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Chapter 12: Q. 7 (page 800)

Which of the following is a categorical variable?

(a) The weight of automobiles

(b) The time required to complete the Olympic marathon

(c) The average gas mileage of a hybrid car

(d) The brand of shampoo purchased by shoppers in a

grocery store

(e) The average closing price of a particular stock on the

New York Stock Exchange

Short Answer

Expert verified

The final answer is an option (d) The brand of shampoo purchased by shoppers in a grocery store.

Step by step solution

01

Given Information

We need to find the categorical variable from the given options.

02

Explanation

We know, that a categorical variable contains a finite amount of categories. An example is, roll a die, categories are (1,2,3,4,5,6).

For option a: Weights are in pounds which are not in categories.

For option b: Time is in seconds/minutes which is not a category.

For option c: The average gas per mile for a hybrid car is in mpg which is not a category (well technically empg, but doesn't change the context)

For option d: There are only a limited number of brands for shampoo. This is categorical.

For option e: The average closing price is in dollars and cents which is not a categorical value.

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Most popular questions from this chapter

Beer and BAC How well does the number of beers a person drinks predict his or her blood alcohol content (BAC)? Sixteen volunteers with an initial BAC of 0drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their BAC. Least-squares regression was performed on the data. A residual plot and a histogram of the residuals are shown below. Check whether the conditions for performing inference about the regression model are met.

Prey attracts predators Refer to Exercise 3. Computer output from the least-squares regression analysis on the perch data is shown below.

The model for regression inference has three parameters: α,βand σ. Explain what each parameter represents in context. Then provide an estimate for each.

The P-value for the test in Question 5 is 0.0087. A correct interpretation of this result is that

(a) the probability that there is no linear relationship between an average number of putts per hole and total winnings for these 69players is 0.0087.

(b) the probability that there is no linear relationship between the average number of putts per hole and total winnings for all players on the PGA Tour’s world money list is 0.0087.

(c) if there is no linear relationship between an average number of putts per hole and total winnings for the players in the sample, the probability of getting a random sample of 69players yields a least-squares regression line with a slope of -4139198or less is 0.0087.

(d) if there is no linear relationship between an average number of putts per hole and total winnings for the players on the PGA Tour’s world money list, the probability of getting a random sample of 69 players yields a least-squares regression line with a slope of -4139198or less is 0.0087.

(e) the probability of making a Type II error is0.0087.

Can physical activity in youth lead to mental sharpness in old age? A2010study investigating this question involved 9344randomly 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,50s, 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 lower 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 (b)? 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 lower 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.

The previous Check Your Understanding (page 750) described some results from a study of body weights and backpack weights. Here, again, is the Minitab output from the least-squares regression analysis for these data.

1. Do these data provide convincing evidence of a linear relationship between pack weight and body weight in the population of ninth-grade students at the school? Carry out a test at the a=0.05significance level. Assume that the conditions for regression inference are met.
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