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Sampling Distributions for Differences in Sample Proportions

AP Statistics· difficulty 3/5

Two independent samples: n₁ = 100 from population with p₁ = 0.5; n₂ = 200 from population with p₂ = 0.4.

σ_(p̂₁ − p̂₂) = √(p₁q₁/n₁ + p₂q₂/n₂)

What is the standard deviation of p̂₁ − p̂₂?

  • A

    ≈ 0.005

  • B

    ≈ 0.060

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  • C

    ≈ 0.10

  • D

    ≈ 0.030

Explanation

SD = √(0.5·0.5/100 + 0.4·0.6/200) = √(0.0025 + 0.0012) = √0.0037 ≈ 0.060.

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