AP Stats AP Stats Inference for Categorical Data 1 — Questions and Answers
Question 1: Which chi-square test is used to determine whether the distribution of a categorical variable matches a claimed distribution?
- Chi-square test for homogeneity
- Chi-square test for independence
- Chi-square goodness-of-fit test (Correct answer)
- Chi-square test for association
Correct answer: Chi-square goodness-of-fit test
The chi-square goodness-of-fit test compares an observed distribution to an expected (claimed) distribution for a single categorical variable.
Question 2: In a chi-square test, the expected count for each cell is calculated as:
- (row total × column total) / grand total (Correct answer)
- (observed − expected)² / expected
- observed / expected
- (row total + column total) / n
Correct answer: (row total × column total) / grand total
Expected cell count = (row total × column total) / grand total, ensuring marginal totals are preserved under the null hypothesis.
Question 3: What is the minimum expected cell count required in each cell before performing a chi-square test?
- 1
- 5 (Correct answer)
- 10
- 30
Correct answer: 5
AP Statistics requires all expected cell counts to be at least 5 for the chi-square approximation to be valid.
Question 4: A chi-square test for independence tests whether two categorical variables are independent. A very small p-value indicates:
- The variables are definitely not related
- There is strong evidence against independence (Correct answer)
- The sample size was too small
- The test statistic equals zero
Correct answer: There is strong evidence against independence
A small p-value provides strong evidence against the null hypothesis of independence, suggesting the two variables are associated.
Question 5: For a 3×4 contingency table, what are the degrees of freedom for the chi-square test for independence?
- 6 (Correct answer)
- 12
- 7
- 11
Correct answer: 6
Degrees of freedom = (rows − 1)(columns − 1) = (3 − 1)(4 − 1) = 2 × 3 = 6.
Question 6: Which condition is NOT required for a valid chi-square goodness-of-fit test?
- Random sample
- All expected counts ≥ 5
- Normal distribution of the variable (Correct answer)
- Independent observations
Correct answer: Normal distribution of the variable
The chi-square test applies to categorical data, so normality of the variable is irrelevant; the test uses counts, not means.
AP Stats AP Stats Inference for Categorical Data 1
Which chi-square test is used to determine whether the distribution of a categorical variable matches a claimed distribution?