AP Statistics Spring 2024 Quiz 4 Unit 11

In 2011, 17 percent of a random sample of 200 adults in the United States indicated that they consumed at least 3 pounds of bacon that year. In 2016, 25 percent of a random sample of 600 adults in the United States indicated that they consumed at least 3 pounds of bacon that year.

Assuming all conditions for inference are met, which of the following is the most appropriate test statistic to use to investigate whether the proportion of all adults in the United States who consume at least 3 pounds of bacon in 2016 is different from that of 2011?

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CCSS.HSS.IC.B.4

In a study researching how donating to charity can affect a person’s happiness, 96 participants were given $5 a day for one week. Each participant was randomly assigned to one of two groups. Those assigned to the first group were asked to spend the money on themselves, and those assigned to the second group were asked to donate the money to charity. At the end of the week, all of the participants were asked to rate their overall level of happiness on a scale from 0 to 100, with higher scores indicating greater levels of happiness.

Which of the following are the appropriate null and alternative hypotheses to test whether the sample data provide convincing statistical evidence that donating to charity results in greater happiness than spending on oneself, on average?

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A statistics student wants to compare the mean times needed to access flight information for two major airlines. Twenty randomly selected students accessed one airline's Web site, and the time required to locate the flight information using the Web site had a mean of 2.5 minutes and a standard deviation of 0.8 minute. Twenty different randomly selected students accessed the other airline's Web site, and the time required to locate the flight information using the Web site had a mean of 2.1 minutes and a standard deviation of 1.1 minutes. Assuming that the conditions for inference are met, which of the following statements about the p-value obtained from the data and the conclusion of the significance test is true?

• The p-value is less than 0.01; therefore, there is a significant difference in mean search times on the two Web sites.

• The p-value is greater than 0.01 but less than 0.05; therefore, there is a significant difference in mean search times on the two Web sites.

• The p-value is greater than 0.05 but less than 0.10; therefore, there is a significant difference in mean search times on the two Web sites.

• The p-value is greater than 0.10; therefore, there is no significant difference in mean search times on the two Web sites.

• Since this is a matched-pairs situation, additional information is needed to perform a test of significance.

An experiment will be conducted to test the effectiveness of a weight-loss supplement. Volunteers will be randomly assigned to take either the supplement or a placebo for 90 days, with 12 volunteers in each group. The subjects will not know which treatment they receive. At the end of the experiment, researchers plan to calculate the mean weight loss for each of the two groups and to construct a two-sample t-confidence interval for the difference of the two treatment means. Which of the following assumptions is necessary for the confidence interval to be valid?

• The sample size is greater than or equal to 10 percent of the population size.

• Each of the two groups has at least 5 successes and at least 5 failures.

• The distributions of weight loss of the two treatments are approximately normally distributed.

• The volunteers in the supplement group are paired with volunteers in the placebo group.

• The expected number of people who lose weight in each group is at least 5.

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CCSS.HSS.IC.B.4

A two-sample t-test of the hypotheses H₀ : μ₁ - μ₂ = 0 versus H_a : μ₁- μ₂ > 0 produces a p-value of 0.03.

Which of the following must be true?

I. A 90 percent confidence interval for the difference in means will contain the value 0.

II. A 95 percent confidence interval for the difference in means will contain the value 0.

III. A 99 percent confidence interval for the difference in means will contain the value 0.

• I only

• III only

• I and II only

• II and III only

• I, II, and III

• 0.7778

• 0.4444

• 0.2222

• 0.2164

• 0.1082

To determine whether an herbal supplement helps relieve knee pain, researchers will select 50 patients with knee pain to participate in a study. The participants will be randomly assigned to one of two groups, with 25 participants in each group. The first group will receive the herbal supplement daily for one week, and the second group will receive a placebo daily for one week. Patients will continue to take their current pain medication during the week. At the end of the week, the patients will record their pain score on a scale of 1 to 10, where 1 represents no pain and 10 represents extreme pain.

Assuming the conditions for inference are met, which of the following would be the most appropriate statistical method to estimate the difference in mean pain score between the herbal supplement and the placebo for all patients with knee pain who are similar to the participants in the study?

• A one-sample z-interval for estimating a population proportion

• A one-sample t-interval for estimating a population mean

• A matched-pairs t-interval for estimating a population mean difference

• A two-sample z-interval for estimating a difference between population proportions

• A two-sample t-interval for estimating a difference between population means

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CCSS.HSS.IC.B.4

An owner of a novelty business operates both an online store and a retail store. The owner took a random sample of 50 sales from each store during the past year and recorded the purchase amount of each sale. Summary statistics are shown in the following table.

Assuming the conditions for inference were met, the owner calculated a 95 percent confidence interval for the difference in mean purchase amounts (online minus retail) as ($11.55,$19.05).

Which of the following is an appropriate interpretation of the 95 percent confidence interval?

• We are 95% confident that the purchase amount from a randomly selected online store sale will be between $11.55 and $19.05 greater than the purchase amount from a randomly selected retail store sale.

• We are 95% confident that the sample mean purchase amount from the online store is between $11.55 and $19.05 greater than the sample mean purchase amount from the retail store for the past year.

• We are 95% confident that the population mean purchase amount from the online store is between $11.55 and $19.05 greater than the population mean purchase amount from the retail store for the past year.

• We are 95% confident that the population mean purchase amount for the past year from both stores combined is between $11.55 and $19.05.

• We are 95% confident that if new samples of the same size were taken from each store, the sample mean purchase amount from the online store would be between $11.55 and $19.05 greater than the sample mean purchase amount from the retail store.

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CCSS.HSS.IC.B.4

A physician believes that the exercise habits of East Coast adults are different from the exercise habits of West Coast adults. To study this, she gathers information on the number of hours of exercise per week from a random sample of East Coast adults and a random sample of West Coast adults. Which of the following might be an appropriate null hypothesis for this study?

• The average number of hours of exercise per week for East Coast adults is different from the average number of hours of exercise per week for West Coast adults.

• The average number of hours of exercise per week for East Coast adults is the same as the average number of hours of exercise per week for West Coast adults.

• The average number of hours of exercise per week for East Coast adults is greater than the average number of hours of exercise per week for West Coast adults.

• The average number of hours of exercise per week for East Coast adults is less than the average number of hours of exercise per week for West Coast adults.

• The probability is 0.5 that an East Coast adult and a West Coast adult exercise an equal number of hours per week.

As part of a national sleep study, a random sample of adults was selected and surveyed about their physical activity and the number of hours they sleep each night. Of the 183 adults who exercised regularly (exercisers), 59 percent reported sleeping at least seven hours at night. Of the 88 adults who did not exercise regularly (nonexercisers), 52 percent reported sleeping at least seven hours at night. Which of the following is the most appropriate standard error for a confidence interval for the difference in proportions of adults who sleep at least seven hours at night among exercisers and nonexercisers?

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