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Problem-Solving and Data AnalysisMediumWhat happens to the margin of error when the sample shrinks

Problem-Solving and Data Analysis practice question

A poll of 1,600 randomly chosen voters has a margin of error of 2.5 percentage points. If a similar poll were taken with only 400 voters, which of the following would most likely be true of its margin of error?

  1. A. It would be about 5 percentage points — larger, because the sample is smaller.Correct
  2. B. It would be about 1.25 percentage points — smaller, because fewer people were asked.
  3. C. It would be 2.5 percentage points, because both polls are random.
  4. D. It would be 10 percentage points, because the sample is a quarter the size.

Answer: A. It would be about 5 percentage points — larger, because the sample is smaller.

The margin scales with 1/√n. A quarter of the sample gives √4 = 2 times the margin: about 5 points.

Why the other answers are wrong

B. It would be about 1.25 percentage points — smaller, because fewer people were asked.
A smaller sample gives a larger margin, not smaller.
C. It would be 2.5 percentage points, because both polls are random.
Randomness controls bias; size controls precision.
D. It would be 10 percentage points, because the sample is a quarter the size.
Quartering the sample doubles the margin (via the square root), not quadruples it.

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