Two polls of the same population asked the same question. Poll 1 surveyed 400 randomly selected people: 52% in favour, margin of error 5 points. Poll 2 surveyed 1,600 randomly selected people: 48% in favour, margin of error 2.5 points. Which conclusion is best supported?

Question

Accepted Answer

A. Both polls are consistent with support of about 50%; the gap between 52% and 48% is within their margins of error.. Poll 1's plausible range is 47% to 57%; Poll 2's is 45.5% to 50.5%. The ranges overlap around 47%–50.5%, so a single true value near 50% fits both.

Answer

B. Support fell from 52% to 48% between the two polls. — A 4-point gap is smaller than Poll 1's margin alone; it doesn't establish a change.

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C. Poll 2 must be flawed, because it disagrees with Poll 1. — The polls don't actually disagree once margins of error are taken into account.

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D. Support is exactly 50%. — 'Exactly' overstates it; the polls narrow the value to a range, not a point.

Problem-Solving and Data Analysis practice question

Answer: A. Both polls are consistent with support of about 50%; the gap between 52% and 48% is within their margins of error.

Why the other answers are wrong

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