The Chronicle of Higher Education (January 13, 1993) reported that 72.1% of those responding to a national survey of college freshmen were attending the college of their first choice. Suppose that n = 500 students responded to the survey (the actual sample size was much larger).

a. Using the sample size n = 500, calculate a 99% confidence interval for the proportion of college students who are attending their first choice of college.

b. Compute and interpret a 95% confidence interval for the proportion of students who are not attending their first choice of college.

c. The actual sample size for this survey was much larger than 500. Would a confidence interval based on the actual sample size have been narrower or wider than the one computed in Part (a)?