A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a $7 \%$ margin of error at a $99 \%$ confidence level, what size of sample is needed? Give your answer in whole people.
Question Help: $\square$ Message instructor
Answer
\(\boxed{339}\) is the required sample size.
Step 1 ：We are given a Z-score for a 99% confidence level which is approximately 2.576, the margin of error E is 0.07 (7%), and we'll use p = 0.5.
Step 2 ：We need to use the formula for the sample size in a proportion: \(n = \frac{{Z^2 * p * (1-p)}}{{E^2}}\)
Step 3 ：Substitute the given values into the formula: \(n = \frac{{(2.576)^2 * 0.5 * (1-0.5)}}{{(0.07)^2}}\)
Step 4 ：Calculate the value of n. Since we can't have a fraction of a person, we'll round up to the nearest whole number.
Step 5 ：\(\boxed{339}\) is the required sample size.
