Refer to The Sport Journal (Winter 2004) study on the effectiveness of a speed-training program for football players, Exercise 7.26 (p. 326). The decreases in 40-yard sprint times (time after training minus time before training) for 38 players are saved in the SPRINT file. An athlete's sprint performance will be classified as "Improved" if the "after" time is less than the "before" time, and classified as "Not Improved" if otherwise.
a. Find an estimate for the true proportion of all high school athletes who attain improved sprint times after participating in the speed-training program.
b. Convert the estimate, part a, into a 95% confidence interval. Give a practical interpretation of the result.
c. How many high school athletes should be sampled to estimate the true proportion to within .03 with 95% confidence?