AP Stats AP Stats Inference for Categorical Data 2 — Questions and Answers
Question 1: The chi-square test statistic is calculated as the sum of which values across all cells?
- (O − E) / E
- (O − E)² / E (Correct answer)
- (O − E)² / O
- (O + E)² / E
Correct answer: (O − E)² / E
The chi-square statistic = Σ(O − E)² / E, summing the squared standardized residuals over all cells.
Question 2: A researcher tests whether political party affiliation is independent of region in the US using a 3×4 table of 600 respondents. What is the null hypothesis?
- Party affiliation and region are associated
- Party affiliation and region are independent (Correct answer)
- Party affiliation differs by region
- Region affects party affiliation
Correct answer: Party affiliation and region are independent
The null hypothesis for a chi-square test for independence states that the two categorical variables are independent (not associated).
Question 3: Which test should be used when comparing the distribution of a categorical variable across two or more independent groups?
- Chi-square goodness-of-fit test
- Chi-square test for independence
- Chi-square test for homogeneity (Correct answer)
- Two-proportion z-test
Correct answer: Chi-square test for homogeneity
The chi-square test for homogeneity compares the distribution of a categorical variable across multiple independent populations or groups.
Question 4: In a two-way table, a standardized residual greater than 2 or less than −2 suggests:
- That cell contributes little to the chi-square statistic
- A large discrepancy between observed and expected in that cell (Correct answer)
- The overall test is not significant
- The sample size is too large
Correct answer: A large discrepancy between observed and expected in that cell
Standardized residuals beyond ±2 indicate cells where observed counts differ substantially from expected, contributing heavily to a significant chi-square result.
Question 5: When is it appropriate to use a two-proportion z-test instead of a chi-square test?
- When comparing more than two proportions
- When comparing exactly two proportions from two independent groups (Correct answer)
- When the variable has more than two categories
- When sample sizes are less than 30
Correct answer: When comparing exactly two proportions from two independent groups
The two-proportion z-test is used specifically when comparing two proportions from two independent groups and allows for one-sided alternatives.
Question 6: A chi-square test yields χ² = 0.12 with df = 4. What can you conclude?
- Strong evidence against the null hypothesis
- Very little evidence against the null hypothesis (Correct answer)
- The sample size was too small to detect differences
- The expected counts were all zero
Correct answer: Very little evidence against the null hypothesis
A chi-square statistic of 0.12 with 4 degrees of freedom produces a very large p-value, providing almost no evidence against the null hypothesis.
AP Stats AP Stats Inference for Categorical Data 2
The chi-square test statistic is calculated as the sum of which values across all cells?