86 Speed training in football. Refer to The Sport Journal

(Winter 2004) study on the effectiveness of a speed training program for football players, Exercise 60 . The confidence interval for the population proportion of athletes who improve their sprint times after participating in the speed-training program was fairly wide due to the relatively small number of athletes ( n = 38 ) who participated in the program. In order to find a valid, narrower confidence interval for the true proportion, the researchers would need to include more athletes in the study. How many high school athletes should be sampled to estimate the true proportion to within .03 with 95% confidence?