Problem-Solving and Data AnalysisHardEffect of a larger sample on an estimate
Problem-Solving and Data Analysis practice question
Two random samples are drawn from the same city to estimate the share of residents who cycle to work. Sample A has 200 people and Sample B has 2,000. Which statement is true?
- A. Sample B's estimate has a smaller margin of error than Sample A's.Correct
- B. Sample A's estimate has a smaller margin of error than Sample B's.
- C. The two estimates have the same margin of error.
- D. Sample B's estimate must equal the true share exactly.
Answer: A. Sample B's estimate has a smaller margin of error than Sample A's.
A larger random sample gives a smaller margin of error.
Why the other answers are wrong
- B. Sample A's estimate has a smaller margin of error than Sample B's.
- The smaller sample has the larger margin.
- C. The two estimates have the same margin of error.
- Sample size changes the margin.
- D. Sample B's estimate must equal the true share exactly.
- Even a large sample has some error.
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