16Hit1600
Problem-Solving and Data AnalysisMediumChoosing a change that reduces margin of error

Problem-Solving and Data Analysis practice question

A survey of 500 randomly selected residents of a city estimated the proportion who use public transport daily, with a margin of error of 3.1 percentage points at a 95% confidence level.

Which change would be most likely to decrease the margin of error, assuming all other aspects of the survey are unchanged?

  1. A. Surveying 2,000 randomly selected residents instead of 500.Correct
  2. B. Surveying 100 randomly selected residents instead of 500.
  3. C. Reporting the result at a 99% confidence level instead of 95%.
  4. D. Asking the same 500 residents the same question a second time.

Answer: A. Surveying 2,000 randomly selected residents instead of 500.

Margin of error falls as the sample size rises. Quadrupling the sample from 500 to 2,000 is the only change here that increases how much independent information the estimate is based on, so it is the only one that narrows the interval.

Why the other answers are wrong

B. Surveying 100 randomly selected residents instead of 500.
This is the right lever pulled the wrong way. A smaller sample gives a less precise estimate, so the margin of error would grow, not shrink.
C. Reporting the result at a 99% confidence level instead of 95%.
Demanding more confidence forces a WIDER interval — you buy extra certainty by casting a bigger net. Raising 95% to 99% increases the margin of error.
D. Asking the same 500 residents the same question a second time.
Re-asking the same 500 people adds no new residents to the sample. The estimate is still based on 500 people's views, so its precision is unchanged.

More Problem-Solving and Data Analysis questions

Not affiliated with the College Board. SAT is a trademark of the College Board.