steps on how to figure this problem

Question

A political candidate has asked you to conduct a poll to determine what percentage of people support her.

If the candidate only wants a 10% margin of error at a 99% confidence level, what size of sample is needed?

Give your answer in whole people.

Answer 1

First, remember the margin of error formula. MoE = z* × s.e. (where s.e. is the standard error).

Next, use the formula for standard error for a proportion. s.e. = √(p(1-p)/N), where p is the success probability and N is the sample size.

Lastly, we want the worst-case scenario for the standard error. This will happen when p = 0.5.

So you plug in p = 0.5 to the standard error formula, and 0.10 (or 10%) for the margin of error. This should get you a formula with the sample size N as the only unknown. You can solve for N that way (and round up to the nearest whole number because you can't survey half a person).