Confidence Intervals for the Difference of Two Proportions

AP Statistics· difficulty 3/5

p̂₁ = 0.50 (n₁=200), p̂₂ = 0.40 (n₂=200). 90% CI for p₁ − p₂.

SE = sqrt(0.5·0.5/200 + 0.4·0.6/200) ≈ 0.0492 z* = 1.645

What is the 90% CI?

  • A

    (0.019, 0.181)

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  • B

    (0.049, 0.151)

  • C

    (0.000, 0.200)

  • D

    (0.004, 0.196)

Explanation

0.10 ± 1.645·0.0492 = 0.10 ± 0.0809 ≈ (0.019, 0.181).

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