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Constructing a Confidence Interval for a Population Proportion

AP Statistics· difficulty 2/5

A random sample of 400 voters finds 240 support a ballot measure. Conditions for inference are met.

0.552 p̂ = 0.60 0.648 95% CI for p

Which is the 95% confidence interval for the population proportion?

  • A

    (0.560, 0.640)

  • B

    (0.500, 0.700)

  • C

    (0.540, 0.660)

  • D

    (0.552, 0.648)

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Explanation

p̂ = 0.60. SE = sqrt(0.6·0.4/400) = 0.0245. ME = 1.96·0.0245 ≈ 0.048. CI: 0.60 ± 0.048 = (0.552, 0.648).

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