1. A university wants to estimate the proportion of its studentswho smoke regularly. Suppose that this university has N = 30, 000students in total and a SRSWOR of size n will be taken from thepopulation. a) If the university wants the proportion estimator ˆpto achieve the precision with tolerance level e = 0.03 and risk ? =0.1. Estimate the minimal sample size needed for this estimation.(z0.1 = 1.28, z0.05 = 1.65) b) Suppose that, in a pilot study, theuniversity takes a SRSWOR of size 20 students, among which only 2students are found to be smokers. Based on this preliminary result,re-compute the minimal sample size for part (a). c) Suppose theuniversity chooses the sample size estimated from (b), and findsthat the sample proportion is ˆp = 0.15. Construct a 90% confidenceinterval for the population proportion p
