If you want to be 95 confident of estimating the population

If you want to be 95% confident of estimating the population proportion to within a sampling error of +or- 0.02 and there is historical evidence that the population proportion is approximately 0.40, what sample size is needed?

Solution

Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Samle Proportion = 0.4
ME = 0.02
n = ( 1.96 / 0.02 )^2 * 0.4*0.6
= 2304.96 ~ 2305