selects 10 members of her swim team and asks them how many hours they typically train or practice. Use the data to construct a 90% confidence interval to estimate the true mean number of hours athletes at this school train or practice each day. Have the conditions for inference been met?

No, the sample is not random.

Josie believes that her mom calls her at the most inconvenient times. As a matter of fact, Josie thinks that 80% of the times that her mom calls, she is busy doing important tasks such as schoolwork, driving, or feeding the family pets. Which is the best interpretation of this probability?

Over the course of many weeks, about 80% of the calls from Josie's' mom will come when she is busy doing important tasks.

A researcher randomly selected 132 high school students and asked them about their study habits and lighting preference when studying. The two-way table displays the data. Suppose one of the students is randomly selected. Let L = the student prefers low light and S = the student sometimes studies. Which of the following is the correct value and interpretation of P(S|L)?

P(S|L) = 0.57; given that the student prefers low light, there is a 0.57 probability that they sometimes study.

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?

P(X ≥ 4)

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?

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

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, ?

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 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). Based on this interval, what conclusion should the candidate make about the proportion of likely voters who would vote for her in the upcoming election?

The candidate cannot conclude that the proportion of likely voters who would vote for her has increased.

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?

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?

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.

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?

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

Hannah and Claire each have a chicken coop with 6 hens. Let H represent the total number of eggs the hens lay on a randomly chosen day in Hannah's coop and let C represent the total number of eggs the hens lay on a randomly chosen day in Claire's coop. The two distributions are displayed in the table and histograms. Which statement correctly compares the variability of the distributions?

The standard deviation of the number of eggs laid by Claire's hens is greater than the standard deviation of the number of eggs laid by Hannah's hens.

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?

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.

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?

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

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. Are the conditions for inference met?

Yes, all conditions for inference are met.

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. The dotplots show the data.

Yes, all three conditions for inference are met.

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?

Yes, the confidence interval consists entirely of positive numbers.

In a certain board game, a 12-sided number cube showing numbers 1-12 is rolled. In this game, a number cube must be rolled until a number 9 or higher appears. Is it appropriate to use the geometric distribution to calculate probabilities in this situation?

Yes, the geometric distribution is appropriate.

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?

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 researcher is 95% confident that the interval from 5.8 minutes to 9.3 minutes captures the true mean amount of time it takes to pump a full tank of gas in a certain type of SUV.

Yes, this is a plausible value for the population mean, because 9 is within the 95% confidence interval.

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?

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?

constructing a 90% confidence interval

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 amount of sleep that high school students get per night to be 6.5 to 7.5 hours. Which of the following would decrease the width of the interval?

decreasing the confidence level

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?

one-sample z-interval for p

A student would like to estimate the mean length of words in a book report he just finished writing. He selects a random sample of 20 words and determines the mean length to be 4 characters. Later, he discovers how to use a built-in function of his word-processing program that reveals that the mean length of all words in his book report is 4.3 characters. Which of the following describes the number, 4.3?

parameter

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. What are the appropriate test statistic and P-value?

t = 2.88; the P-value is between 0.0025 and 0.005.

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. What is the appropriate inference procedure?

t confidence interval for a difference in means

The school board of a large school district would like to raise taxes in the district to pay for new computers. To see if there is support for a tax increase, they send a survey home with a random sample of students in the district. If the survey is not completed, calls are made to ensure responses are obtained from the parents of every selected student. The survey asks, "Would you be in favor of a modest tax increase to fund the purchase of new computers for all students?" The confidence interval for the true proportion of families that are in favor of a tax increase is 0.70 to 0.80. Members of the community who do not have children in the district complain about not being included in this study. Which of the following sources of bias affected the confidence interval, but is not included among the sources covered by the margin of error?

undercoverage bias