You are planning a survey and will calculate a 95 confidence

You are planning a survey and will calculate a 95% confidence inteval for the difference in two pro-protions when the data is collected. You would like the margin of error of the inteval to be less than or equal to 0.075. You will use the same sample size n for both populations. How large of a value of n is needed? explain how you arrived at your answer and the assumptions that you made.

Solution

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

We ues p=0.5 as estimated.

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

=(1.96/0.075)^2*0.5*0.5

=170.7378

Take n=171