Question

A political candidate has asked you to conduct a poll to determine what percentage of people support him. If the candidate only wants a 5% margin of error at a 99.5% confidence level, what size of sample is needed?

Answer 1

900

Explanation:

Margin of error = critical value × standard error

The margin of error is given to be 0.05.

At 99.5% confidence, the critical value is z = 3.

The standard error for a proportion is √(pq/n). Since p is not given, we will assume p = 0.5.

0.05 = 3 √(0.5 × 0.5 / n)

n = 900