The campus wellness center wants to estimate the proportion of students that are getting at least 7 hours of sleep every night during finals week, and they require an estimate with 99% confidence and...

(a) If a similar survey from last year showed that p̂ = 0.38, what is the minimal number of students that must be surveyed this year?



(b) If the center decides their data from last year is not comparable to this year due to the circumstances of online final exams, and so has no prior information regarding p̂, what is the minimal sample size needed?