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Chapter 12: Q.26 (page 793)

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=footlength&y=heightere 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:

26. Which of the following is the best interpretation of the value 0.4117in the computer output?

a. For each increase of 1cmin foot length, the average height increases by about0.4117cm

b. When using this model to predict height, the predictions will typically be off by about 0.4117cm.

c. The linear relationship between foot length and height accounts for 41.17%of the variation in height.

d. The linear relationship between foot length and height is moderate and positive.

e. In repeated samples of size 25the slope of the sample regression line for predicting height from foot length will typically vary from the population slope by about 0.4117.

Short Answer

Expert verified

The correct option is option (e)

In repeated samples of size25the slope of the sample regression line for predicting height from foot length will typically vary from the population slope by about 0.4117

Step by step solution

01

Given Information

Given in the question that

we have to determine the correct option.

02

Explanation 

The number 0.4117is mentioned in the column "SE Coef" and in the row "foot length," indicating that 0.4117is the standard error of the slope SEb1

The average deviation of the slope of the sample regression line from the population regression line is shown by the standard error of the slope.

As a result, the best solution is (e)

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Most popular questions from this chapter

Exercises T12.4鈥揟12.8 refer to the following setting. An old saying in golf is 鈥淵ou drive for show and you putt for dough.鈥� 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鈥檚 world money list are examined. The average number of putts per hole (fewer is better) and the player鈥檚 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:

T12.6 The P -value for the test in Exercise T12.5 is 0.0087. Which of the following is a correct interpretation of this result?
a. The probability there is no linear relationship between average number of putts per hole and total winnings for these 69 players is 0.0087.
b. The probability there is no linear relationship between average number of putts per hole and total winnings for all players on the PGA Tour鈥檚 world money list is 0.0087.
c. If there is no linear relationship between average number of putts per hole and total winnings for the players in the sample, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of 鈭�4,139,198 or less is 0.0087.
d. If there is no linear relationship between average number of putts per hole and total winnings for the players on the PGA Tour鈥檚 world money list, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of 鈭�4,139,198 or less is 0.0087.
e. The probability of making a Type I error is 0.0087.

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=footlength&y=heightwere 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 would have resulted in a violation of the conditions for inference?

a. If the entire sample was selected from one classroom

b. If the sample size was 15instead of 25

c. If the scatterplot of x=footlength&y=heightdid not show a perfect linear relationship

d. If the histogram of heights had an outlier

e. If the standard deviation of foot length was different from the standard deviation of height

In a recent poll, randomly selected New York State residents at various fast-food restaurants were asked if they supported or opposed a "fat tax" on sugared soda. Thirtyone percent said that they were in favor of such a tax and 66% were opposed. But when asked if they would support such a tax if the money raised were used to fund health care given the high incidence of obesity in the United States, 48% said that they were in favor and 49% were opposed.
(a) In this situation, explain how bias may have been introduced based on the way the questions were worded and suggest a way that the questions could have been worded differently in order to avoid this bias.
(b) In this situation, explain how bias may have been introduced based on the way the sample was taken and suggest a way that the sample could have been obtained in order to avoid this bias.
(c) This poll was conducted only in New York State. Suppose the pollsters wanted to ensure that estimates for the proportion of people who would support a tax on sugared soda were available for each state as well as an overall estimate for the nation as a whole. Identify a sampling method that would achieve this goal and briefly describe how the sample would be taken.

T12.9 Which of the following would provide evidence that a power model of the form y=axp, wherep鈮�0and p鈮�1, describes the relationship between a response variable y and an explanatory variable x?
a. A scatterplot of y versus x looks approximately linear.
b. A scatterplot of Iny versus x looks approximately linear.
c. A scatterplot of y versus lnx looks approximately linear.
d. A scatterplot of Iny versus lnx looks approximately linear.
e. None of these

Stats teachers鈥� cars A random sample of 21 AP庐 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庐 Statistics teachers are typical drivers. Explain why an appropriate pair of hypotheses for this test is role="math" localid="1654244859513" H0:尾1=15,000versus Ha:尾1鈮�15,000.

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