Confidence Intervals (Sample Size) 90% cofidence level 2% margin

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 2% margin of error at a 90% confidence level, what size of sample is needed?

Answer 1

The formula for the margin of error of a given sample size is e = (zσ)/√n, where n is the sample size and σ is the standard deviation. If you solve this for an unknown n, the formula is [(zσ)/e]².

Since this margin of error is given as a percentage, this is a standard normal distribution with a mean of 0 and a standard deviation of 1. The only other thing we need to know. We may be given this, or we may have a normal distribution calculator or table that tells us that a confidence level of 90% has a z value of 1.28. Now we have everything we need to put into our formula.

n = [(1.28*1)/0.02]² = 64² = 4096.