AP Stats AP Stats Inference for Categorical Data 2

Question 1

The chi-square test statistic is calculated as the sum of which values across all cells?

Accepted Answer

(O − E)² / E

Answer

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?

Accepted Answer

Party affiliation and region are independent

Answer

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?

Accepted Answer

Chi-square test for homogeneity

Answer

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:

Accepted Answer

A large discrepancy between observed and expected in that cell

Answer

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?

Accepted Answer

When comparing exactly two proportions from two independent groups

Answer

The two-proportion z-test is used specifically when comparing two proportions from two independent groups and allows for one-sided alternatives.

AP Practice Test

AP Practice Test

AP Stats AP Stats Inference for Categorical Data 2