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Problem-Solving and Data AnalysisVery hardInterpreting a poll with a margin of error

Problem-Solving and Data Analysis practice question

A poll of 400 randomly selected voters estimates support for a measure at 52 percent, with a margin of error of 5 percentage points. Which of the following is the most appropriate conclusion?

  1. A. Support among all voters is plausibly anywhere from 47 to 57 percent, so the poll cannot establish whether a majority supports the measure.Correct
  2. B. Exactly 52 percent of all voters support the measure.
  3. C. A majority of all voters supports the measure.
  4. D. Between 47 and 57 percent of the 400 voters polled support the measure.

Answer: A. Support among all voters is plausibly anywhere from 47 to 57 percent, so the poll cannot establish whether a majority supports the measure.

The interval 47 to 57 percent includes values below and above 50 percent.

Why the other answers are wrong

B. Exactly 52 percent of all voters support the measure.
A poll estimates; it does not give an exact population figure.
C. A majority of all voters supports the measure.
The interval includes values below 50 percent.
D. Between 47 and 57 percent of the 400 voters polled support the measure.
The margin of error applies to the population, not to the sample, where the figure is exactly 52 percent.

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