please help me solve this

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% confident that your estimate is within 1% of the true population proportion. How large of a sample size is required?

n = 

Answer 1

Make the assumption that the population proportion is 0.5. This maximizes the standard deviation of the sampling distribution of the sampling proportion (i.e. standard error), which is calculated as √(pq÷n).

The critical z-value for a 99% confidence interval is 2.576. You can now solve for the sample size n

2.576 = 0.01/√(0.5 × 0.5 ÷ n)

n = 16590