update: I think it's supposed to be 849, not 8.49
I've been agonizing over this problem involving a sample mean and margin of error. I feel like the sample size I got as my answer is too small?
Question is:
How large a sample is needed to estimate a population proportion to within a margin of error of 4 % at the 98 % confidence level?
First, I calculated the critical value as 2.33 and then plugged the margin of error, .4, and 2.33 into the formula:
n = (z* divided by E)^2 x p-hat x q-hat or (2.33 divided by .4) ^2 x 1/2 x 1/2
I got the 1/2 since p-hat and q-hat are both unknowns so you have to use the most conservative estimate, or 1/2.
Anyway, my answer is 8.49 or sample size of 9
I feel like this is way too small of a sample size! What'd I do wrong?
Since we have that , must equal 0.02 and . So, the z value we are looking for is . We then require that
.
Since the we do not know anything about we use .
I have not computed the value, but if you just solve for n you should find your answer. However, I think your answer is correct.