Sampling Distributions for Differences in Sample Means

AP Statistics· difficulty 3/5

Population 1 has μ₁ = 70, σ₁ = 8. Population 2 has μ₂ = 65, σ₂ = 6. Independent samples of n₁ = 25 and n₂ = 36 are drawn.

μ_(x̄₁ − x̄₂) = μ₁ − μ₂

What is the mean and standard deviation of the sampling distribution of x̄₁ − x̄₂?

  • A

    Mean 5; SD √(64/25 + 36/36) ≈ 1.92

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  • B

    Mean 5; SD 8/√25 + 6/√36

  • C

    Mean 5; SD 14/√61

  • D

    Mean 0; SD 14

Explanation

Mean = μ₁ − μ₂ = 5. SD = √(σ₁²/n₁ + σ₂²/n₂) = √(64/25 + 36/36) = √(2.56 + 1) ≈ 1.92.

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