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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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
- Ccheck_circle
1.6
- D
2.0
Why
SE = √(36/25 + 25/25) = √(1.44 + 1) = √2.44 ≈ 1.56.
- A
Sample 2difficulty 4/5
Continuing: t-statistic for H₀: μ₁ = μ₂ ≈
- A
3.0
- B
1.0
- Ccheck_circle
1.9
- D
5.0
Why
t = (50 − 47)/1.56 ≈ 1.92.
- A
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
- Ccheck_circle
Fail to reject H₀ — not enough evidence to conclude μ₁ ≠ μ₂
- D
Accept H₀
Why
p-value > α → fail to reject (insufficient evidence).
- A