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How Important Is Regular Exercise? In a recent poll \(^{50}\) of 1000 American adults, the number saying that exercise is an important part of daily life was 753 , Use StatKey or other technology to find and interpret a \(90 \%\) confidence interval for the proportion of American adults who think exercise is an important part of daily life.

Investigating the Width of a Confidence Interval Comparing Exercise 3.120 to Exercise \(3.121,\) you should have found that the confidence interval when utilizing the paired structure of the data was narrower than the confidence interval ignoring this structure (this will generally be the case, and is the primary reason for pairing). How else could we change the width of the confidence interval? More specifically, for each of the following changes, would the width of the confidence interval likely increase, decrease, or remain the same? (a) Increase the sample size. (b) Simulate more bootstrap samples. (c) Decrease the confidence level from \(99 \%\) to \(95 \%\).

3.124 Donating Blood to Grandma? There is some evidence that "young blood" might improve the health, both physically and cognitively, of elderly people (or mice). Exercise 2.69 on page 75 introduces one study in which old mice were randomly assigned to receive transfusions of blood from either young mice or old mice. Researchers then measured the number of minutes each of the old mice was able to run on a treadmill. The data are stored in YoungBlood. We wish to estimate the difference in the mean length of time on the treadmill, between those mice getting young blood and those mice getting old blood. Use StatKey or other technology to find and interpret a \(90 \%\) confidence interval for the difference in means.

Daily Tip Revenue for a Waitress Data 2.12 on page 123 describes information from a sample of 157 restaurant bills collected at the First Crush bistro. The data is available in RestaurantTips. Two intervals are given below for the average tip left at a restaurant; one is a \(90 \%\) confidence interval and one is a \(99 \%\) confidence interval. Interval A: 3.55 to 4.15 Interval B: 3.35 to 4.35 (a) Which one is the \(90 \%\) confidence interval? Which one is the \(99 \%\) confidence interval? (b) One waitress generally waits on 20 tables in an average shift. Give a range for her expected daily tip revenue, using both \(90 \%\) and \(99 \%\) confidence. Interpret your results.

Who Smokes More: Male Students or Female Students? Data 1.1 on page 4 includes lots of information on a sample of 362 college students. The complete dataset is available at StudentSurvey. We see that 27 of the 193 males in the sample smoke while 16 of the 169 females in the sample smoke. (a) What is the best point estimate for the difference in the proportion of smokers, using male proportion minus female proportion? Which gender smokes more in the sample? (b) Find and interpret a \(99 \%\) confidence interval for the difference in proportions.