What size of sample is needed?

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 0.2% margin of error at a 99% confidence level, what size of sample is needed? When finding the z-value, round it to four decimal places.

Answer 1

Hi Annie,

The formula for this is:

n = (z*/m)²*p*q

n= sample size

z*=z-critical value

m=margin of error

p=probability of success (person supports candidate)

q=probabiility of failure (person opposes candidate)

When you know nothing in advance about your population, you must assume p and q are 0.5. Now, in general, the z-critical value for 99% confidence intervals is 2.5760. You may want to memorize this as it comes up a lot in statistics classes. Anyway, that means:

z*= 2.5760

m= 0.002–divide your 0.2 by 100 to get the appropriate margin of error

p=0.5

q=0.5

n=(z*/m)²*p*q

n= (2.576/0.002)²*0.5*0.5

n=414736

This is very high because your candidate wanted an extremely low margin of error. This value wound up in the denominator, which means the sample size will increase substantially, I hope this helps.