AP Statistics · Topic 6.10
Tests for the Difference of Two Proportions Practice
Part of Inference for Categorical Data: Proportions.(VAR-6.E)
Practice questions
9
Sample questions
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Sample 1difficulty 2/5
Hₐ: p ≠ p₀ at α = 0.05.
The rejection region is:
- A
z < −1.96
- B
|z| > 1.645
- C
z > 1.96
- Dcheck_circle
|z| > 1.96
Why
For two-sided test at α = 0.05, reject if |z| > 1.96.
- A
Sample 2difficulty 3/5
For two-sample inference about proportions.
Why pool for the test but not the CI?
- Acheck_circle
The null assumes p₁ = p₂; pooling gives best estimate of the common proportion.
- B
Pooling violates assumptions for CIs.
- C
Pooling reduces df.
- D
Unpooled is always more conservative.
Why
Under H₀, the proportions are equal, so we use pooled p̂_p. The CI does not assume equality.
- A
Sample 3difficulty 3/5
Sample 1: 110 of 200. Sample 2: 90 of 200. Test H₀: p₁ = p₂ vs Hₐ: p₁ ≠ p₂.
What is z?
- A
1.00
- B
4.00
- Ccheck_circle
2.00
- D
0.50
Why
z = (0.55 − 0.45)/0.05 = 2.00.
- A
Sample 4difficulty 3/5
Two independent random samples are used to compare proportions p₁ and p₂.
For a two-sample z-test for proportions, the Large Counts condition uses:
- A
Each sample's own p̂ only.
- B
Only n₁ and the average proportion.
- C
The smaller of p̂₁ and p̂₂.
- Dcheck_circle
The pooled proportion p̂_p applied to both n₁ and n₂.
Why
For the test (under H₀: p₁ = p₂), conditions use the pooled proportion applied to each sample size.
- A
Sample 5difficulty 3/5
Test H₀: p = 0.20 with sample n = 100, p̂ = 0.25.
What is the standard error used in the test?
- A
0.0433
- B
0.020
- C
0.050
- Dcheck_circle
0.040
Why
SE₀ uses p₀: sqrt(0.20·0.80/100) = sqrt(0.0016) = 0.040.
- A