91Ó°ÊÓ

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 $15,000$miles 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" $H_0:{\mathrm{β}}_1=15,000$versus $H_a:{\mathrm{β}}_1≠15,000$.

c. Compute the standardized test statistic and P -value for the test in part (b). What conclusion would you draw at the $\mathrm{Î\pm }=0.05$significance level?

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

Step by step solution

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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 (c) Step 2: Simplify

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Part (d) Step 1: Given Information

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Part (d) Step 2: Simplify

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