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

Question

If the candidate only wants a 4% margin of error at a 99% confidence level, what size of sample is needed?

Give your answer in whole people.

Answer 1

To determine a required sample size based on a desired margin of error, we rearrange the formula used to determine the margin of error in a confidence interval.

For a Proportion:

Margin of error = Z_.99 √(p*(1-p)/n)

where p is the sample proportion, n is sample size

If you do not have an estimate for the proportions, you will use p=.5

rearranging and squaring we get the equation:

n=((Z₉₉)² (.5)(.5)) / Margin of error²

For a mean with population standard deviation (σ) known, you would use this formula:

n= ((Z₉₉ * σ)/Margin of error))²