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 6% margin of error at a 99% confidence level, what size of sample is needed? The political candidate will need to sample people.

Answer 1

Solution,

Given that,

$\hat p$ =  1 - $\hat p$ = 0.5

margin of error = E = 0.06

At 99% confidence level

$\alpha$ = 1 - 99%  

$\alpha$ = 1 - 0.99 =0.01

$\alpha$/2 = 0.005

Z$\alpha$/2 = Z0.005 = 2.576

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

= (2.576 / 0.06)2 * 0.5 * 0.5

= 461.18

sample size = n = 462