Researchers at the University of Pennsylvania’s Wharton Sports Business Initiative collaborated with the National Football League Players Association (NFLPA) to produce the first NFL Player Survey. Of the 1,696 active NFL players, 1,355 (almost 80%) responded to the survey. One of the survey questions asked, “Who is the coach—professional, college, or high school—that has been the most influential in your career?” Of the 1,355 respondents, 759 selected an NFL (professional) coach.

a. Construct a 95% confidence interval for the true proportion of active NFL players who select a professional coach as the most influential in their careers.

b. Why is it necessary to use the continuity correction factor in the construction of the interval, part a?

c. Give a practical interpretation of the interval, part a.