Question bank / Inference from sample statistics and margin of error

Math · Problem-Solving and Data AnalysisHard

In a random sample of 400400 likely voters in a city, 52%52\% said they support candidate A for mayor. The margin of error for the estimate is 55 percentage points. Which of the following is the most appropriate conclusion?

A

A majority of all likely voters in the city support candidate A.

B

Exactly 52%52\% of all likely voters in the city support candidate A.

C

Fewer than half of all likely voters in the city support candidate A.

D

The poll does not provide convincing evidence that a majority of all likely voters in the city support candidate A.

Show answer and explanation

Answer: D

The plausible values for the population percentage are 52%±5%52\% \pm 5\%, or 47%47\% to 57%57\%. This interval includes values below 50%50\% as well as above 50%50\%. So it is plausible that a majority supports candidate A, but it is also plausible that a majority doesn't; the poll is not convincing either way.

Choice A is tempting because the sample percentage is above 50%50\%, but the interval of plausible values extends below 50%50\%.

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