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 90% confidence level, what size of sample is needed?

Give your answer in whole people

Answer 1

Solution :

Given that,

$\hat p$ = 0.5

1 - $\hat p$ = 0.5

margin of error = E = 0.01

Z_$\alpha$/2 = 1.645

sample size = n = (Z_{$\alpha$ / 2} / E)² * $\hat p$ * (1 - $\hat p$ )

= (1.645 / 0.01)² * 0.5 * 0.5

= 6766

sample size = n = 6766