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Chapter 12: Q. T12.9 (page 824)

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

Short Answer

Expert verified

The correct answer is option (d) A scatterplot of Inyversus Inx looks approximately linear.

Step by step solution

01

Given information

To determine the relationship between a response variable yand an explanatory variable x.

02

Explanation

Since, the explanatory Variable also known as the independent variable.

To determine which of the following would give evidence that the relationship between a response variable y and an explanatory variable xis described by a power model of the type y=axp, wherep鈮�0,p鈮�1.
As a result, if we convert both variables to their logarithms, the scatterplot of a power model becomes linear, and option (d) is the proper option, resulting in a scatterplot of Inyversus Inxthat looks approximately linear.

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Most popular questions from this chapter

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.

Recycle and Review Exercises 29-31 refer to the following setting. Does the color in which words are printed affect your ability to read them? Do the words themselves affect your ability to name the color in which they are printed? Mr. Starnes designed a study to investigate these questions using the 16 students in his AP Statistics class as subjects. Each student performed the following two tasks in random order while a partner timed his or her performance: (1) Read 32words aloud as quickly as possible, and (2) say the color in which each of 32words is printed as quickly as possible. Try both tasks for yourself using the word list given.

Color words (10.3) Now let's analyze the data,

a Calculate the difference (Colors-Words) (Colors - Words) for each subject and surmmarize thedistribution of differences with a boxplot. does the graph provide evidence of a difference in the average time required to perform the two tests? Explain your answer.

b. Explain why it is not safe to use paired & procedures to do inference about the mean difference in time in complete the Two tasks.

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:

T12.5 Suppose that the researchers test the hypotheses H0:尾1=0 versus

Ha:尾1<0. Which of the following is the value of the t statistic for this

test?

a. 2.61

b. 鈭�2.44

c. 2.44

d. 鈭�20.24

e. 0.081

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:

T12.4 By about how much does the sample slope typically vary from the population slope in repeated random samples of n=69 golfers?
a. 7,897,179
b. 1,698,371
c. 3,023,782
d. 281,777
e. 鈭�4,139,198

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:

T12.8 Which of the following would make the calculation in Exercise T12.7 invalid?

a. If the scatterplot of the sample data wasn鈥檛 perfectly linear.

b. If the distribution of earnings has an outlier.

c. If the distribution of earnings wasn鈥檛 approximately Normal.

d. If the earnings for golfers with small putting averages was much more variable than the earnings for golfers with large putting averages.

e. If the standard deviation of earnings is much larger than the standard deviation of putting average.
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