AP Statistics Practice Quiz: Setting Up a Chi-Square Test for Homogeneity or Independence
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Test your understanding with short quizzes. This quiz has 16 questions to check your progress.
Question 1 of 16
All Questions (16)
A) There is no difference in the distribution of favorite music genres across the three cities.
B) There is an association between city and favorite music genre.
C) The observed counts of favorite music genres are equal to the expected counts.
D) There is a difference in the distribution of favorite music genres across the three cities.
Correct Answer: A
Based on the provided content, for a chi-square test for homogeneity, the null hypothesis (H0) states that there is no difference in the distributions of a categorical variable across different populations or treatments. Option D is the alternative hypothesis.
A) There is no difference in the distribution of pet ownership across education levels.
B) There is no association between the highest level of education and pet ownership for adults in this population.
C) There is an association between the highest level of education and pet ownership for adults in this population.
D) The distribution of pet ownership is different for each education level.
Correct Answer: B
The provided content states that for a chi-square test for independence, the null hypothesis (H0) states there is no association between two categorical variables. This scenario involves one population and two variables, making it a test for independence.
A) A chi-square test for goodness-of-fit.
B) A chi-square test for independence.
C) A chi-square test for homogeneity.
D) A two-sample z-test for proportions.
Correct Answer: C
The content specifies that a chi-square test for homogeneity compares distributions of a categorical variable (personality type) from different populations (cat owners and dog owners). Since there are two separate samples from two distinct populations, the test for homogeneity is appropriate.
A) All observed counts in the two-way table must be at least 5.
B) The total sample size must be at least 5.
C) All expected counts in the two-way table must be at least 5.
D) The number of categories for each variable must be at least 5.
Correct Answer: C
The provided content explicitly states that for chi-square tests on two-way tables, the Large Counts condition requires that all expected counts are greater than or equal to 5. It is a common mistake to check the observed counts instead of the expected counts.
A) There is no association between preferred social media platform and primary news source.
B) There is an association between preferred social media platform and primary news source.
C) The distribution of primary news sources is the same for all social media platforms.
D) The distribution of primary news sources is different for at least one social media platform.
Correct Answer: B
The null hypothesis for a test of independence states there is no association. The alternative hypothesis is the opposite of the null, stating that there is an association between the two categorical variables.
A) Comparing the distribution of political affiliations among random samples of voters from four different states.
B) Determining if a single six-sided die is fair by rolling it 60 times and counting the outcomes.
C) Investigating if there is a relationship between gender and opinion on a new school policy, based on a single random sample of 300 students.
D) Comparing the effectiveness of three different fertilizers by measuring the proportion of plants that survive for each treatment group.
Correct Answer: C
The content states that a chi-square test for independence assesses whether two categorical variables are associated in a single population. This scenario uses one sample to examine the relationship between two variables (gender and opinion), which is the definition of a test for independence. Option A describes a test for homogeneity.
A) The data must come from a Normal distribution.
B) The samples or observations must be independent.
C) The sample sizes for each group must be equal.
D) The relationship between the variables must be linear.
Correct Answer: B
The provided content specifies two conditions for chi-square tests on two-way tables: independence and large counts. The independence condition refers to the method of data collection (e.g., random sampling).
A) There is no difference in the distribution of patient outcomes between the drug and placebo groups.
B) There is no association between the treatment received and patient outcome.
C) The distribution of patient outcomes is the same for the drug and placebo groups.
D) There is a difference in the distribution of patient outcomes between the drug and placebo groups.
Correct Answer: D
The null hypothesis for a test of homogeneity states there is no difference in distributions. The alternative hypothesis (Ha) is the statement we are trying to find evidence for, which is that there is a difference in the distribution of outcomes between the two treatment groups (populations).
A) A single quantitative variable.
B) The relationship between two quantitative variables.
C) Data from a two-way table of categorical variables.
D) Paired quantitative data.
Correct Answer: C
The content indicates that the appropriate testing method for comparing distributions in two-way tables is a chi-square test. These tables are used to organize categorical data.
A) Determine if two categorical variables are associated within a single population.
B) Compare the distributions of a single categorical variable across two or more distinct populations or treatments.
C) Test if the observed distribution of a single categorical variable matches a hypothesized distribution.
D) Estimate the true difference between two population proportions.
Correct Answer: B
The provided content defines the chi-square test for homogeneity as a method to compare distributions of a categorical variable from different populations. This distinguishes it from the test for independence, which uses one population.
A) Determine if the distribution of a categorical variable is the same across multiple populations.
B) Assess whether an association exists between two categorical variables within a single population.
C) Compare the means of a quantitative variable across several groups.
D) Check if a sample's proportions match a known set of population proportions.
Correct Answer: B
The provided content defines the chi-square test for independence as a method to assess whether two categorical variables are associated in a single population. This distinguishes it from the test for homogeneity, which uses multiple populations.
A) The researcher can proceed with the test because the observed count might be 5 or more.
B) The researcher cannot proceed with the test because the Large Counts condition is not met.
C) The researcher can proceed with the test as long as the total sample size is large.
D) The researcher cannot proceed with the test because the independence condition is not met.
Correct Answer: B
The content specifies that a critical condition for chi-square tests is that all expected counts must be greater than or equal to 5. An expected count of 3.8 violates this condition, making the results of the test unreliable. The condition applies to expected, not observed, counts.
A) I is for homogeneity, II is for independence.
B) I is for independence, II is for homogeneity.
C) Both I and II are for a test of independence.
D) Both I and II are for a test of homogeneity.
Correct Answer: B
The content states that for a test of independence, H0 says there is no association. For a test of homogeneity, H0 says there is no difference in distributions across populations. Therefore, hypothesis I is for a test of independence, and hypothesis II is for a test of homogeneity.
A) Calculating the expected counts for each cell.
B) Verifying the Large Counts condition.
C) Identifying and stating the null and alternative hypotheses.
D) Computing the chi-square test statistic.
Correct Answer: C
The first step in any hypothesis test, including a chi-square test, is to identify and state the appropriate null and alternative hypotheses that frame the research question. All other steps, such as checking conditions and calculating statistics, follow.
A) The independence of the two categorical variables being studied.
B) The independence of the individual observations within the sample.
C) The independence of the rows and columns in the two-way table.
D) The independence of the expected counts from the observed counts.
Correct Answer: B
The "independence" condition for inference refers to the data collection method. It requires that individual observations are independent of each other (e.g., from a random sample). The test itself is used to determine if the two variables are independent, which is what is stated in the null hypothesis.
A) Test for independence; H0: There is no association between university and study environment preference.
B) Test for homogeneity; H0: There is no association between university and study environment preference.
C) Test for independence; H0: There is no difference in the distribution of study environment preferences between the two universities.
D) Test for homogeneity; H0: There is no difference in the distribution of study environment preferences between the two universities.
Correct Answer: D
Since the data come from two separate random samples from two different populations (University A and University B), a chi-square test for homogeneity is appropriate. The null hypothesis for this test states that there is no difference in the distributions of the categorical variable (study preference) across the two populations.