Suppose that you were going to take a sample of UF students

Suppose that you were going to take a sample of UF students. You were interested in estimating the proportion who had at least one non-related roommate. You were uncertain what this proportion was; however, you wanted to be 95% confident with a margin of error equal to 0.024. What sample size do you need?

Solution

We use p=0.5 as estimated.

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So n=(Z/E)^2*p*(1-p)

=(1.96/0.024)^2*0.5*0.5

=1667.361

Take n=1668

Answer: 1668