Statistics Question

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 1% margin of error at a 98% confidence level, what size of sample is needed?

The political candidate will need to sample ____ people.

Answer 1

When we don't know the proportion ahead of time, we assume that p=0.5. This assumption gives us the largest possible sample size since we multiply p(1-p).

The formula you need is

n=1/4 (z/E)²

where 1/4 is p(1-p) when p=1/4

z = z-score for a 98% confidence level = 2.33

E = margin of error = 0.01

n= (1/4)(2.33/.01)² =13572.25 = 13573

When determining sample size, always round up, even when normal rounding rules would suggest otherwise.