Unit 11 Review Warm Up Stats 11.14.25

Researchers on car safety studied driver reaction time and cell phone use while driving. Participants in the study talked on either a hands-free phone or a handheld phone while driving in a car simulator. A two-sample t-test for a difference in means was conducted to investigate whether the mean driver reaction time between the two groups of participants was different. All conditions for inference were met, and the test produced a test statistic of t = -2.763 and a p-value of 0.03. Which of the following is a correct interpretation of the p-value?

• Assuming that the mean reaction times for hands-free and handheld phones are equal, the probability of obtaining a test statistic less than -2.763 is 0.03.

• Assuming that the mean reaction times for hands-free and handheld phones are equal, the probability of obtaining a test statistic greater than 2.763 or less than -2.763 is 0.03.

• Assuming that the mean reaction times for hands-free and handheld phones are not equal, the probability of obtaining a test statistic less than -2.763 is 0.03.

• Assuming that the mean reaction times for hands-free and handheld phones are not equal, the probability of obtaining a test statistic greater than 2.763 or less than -2.763 is 0.03.

• The probability that the mean reaction time for hands-free phones will be less than that for handheld phones is 0.03.

Answer explanation

A reporter responsible for the food section of a magazine investigated the belief that grocery stores sell beef at a higher price in the fall than in the spring. The reporter selected independent random samples of grocery-store beef prices in November and April and computed the mean and standard deviation for the samples. Which of the following are the correct null and alternative hypotheses for the reporter’s investigation, where μF represents the mean price of beef in the fall and μS represents the mean price of beef in the spring?

Answer explanation

Correct. The null hypothesis states that there is no difference between the population mean price of beef in the fall and the population mean price of beef in the spring, and the alternative hypothesis states that the population mean price of beef is greater in the fall than in the spring.

A two-sample t-test for a difference in means was conducted to investigate whether defensive players on a football team can bench-press more weight, on average, than offensive players. The conditions for inference were met, and the test produced a test statistic of t = 1.083 and a p-value of 0.15. Based on the p-value and a significance level of α = 0.05, which of the following is the correct conclusion?

• Reject the null hypothesis because the p-value (0.15) is less than the significance level (0.05).

• Fail to reject the null hypothesis because the p-value (0.15) is greater than the significance level (0.05).

• The test statistic is not significant at the 0.05 level.

• There is sufficient evidence to conclude that defensive players can bench-press more weight than offensive players.

A two-sample t-test for a difference in means was conducted to investigate whether defensive players on a football team can bench-press more weight, on average, than offensive players. The conditions for inference were met, and the test produced a test statistic of t = 1.083 and a p-value of 0.15.

• Reject the null hypothesis because 0.15 > 0.05. There is not convincing evidence that defensive players can bench-press more weight, on average, than offensive players.

• Reject the null hypothesis because 0.15 > 0.05. There is convincing evidence that defensive players can bench-press more weight, on average, than offensive players.

• Fail to reject the null hypothesis because 0.15 > 0.05. There is not convincing evidence that defensive players can bench-press more weight, on average, than offensive players.

• Fail to reject the null hypothesis because 0.15 > 0.05. There is convincing evidence that defensive players can bench-press more weight, on average, than offensive players.

• Fail to reject the null hypothesis because 0.15 > 0.05. There is convincing evidence that defensive players can bench-press the same amount of weight, on average, as offensive players.

• We are 95 percent confident that the mean cost of a hospital visit for all parrot owners in the state is between 44.99 and 80.27.

• We are 95 percent confident that the mean cost of a hospital visit for the parrot owners in the sample is between 44.99 and 80.27.

• For all parrot owners in the state, 95 percent of hospital visits for parrot care cost between 44.99 and 80.27.

• There is a 0.95 probability that the mean cost of a hospital visit for all parrot owners in the state is between 44.99 80.27.

• There is a 0.95 probability that the mean cost of a hospital visit for the parrot owners in the sample is between 44.99 and 80.27.

Tags

CCSS.HSS.IC.B.4

A team of ecologists will select a random sample of nesting robins in a certain region to estimate the average number of eggs per nest for all robins in the region. Which of the following is a correct inference procedure for the ecologists to use?

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

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

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

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

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

Tags

CCSS.HSS.IC.B.4