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Problem-Solving and Data AnalysisVery hardComparing margins of error for two sample sizes

Problem-Solving and Data Analysis practice question

Two random samples are drawn from the same population to estimate its mean. Sample A has 100 people and sample B has 900 people. Which of the following best compares their margins of error?

  1. A. Sample B's margin of error is about one third of sample A's.Correct
  2. B. Sample B's margin of error is about one ninth of sample A's.
  3. C. The two margins of error are about the same.
  4. D. Sample B's margin of error is about three times sample A's.

Answer: A. Sample B's margin of error is about one third of sample A's.

The margin of error shrinks with the square root of the sample size, and the square root of 9 is 3.

Why the other answers are wrong

B. Sample B's margin of error is about one ninth of sample A's.
One ninth would apply if the margin shrank in direct proportion to the sample size.
C. The two margins of error are about the same.
A larger sample gives a smaller margin.
D. Sample B's margin of error is about three times sample A's.
Larger samples give smaller, not larger, margins.

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