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Problem-Solving and Data AnalysisVery hardWhat a margin of error does and does not say

Problem-Solving and Data Analysis practice question

A random sample of 400 households in a city found that 36% recycle weekly, with a margin of error of 5 percentage points at the 95% confidence level. Which of the following is the most appropriate conclusion?

  1. A. It is plausible that between 31% and 41% of all households in the city recycle weekly.Correct
  2. B. Exactly 36% of all households in the city recycle weekly.
  3. C. Between 31% and 41% of the 400 sampled households recycle weekly.
  4. D. 95% of the city's households recycle between 31% and 41% of their waste.

Answer: A. It is plausible that between 31% and 41% of all households in the city recycle weekly.

The margin of error gives a plausible interval, 36% ± 5, for the population proportion.

Why the other answers are wrong

B. Exactly 36% of all households in the city recycle weekly.
A sample cannot pin down the population proportion exactly.
C. Between 31% and 41% of the 400 sampled households recycle weekly.
The sample proportion is known exactly (36%); the interval is about the population.
D. 95% of the city's households recycle between 31% and 41% of their waste.
This misreads the confidence level as a share of households and the percentages as waste amounts.

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