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Confidence Intervals for the Difference of Two Proportions

AP Statistics· difficulty 3/5

Group A: 80 successes in 200. Group B: 60 successes in 200. Conditions met.

p̂_A = 0.40, p̂_B = 0.30 p̂_A − p̂_B = 0.10 SE = sqrt(0.4·0.6/200 + 0.3·0.7/200) ≈ 0.0476

What is the 95% CI for p_A − p_B?

  • A

    (0.020, 0.180)

  • B

    (0.050, 0.150)

  • C

    (0.007, 0.193)

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  • D

    (−0.093, 0.293)

Explanation

Difference 0.10 ± 1.96·0.0476 = 0.10 ± 0.0933 ≈ (0.007, 0.193).

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