What does n=? (statistics)

Question

A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2 percentage points with 90​% confidence if

​(a) he uses a previous estimate of

22​%?

​(b) he does not use any prior​ estimates?

n= ? (Round up to nearest integer)

Answer 1

The formula to find the minimum sample size is n = pˆqˆ(z_c/E)²

pˆ is the estimated pop'n proportion of successes (0.22); qˆ is the proportion of failures (0.78)

z_c = factor for 90% confidence (1.645); E is confidence interval (0.02).

n = (0.22)(0.78)(1.645/0.02)² ≅ 1,161

If there's no prior estimate, use 0.5 for pˆ and qˆ.