Xr12-91* There is a looming crisis in universities and colleges across North America. In most places, enrollments are increasing; this requires more instructors. However, there are not enough PhDs to fill the vacancies now. Moreover, among current professors, a large proportion are nearing retirement age. On top of these problems, some universities allow professors over age 60 to retire early. To help devise a plan to deal with the crisis, a consultant surveyed 521 55- to 64-year-old professors and asked each one whether he or she intended to retire before 65. The responses are 1  No and 2  Yes.

a. Estimate with 95% confidence the proportion of professors who plan on early retirement.

b. Write a report for the university president describing your statistical analysis.