The course I am in is ‘Sampling Methodology in Finite Populations. This is a homework problem. The first part of the problem I understand. However for part b I am wondering if CI’s for SRS with replacement are different from regular SRS without replacement. For example, is the SE(ybar) calculated differently from SE(ybar) = sqrt((1-n/N)(s^2/n).
Consider a population of N=580 patients of a clinic. A quantity of in-terest is the percentage of patients that overdue for a vaccination.(a) What sample size in a SRS(without replacement) would be necessary toestimate the proportion with 95% con dence and margin of error 0.10.(b) Suppose a SRSWR(with replacement) of size 120, yielded 27 whom werenot overdue for vaccination. Give a 95% CI for the proportion of children notoverdue for vaccination