Beyond Common Core
Problem 37 of 45s12-037
A poll will estimate a proportion with a margin of error of at most 4 percentage points at 90% confidence (). There is no prior estimate. What is the smallest sample size?
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Solution walkthrough2:12
- The margin of error shrinks as the sample size grows. Find the first where it is at most .
- No estimate is given, so use : then .
- Solve for : .
- With the margin is just over ; with it is under. Round up: .
- Traps: rounds down, forgets to square, and uses in place of .