AP Statistics · Topic 6.4
Setting Up a Test for a Population Proportion Practice
Part of Inference for Categorical Data: Proportions.(VAR-6.B)
Practice questions
8
Sample questions
5 of 8 — sign in to practice the rest with adaptive difficulty and mastery tracking.
Sample 1difficulty 2/5
A manufacturer claims 90% of products pass inspection. A sample of 200 products has 170 passing. Test whether the true rate is less than 90%.
What is the test statistic z?
- A
−1.41
- B
−2.50
- C
−1.96
- Dcheck_circle
−2.36
Why
p̂ = 170/200 = 0.85. SE₀ = sqrt(0.9·0.1/200) = 0.0212. z = (0.85 − 0.90)/0.0212 ≈ −2.36.
- A
Sample 2difficulty 2/5
Hₐ: p > p₀ at α = 0.05.
The rejection region is:
- Acheck_circle
z > 1.645
- B
|z| > 1.96
- C
z > 1.96
- D
z < −1.645
Why
For right-sided test at α = 0.05, reject if z > 1.645.
- A
Sample 3difficulty 2/5
Manufacturer claims defect rate is at most 2%.
To test the manufacturer's claim, set:
- A
H₀: p > 0.02, Hₐ: p ≤ 0.02
- B
H₀: p = 0.02, Hₐ: p < 0.02
- C
H₀: p̂ = 0.02, Hₐ: p̂ > 0.02
- Dcheck_circle
H₀: p = 0.02, Hₐ: p > 0.02
Why
To test if defect rate exceeds 2% (manufacturer's max claim violated), Hₐ: p > 0.02.
- A
Sample 4difficulty 2/5
Test H₀: p = 0.5 with n = 400.
What is SE₀?
- A
0.0500
- B
0.0125
- C
0.0006
- Dcheck_circle
0.025
Why
SE₀ = sqrt(0.5·0.5/400) = sqrt(0.000625) = 0.025.
- A
Sample 5difficulty 2/5
A teacher wants to test whether more than 60% of students prefer online learning.
Which is the correct setup?
- A
H₀: p̂ = 0.60, Hₐ: p̂ > 0.60
- B
H₀: p ≠ 0.60, Hₐ: p = 0.60
- C
H₀: p > 0.60, Hₐ: p = 0.60
- Dcheck_circle
H₀: p = 0.60, Hₐ: p > 0.60
Why
H₀ is equality; Hₐ matches the research claim ("more than 60%"); use the parameter p.
- A