Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗=32%. You would like to be 99% confident that your esimate is within 4% of the true population proportion. How large of a sample size is required?

n =

Answer 1

The following information is provided,
Significance Level, α = 0.01, Margin of Error, E = 0.04

The provided estimate of proportion p is, p = 0.32
The critical value for significance level, α = 0.01 is 2.58.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.32*(1 - 0.32)*(2.58/0.04)^2
n = 905.27

n = 905 (906 if we round to next integer)