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Chapter 12: Q. 21 (page 792)

Stats teachers’ cars A random sample of 21 AP® Statistics teachers was asked to report the age (in years) and mileage of their primary vehicles. Here is a scatterplot of the data:

Here is some computer output from a least-squares regression analysis of these data. Assume that the conditions for regression inference are met.

a. Verify that the 95%confidence interval for the slope of the population regression line is (9016.4,14,244.8).

b. A national automotive group claims that the typical driver puts 15,000miles per year on his or her main vehicle. We want to test whether AP® Statistics teachers are typical drivers. Explain why an appropriate pair of hypotheses for this test is role="math" localid="1654244859513" H0:β1=15,000versus Ha:β1≠15,000.

c. Compute the standardized test statistic and P -value for the test in part (b). What conclusion would you draw at the α=0.05significance level?

d. Does the confidence interval in part (a) lead to the same conclusion as the test in part (c)? Explain your answer.

Short Answer

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Part (a) Step 1: Given Information

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Part (a) Step 2: Simplify

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Part (b) Step 1: Given Information

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Part (b) Step 2: Simplify

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Part (c) Step 1: Given Information

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Part (d) Step 1: Given Information

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Most popular questions from this chapter

If P(A)=0.2and P(B)=0.52 and events A and B are independent, what is P(A or B)?

a. 0.1248

b. 0.28

c. 0.6352

d. 0.76

e. The answer cannot be determined from the given information.

Prey attracts predators Here is one way in which nature regulates the size of animal populations: high population density attracts predators, which remove a higher proportion of the population than when the density of the prey is low. One study looked at kelp perch and their common predator, the kelp bass. On each of four occasions, the researcher set up four large circular pens on sandy ocean bottoms off the coast of southern California. He randomly assigned young perch to 1of 4pens so that one pen had 10perch, one pen had 20perch, one pen had 40perch, and the final pen had 60perch. Then he dropped the nets protecting the pens, allowing bass to swarm in, and counted the number of perch killed after two hours. A regression analysis was performed on the 16data points using x=number of perch in pen and y=proportion of perch killed. Here is a residual plot and a histogram of the residuals. Check whether the conditions for performing inference about the regression model are met.

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of 25students was selected from a large high school. For each student, x=foot length and y=height were recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

Which of the following is the equation of the least-squares regression line for predicting height from foot length?

a. height^=10.2204+0.4117(foot length) height^=10.2204+0.4117(foot length)

b.height^=0.4117+3.0867 (foot length) height^=0.4117+3.0867(foot length)

c. height^=91.9766+3.0867(foot length) height^=91.9766+3.0867(foot length)

d. height^=91.9766+6.47044 (foot length)height^=91.9766+6.47044(foot length)

e. height^=3.0867+6.47044(foot length)heiight^=3.0867+6.47044(foot length)

Can physical activity in youth lead to mental sharpness in old age? A 2010study investigating this question involved9344randomly selected, mostly white women over age 65from four U.S. states. These women were asked about their levels of physical activity during their teenage years, 30s,50 s, and later years. Those who reported being physically active as teens enjoyed the lowest level of cognitive decline-only 8.5% had cognitive impairment-compared with 16.7% of women who reported not being physically active at that time.
(a) State an appropriate pair of hypotheses that the researchers could use to test whether the proportion of women who suffered a cognitive decline was significantly smaller for women who were physically active in their youth than for women who were not physically active at that time. Be sure to define any parameters you use.
(b) Assuming the conditions for performing inference are met, what inference method would you use to test the hypotheses you identified in part (a)? Do not carry out the test.
(c) Suppose the test in part (b) shows that the proportion of women who suffered a cognitive decline was significantly smaller for women who were physically active in their youth than for women who were not physically active at that time. Can we generalize the results of this study to all women aged65 and older? Justify your answer.
(d) We cannot conclude that being physically active as a teen causes a lower level of cognitive decline for women over 65, due to possible confounding with other variables. Explain the concept of confounding and give an example of a potential confounding variable in this study.

Beer and BAC Refer to Exercise 5. Here is computer output from the least-squares regression analysis of the beer and blood alcohol data.

a. What is the estimate for β0? Interpret this value.

b. What is the estimate for β1? Interpret this value.

c. What is the estimate for σ? Interpret this value.

d. Give the standard error of the slope SEb1. Interpret this value.
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