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Confidence Intervals for the Difference of Two Proportions

AP Statistics· difficulty 3/5

Sample A: 25 of 50. Sample B: 15 of 50.

p̂_A = 0.5, p̂_B = 0.3 SE_unpooled = sqrt(0.5·0.5/50 + 0.3·0.7/50) ≈ 0.0954

What is the 95% CI for p_A − p_B?

  • A

    (0.105, 0.295)

  • B

    (0.000, 0.400)

  • C

    (0.013, 0.387)

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  • D

    (−0.087, 0.487)

Explanation

Difference 0.20 ± 1.96·0.0954 = 0.20 ± 0.187 ≈ (0.013, 0.387).

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