Problem-Solving and Data AnalysisMediumInterpreting a margin of error
Problem-Solving and Data Analysis practice question
A random sample of 400 residents of a city was surveyed, and 52% said they support a new park. The margin of error for the estimate is 4 percentage points. Which of the following is the most appropriate conclusion?
- A. It is plausible that between 48% and 56% of all the city's residents support the new park.Correct
- B. Exactly 52% of all the city's residents support the new park.
- C. 4% of the city's residents oppose the new park.
- D. If 800 residents had been surveyed, the margin of error would have been 8 percentage points.
Answer: A. It is plausible that between 48% and 56% of all the city's residents support the new park.
The margin of error gives a plausible range around the sample estimate: 52% ± 4%, or 48% to 56%, for the whole population.
Why the other answers are wrong
- B. Exactly 52% of all the city's residents support the new park.
- A sample estimates the population value; it doesn't fix it exactly.
- C. 4% of the city's residents oppose the new park.
- The margin of error is not a share of opponents.
- D. If 800 residents had been surveyed, the margin of error would have been 8 percentage points.
- A larger sample gives a smaller margin of error, not a larger one.
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