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, so we assume p=.5. You would like to be 99% confident that you estimate is within 0.2% of the true population proportion. How large of a sample size is required?

Answer 1

416025

Explanation:

For confidence interval of 99%, the range is (0.005, 0.995). Using a z-table, the z-score for 0.995 is 2.58.

Margin of error = 0.2% = 0.002.

Proportion is unknown. So, worse case proportion is 50%. p = 50% = 0.5.

\\
`n = \left(\frac{\texttt{z-score}}{\texttt{margin of error}} \right )^2\cdot p\cdot (1-p) \\ = \left((2.58)/(0.002) \right )^2\cdot 0.5\cdot (1-0.5)=416025`

So, sample size required is 416025.