Problem-Solving and Data AnalysisVery hardOverstating certainty from a poll
Problem-Solving and Data Analysis practice question
A poll of 1,000 randomly selected adults found that 62% oppose a policy, with a margin of error of 3 percentage points. A headline reads: 'Nearly two-thirds of the country oppose the policy — the result is beyond doubt.' Which criticism of the headline is most valid?
- A. The result is well supported, but 'beyond doubt' overstates it: the true percentage could plausibly be anywhere from 59% to 65%.Correct
- B. A sample of 1,000 people is far too small to say anything about a whole country.
- C. The poll should have surveyed every adult in the country.
- D. Random selection of respondents makes the result invalid.
Answer: A. The result is well supported, but 'beyond doubt' overstates it: the true percentage could plausibly be anywhere from 59% to 65%.
A random sample supports an estimate with a margin of error, never certainty. The headline's 'beyond doubt' ignores the ±3 points.
Why the other answers are wrong
- B. A sample of 1,000 people is far too small to say anything about a whole country.
- 1,000 randomly selected people give a margin of about 3 points, which is quite precise.
- C. The poll should have surveyed every adult in the country.
- Surveying everyone is neither necessary nor practical; sampling works, within its margin.
- D. Random selection of respondents makes the result invalid.
- Random selection is what makes the result VALID for the population.
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