Question

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 99.5% confident that you esimate is within 5% of the true population proportion. How large of a sample size is required? n = Do not round mid-calculation. However, use a critical value accurate to three decimal places.

Answer 1

The following information is provided,
Significance Level, α = 0.005, Margin of Error, E = 0.05

The provided estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.005 is 2.807.

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 = 0.5*(1 - 0.5)*(2.807/0.05)^2
n = 787.92

Therefore, the sample size needed to satisfy the condition n >= 787.92 and it must be an integer number, we conclude that the minimum required sample size is n = 788
Ans : Sample size, n = 788