91Ó°ÊÓ

Incentives to Exercise: How Much More Effective Is It to Lose Money? In Exercise \(5.30,\) we see that overweight participants who lose money when they don't meet a specific exercise goal meet the goal more often, on average, than those who win money when they meet the goal, even if the final result is the same financially. In particular, participants who lost money met the goal for an average of 45.0 days (out of 100 ) while those winning money or receiving other incentives met the goal for an average of 33.7 days. In Exercise 5.30 we see that the incentive does make a difference. In this exercise, we ask how big the effect is between the two types of incentives. Find and interpret a \(95 \%\) confidence interval for the difference in mean number of days meeting the goal, between people who lose money when they don't meet the goal and those who win money or receive other similar incentives when they do meet the goal. The standard error for the difference in means from a bootstrap distribution is 4.14 .

55- to 64-year-olds The survey included 411 adults between the ages of 55 and \(64,\) and 50 of them said that they had used online dating. If we use this sample to estimate the proportion of all American adults ages 55 to 64 to use online dating, the standard error is \(0.016 .\) Find a \(95 \%\) confidence interval for the proportion of all US adults ages 55 to 64 to use online dating.