AP Statistics · Topic 8.2
Setting Up a Chi-Square Goodness of Fit Test Practice
Part of Inference for Categorical Data: Chi-Square.(VAR-8.A)
Practice questions
16
Sample questions
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Sample 1difficulty 1/5
A goodness-of-fit test compares observed frequencies in 6 categories to a hypothesized distribution.
What are the degrees of freedom?
- A
4
- B
1
- C
6
- Dcheck_circle
5
Why
For a chi-square goodness-of-fit test, df = k - 1 where k is the number of categories. Here k = 6, so df = 5.
- A
Sample 2difficulty 2/5
A die is rolled 120 times. Under the null hypothesis the die is fair.
What is the expected count for each face under H0?
- A
10
- Bcheck_circle
20
- C
120
- D
60
Why
Under H0, each face is equally likely with probability 1/6. Expected count = 120 × (1/6) = 20.
- A
Sample 3difficulty 2/5
A researcher wants to perform a chi-square goodness-of-fit test on a categorical variable with 5 levels using a sample of 50 observations. The expected counts under H0 are 20, 15, 8, 4, 3.
Which condition is violated?
- A
Normality
- B
Random sample
- Ccheck_circle
Large counts (some E < 5)
- D
Independence
Why
The large-counts condition requires all expected counts >= 5. Here E = 4 and E = 3 fall below this threshold, so the condition is violated.
- A
Sample 4difficulty 2/5
Hypothesized distribution: 40% A, 30% B, 20% C, 10% D. Sample size n = 250.
What are the expected counts?
- A
125, 75, 25, 25
- B
62.5, 62.5, 62.5, 62.5
- Ccheck_circle
100, 75, 50, 25
- D
40, 30, 20, 10
Why
E_i = n × p_i. So 250×0.40=100, 250×0.30=75, 250×0.20=50, 250×0.10=25.
- A
Sample 5difficulty 2/5
A scientist samples 80 birds and records species. There are 5 species being studied.
A test that all five species are equally likely uses df = ?
- A
5
- B
3
- C
9
- Dcheck_circle
4
Why
For GOF with 5 categories, df = k - 1 = 4.
- A