Problem-Solving and Data AnalysisVery hardMargin of error at a larger sample size
Problem-Solving and Data Analysis practice question
For a random sample of 100 people, a poll's margin of error is 6 percentage points. The margin of error shrinks in proportion to the square root of the sample size. With the same method, what would the margin of error be, in percentage points, for a random sample of 900 people?
Answer: 2
The sample is 9 times larger, and √9 = 3, so the margin of error is 3 times smaller: 6/3 = 2.
Common wrong answers
- If you answered 3
- 3 is the factor by which the margin shrinks, not the resulting margin.
- If you answered 18
- 18 multiplies by 3; a larger sample makes the margin SMALLER.
- If you answered 0.67
- 0.67 divides by 9, the ratio of the sample sizes, instead of by its square root, 3.
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