I NEED HELP!!!!!!

Question

A political candidate has asked you to conduct a pool to determine what percentage of people support him. If the candidate only wants a 1% margin of error at a 95% confidence level what size of sample is needed?

Answer 1

For a proportion the margin of error is z critical for 95% * standard error,

where standard error = sqrt (p * (1-p)/n).

z critical for 95% confidence is 1.96

Since we are not given p, we assume a value of p=0.5, so standard error = sqrt(0.5*0.5/n)

We want margin of error <= 0.01 (percent converted to proportion) so we want

1.96 * sqrt(0.25/n) <= 0.01

1.96^2 * 0.25/n <= 0.01^2

1.96^2 *.025/0.01^2 <= n (multiply both sides by n and divide both sides by 0.01^2)

9604 <- n

sample size = 9604