I would appreciate any help I can get with this question.
Suppose we wish to select a simple random sample without replacement from a population of size 1000 to estimate the proportion, P, of population members with a particular characteristic, and we want the relative standard error (RSE) to be about 8%. From a previous survey we have a reliable estimate, 0.32, of this proportion.
Find the minimum sample size required to meet this sample design constraint.
My working:
RSE(P-hat)={SE(P-hat)}/{P-hat}
=>SE(P-hat)=0.08x0.32
=0.0256
SE(P-hat)=sqrt(V-hat)(P-hat))
=>(V-hat)(P-hat))=6.5536x10^{-4}
V-hat=1/n(1-n/N)(n/N-1)(P-hat)(1-(V-hat)))
but solving for n, I got a number less than 1! What have I done wrong?!?! Please help
(and sorry I didn't use Latex, I got an error )