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Problem-Solving and Data AnalysisEasy–MediumEffect of sample size on margin of error

Problem-Solving and Data Analysis practice question

A polling organisation surveyed 400 randomly selected voters and reported a margin of error of 2.5 percentage points. The organisation then repeated the survey using the same methods on the same population, but with 1,600 randomly selected voters.

Compared with the first survey, the margin of error for the second survey will most likely be

  1. A. smaller, because a larger sample estimates the population more precisely.Correct
  2. B. larger, because surveying more people introduces more variation.
  3. C. the same, because the margin of error depends only on the confidence level.
  4. D. zero, because a sample of 1,600 is large enough to be exact.

Answer: A. smaller, because a larger sample estimates the population more precisely.

Increasing the sample size, with the method and population unchanged, makes the sample mean a more precise estimate of the population value, so the margin of error shrinks. Going from 400 to 1,600 quadruples the sample, which roughly halves the margin of error.

Why the other answers are wrong

B. larger, because surveying more people introduces more variation.
More responses give a more stable estimate, not a shakier one. Individual answers still vary, but the variability of the AVERAGE falls as the sample grows.
C. the same, because the margin of error depends only on the confidence level.
The confidence level is one input, but sample size is another — that's exactly why organisations pay to survey more people.
D. zero, because a sample of 1,600 is large enough to be exact.
No sample short of the entire population removes uncertainty. A bigger sample narrows the margin of error; it never drives it to zero.

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