AP Statistics · Topic 7.9

Carrying Out a Test for the Difference of Two Population Means Practice

Part of Inference for Quantitative Data: Means.(VAR-7.D)

Practice questions

3

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Sample questions

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  1. Sample 1difficulty 4/5

    n₁ = 25, x̄₁ = 50, s₁ = 6; n₂ = 25, x̄₂ = 47, s₂ = 5. SE for x̄₁ − x̄₂ ≈

    • A

      0.5

    • B

      3.0

    • C

      1.6

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    • D

      2.0

    Why

    SE = √(36/25 + 25/25) = √(1.44 + 1) = √2.44 ≈ 1.56.

  2. Sample 2difficulty 4/5

    Continuing: t-statistic for H₀: μ₁ = μ₂ ≈

    • A

      3.0

    • B

      1.0

    • C

      1.9

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    • D

      5.0

    Why

    t = (50 − 47)/1.56 ≈ 1.92.

  3. Sample 3difficulty 4/5

    Continuing: at α = 0.05 two-sided, with conservative df = 24, the p-value (~0.07) leads to

    • A

      Need larger n

    • B

      Reject H₀

    • C

      Fail to reject H₀ — not enough evidence to conclude μ₁ ≠ μ₂

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    • D

      Accept H₀

    Why

    p-value > α → fail to reject (insufficient evidence).