Problem-Solving and Data AnalysisHardInterpreting a margin of error
Problem-Solving and Data Analysis practice question
A random sample of 500 households finds that 36% own a bicycle, with a margin of error of 4 percentage points. Which of the following is the most appropriate conclusion?
- A. The percentage of ALL households that own a bicycle is plausibly between 32% and 40%.Correct
- B. Exactly 36% of all households own a bicycle.
- C. Between 32% and 40% of the 500 sampled households own a bicycle.
- D. 4% of households own a bicycle.
Answer: A. The percentage of ALL households that own a bicycle is plausibly between 32% and 40%.
The margin describes the uncertainty about the population percentage.
Why the other answers are wrong
- B. Exactly 36% of all households own a bicycle.
- 36% is the sample's figure; the population value is uncertain.
- C. Between 32% and 40% of the 500 sampled households own a bicycle.
- The sample's own percentage is known exactly: 36%.
- D. 4% of households own a bicycle.
- 4 points is the margin, not a percentage of owners.
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