AP Statistics Flashcards: Setting Up a Chi-Square Test for Homogeneity or Independence
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 14 cards to help you master important concepts.
How is the 'Large Counts' condition met for a chi-square test for independence or homogeneity?
The Large Counts condition is met when all calculated expected counts are greater than or equal to 5.
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How is the 'Large Counts' condition met for a chi-square test for independence or homogeneity?
The Large Counts condition is met when all calculated expected counts are greater than or equal to 5.
What is the alternative hypothesis (Ha) for a chi-square test for homogeneity?
The alternative hypothesis states that there is a difference in the distributions of the categorical variable across the populations or treatments.
What is the null hypothesis (H0) for a chi-square test for homogeneity?
H0 states that there is no difference in the distributions of a categorical variable across the different populations or treatments.
To see if a new teaching method is effective, a researcher compares the distribution of final grades (A, B, C, D, F) for a group taught with the new method versus a group taught with the old method. Which chi-square test is appropriate?
A chi-square test for homogeneity is appropriate because it compares the distribution of one variable (final grades) across two different populations (treatment groups).
What is the primary purpose of a chi-square test for homogeneity?
This test is used to compare the distributions of a single categorical variable from two or more different populations or treatment groups.
During a chi-square test, you calculate an expected count of 3.8 for one of the cells. What condition has been violated?
The Large Counts condition has been violated, as it requires all expected counts to be 5 or greater.
What is the primary purpose of a chi-square test for independence?
This test is used to assess whether two categorical variables are associated with each other within a single population.
What is the null hypothesis (H0) for a chi-square test for independence?
H0 states that there is no association between the two categorical variables being studied in a population.
A researcher surveys a single random sample of 500 voters to see if there is a relationship between their political affiliation and their opinion on a new law. Which chi-square test is appropriate?
A chi-square test for independence is appropriate because it assesses the association between two variables (political affiliation and opinion) in a single population.
What type of variables are analyzed in a two-way table for a chi-square test?
Chi-square tests for homogeneity and independence are used to analyze two-way tables of categorical data.
What is the alternative hypothesis (Ha) for a chi-square test for independence?
The alternative hypothesis states that there is an association between the two categorical variables in the population.
What is the appropriate testing method for comparing distributions of categorical data organized in a two-way table?
An appropriate method is a chi-square test for homogeneity or a chi-square test for independence.
What is the key difference in the sampling method between a test for homogeneity and a test for independence?
A test for homogeneity involves sampling from multiple distinct populations, while a test for independence involves taking a single sample from one population.
What are the two conditions that must be verified for chi-square tests on two-way tables?
The two conditions to check are the Independence condition and the Large Counts condition.