AP Statistics · Topic 7.8
Setting Up a Test for the Difference of Two Population Means Practice
Part of Inference for Quantitative Data: Means.(VAR-7.C)
Practice questions
6
Sample questions
5 of 6 — sign in to practice the rest with adaptive difficulty and mastery tracking.
Sample 1difficulty 4/5
Welch's two-sample t df is
- A
n₁ − 1
- B
n₁ + n₂ − 2
- C
n₁ + n₂
- Dcheck_circle
Approximate, by Welch-Satterthwaite formula
Why
Unpooled t uses an approximate df formula (often computed by software).
- A
Sample 2difficulty 4/5
Two-sample t requires the two samples to be
- A
Drawn from one population
- B
Same size
- Ccheck_circle
Independent of each other
- D
Sorted
Why
Independence is essential; otherwise variance addition fails.
- A
Sample 3difficulty 4/5
Two-sample t CI for μ₁ − μ₂ uses SE
- A
s/√(n₁ + n₂)
- Bcheck_circle
√(s₁²/n₁ + s₂²/n₂)
- C
(s₁ + s₂)/√n
- D
s_pooled
Why
Welch unpooled SE: each sample's SE squared, summed, square root.
- A
Sample 4difficulty 4/5
For two-sample t with n₁ = n₂ = 25 and s₁ = s₂ = 4, SE(x̄₁ − x̄₂) =
- A
2.0
- B
0.8
- Ccheck_circle
1.13
- D
1.6
Why
SE = √(16/25 + 16/25) = √1.28 ≈ 1.13.
- A
Sample 5difficulty 4/5
H₀ for comparing two means is most often
- A
μ₁ ≠ μ₂
- B
μ₁ < μ₂
- C
μ₁ > μ₂
- Dcheck_circle
μ₁ = μ₂
Why
Null = no difference; H_a varies (one or two-sided).
- A