Problem-Solving and Data AnalysisVery hardComparing margins of error from different sample sizes
Problem-Solving and Data Analysis practice question
Two random samples are drawn from the same large population to estimate the same proportion. Sample 1 has 100 people and Sample 2 has 900 people. Which of the following is true about their margins of error?
- A. Sample 2's margin of error is about one third of Sample 1's.Correct
- B. Sample 2's margin of error is about one ninth of Sample 1's.
- C. Sample 2's margin of error is about three times Sample 1's.
- D. The margins of error are equal because both samples are random.
Answer: A. Sample 2's margin of error is about one third of Sample 1's.
The margin of error scales with 1/√n. Nine times the sample size gives √9 = 3 times smaller margin.
Why the other answers are wrong
- B. Sample 2's margin of error is about one ninth of Sample 1's.
- One ninth would apply if the margin scaled with 1/n; it scales with 1/√n.
- C. Sample 2's margin of error is about three times Sample 1's.
- A larger sample gives a smaller margin, not larger.
- D. The margins of error are equal because both samples are random.
- Randomness controls bias; sample size controls precision.
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