Problem-Solving and Data AnalysisMediumEffect of sample size on margin of error
Problem-Solving and Data Analysis practice question
A survey of 200 randomly chosen residents estimates the proportion who use the park weekly, with a margin of error of 7 percentage points. Which change would most reduce the margin of error?
- A. Surveying 800 randomly chosen residents instead of 200Correct
- B. Surveying 200 residents chosen from those already in the park
- C. Asking the same 200 residents a second time
- D. Reporting the result to more decimal places
Answer: A. Surveying 800 randomly chosen residents instead of 200
A larger random sample gives a smaller margin (quadrupling it roughly halves the margin).
Why the other answers are wrong
- B. Surveying 200 residents chosen from those already in the park
- Sampling park users introduces bias and doesn't reduce the margin.
- C. Asking the same 200 residents a second time
- Repeating the same sample adds no new information.
- D. Reporting the result to more decimal places
- Decimal places don't change the uncertainty.
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