Refer to the Journal of Sport Behavior (2001) study of variety in exercise workouts, presented in Exercise. One group of 40 people varied their exercise routine in workouts, while a second group of 40 exercisers had no set schedule or regulations for their workouts. By the end of the study, 15 people had dropped out of the first exercise group and 23 had dropped out of the second group.
a. Find the dropout rates (i.e., the percentage of exercisers who had dropped out of the exercise group) for each of the two groups of exercisers.
b. Find a 90% confidence interval for the difference between the dropout rates of the two groups of exercisers.
c. Give a practical interpretation of the confidence interval you found in part c.
d. Suppose you want to reduce the sampling error in the 90% confidence interval to .1. Determine the number of exercisers to be sampled from each group in order to obtain such an estimate. Assume equal sample sizes, and assume that p1 ≈ .4 and p2 ≈ .6.