Problem-Solving and Data AnalysisHardEffect of sample size on the margin of error
Problem-Solving and Data Analysis practice question
Two polls of the same population are run with the same method and find the same result. Poll A surveys 400 people and Poll B surveys 1,600 people. Which statement about the margins of error is correct?
- A. Poll B's margin of error is about half of Poll A's.Correct
- B. Poll B's margin of error is about one quarter of Poll A's.
- C. Poll B's margin of error is about four times Poll A's.
- D. The two margins of error are the same because the results are the same.
Answer: A. Poll B's margin of error is about half of Poll A's.
The margin of error scales with 1/√n; quadrupling n halves it.
Why the other answers are wrong
- B. Poll B's margin of error is about one quarter of Poll A's.
- One quarter would require 16 times the sample.
- C. Poll B's margin of error is about four times Poll A's.
- A larger sample shrinks the margin, not grows it.
- D. The two margins of error are the same because the results are the same.
- The margin depends on sample size, not on the result.
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