Incentives to Exercise: What Works Best? In the study described in Exercise 5.29, the goal for each of the overweight participants in the study was to walk 7000 steps a day. The study lasted 100 days and the number of days that each participant met the goal was recorded. The participants were randomly assigned to one of four different incentive groups: for each day they met the goal, participants in the first group got only an acknowledgement, participants in the second group got entered into a lottery, and participants in the third group received cash (about \(\$ 1.50\) per day). In the fourth group, participants received all the money up front and lost money (about \(\$ 1.50\) per day) if they didn't meet the goal. The success rate was almost identical in the first three groups (in other words, giving cash did not work much better than just saying congratulations) and the mean number of days meeting the goal for these participants was 33.7. For the participants who would lose money, however, the mean number of days meeting the goal was 45.0. (People really hate to lose money!) Test to see if this provides evidence of a difference in means between those losing money and those with other types of incentives, using the fact that the standard error for the difference in means is 4.14.

Data From Exercise 5.29:

A study was designed to see what type of incentive might be most effective in encouraging people to exercise. In the study, 281 overweight or obese people were assigned the goal to walk 7000 steps a day, and their activity was tracked for 100 days. The participants were randomly assigned to one of four groups, with different incentives for each group. In this problem, we look at the overall success rate. For each participant, we record the number of days that the participant met the goal. For all 281 participants, the average number of days meeting the goal is 36.5. The standard error for this estimate is 1.80. Test to see if this provides evidence that the mean number of days meeting the goal, for people in a 100-day program to encourage exercise, is greater than 35. Show all details of the test.