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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

Boyle’s law Refer to Exercise 34. Here is a graph of 1Pressureversus volume along with output from a linear regression analysis using these variables:

a. Give the equation of the least-squares regression line. Define any variables you use. b. Use the model from part (a) to predict the pressure in the syringe when the volume is 17cubic centimeters.

Which of the following is a categorical variable?

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c. The fuel efficiency (in miles per gallon) of a hybrid car

d. The brand of shampoo purchased by shoppers in a grocery store

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Each morning, coffee is brewed in the school workroom by one of three faculty members, depending on who arrives first at work. Mr. Worcester arrives first 10% of the time, Dr. Currier arrives first 50%of the time, and Mr. Legacy arrives first on the remaining mornings. The probability that the coffee is strong when brewed by Dr. Currier is 0.1, while the corresponding probabilities when it is brewed by Mr. Legacy and Mr. Worcester are 0.2 and 0.3, respectively. Mr. Worcester likes strong coffee!
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Exercises T12.4–T12.8 refer to the following setting. An old saying in golf is “You drive for show and you putt for dough.” The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour’s world money list are examined. The average number of putts per hole (fewer is better) and the player’s total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for inference about the slope are met. Here is computer output from the regression analysis:

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After a name-brand drug has been sold for several years, the Food and Drug Administration (FDA) will allow other companies to produce a generic equivalent. The FDA will permit the generic drug to be sold as long as there isn't convincing evidence that it is less effective than the name-brand drug. For a proposed generic drug intended to lower blood pressure, the following hypotheses will be us

where

μG=true mean reduction in blood pressureusing the generic drug μG=true mean reduction in blood pressureusing the name@brand drug

μG=true mean reduction in blood pressure

using the generic drug

μG=true mean reduction in blood pressure

using the name@brand drug

In the context of this situation, which of the following describes a Type I error?

a. The FDA finds convincing evidence that the generic drug is less effective, when in reality it is less effective.

b. The FDA finds convincing evidence that the generic drug is less effective, when in reality it is equally effective.

c. The FDA finds convincing evidence that the generic drug is equally effective, when in reality it is less effective.

d. The FDA fails to find convincing evidence that the generic drug is less effective, when in reality it is less effective.

e. The FDA fails to find convincing evidence that the generic drug is less effective, when in reality it is equally effective.
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