16Hit1600
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?

  1. A. Poll B's margin of error is about half of Poll A's.Correct
  2. B. Poll B's margin of error is about one quarter of Poll A's.
  3. C. Poll B's margin of error is about four times Poll A's.
  4. 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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