A university is contemplating switching from the quarter system to the semester system. The administration conducts a survey of a random sample of 50 students and finds that 30 of them prefer to remain on the quarter system.

Someone pointed out that the sample size was rather small and that perhaps another survey should be conducted. What is the minimum sample size needed to estimate the proportion of students in favor of remaining on the quarter system within a margin of error of about 0.048 with 95% confidence? Use the estimated proportion from the original sample as your estimate of p.