PrepGo

AP Statistics Practice Quiz: Skills Focus: Selecting an Appropriate Inference Procedure for Categorical Data

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 7 questions to check your progress.

Question 1 of 7

A national health organization claims that 35% of adults in the United States have a pet dog. A sociologist believes this proportion is different in her large city. She obtains a random sample of 200 adults from the city and records whether or not they have a pet dog. Which of the following is the most appropriate inference procedure to test the sociologist's belief?

All Questions (7)

A national health organization claims that 35% of adults in the United States have a pet dog. A sociologist believes this proportion is different in her large city. She obtains a random sample of 200 adults from the city and records whether or not they have a pet dog. Which of the following is the most appropriate inference procedure to test the sociologist's belief?

A) A two-sample z-test for a difference in proportions

B) A chi-square goodness-of-fit test

C) A one-sample z-test for a proportion

D) A chi-square test for independence

Correct Answer: C

The sociologist is testing a claim about a single proportion (the proportion of adults in her city who have a pet dog) against a known or hypothesized value (the national claim of 35%). This involves one sample from one population. Therefore, a one-sample z-test for a proportion is the appropriate procedure.

A pharmaceutical company has developed a new allergy medication. To test its effectiveness, 300 volunteers with allergies are randomly assigned to one of two groups. One group receives the new medication, and the other group receives a placebo. After one week, each volunteer is asked if they experienced a significant reduction in their allergy symptoms. The company wants to determine if there is a difference in the proportion of people who experience symptom reduction between the two groups. What is the most appropriate statistical test?

A) A chi-square test for independence

B) A two-sample z-test for a difference in proportions

C) A one-sample z-interval for a proportion

D) A chi-square goodness-of-fit test

Correct Answer: B

This scenario involves comparing a categorical outcome (symptom reduction: yes/no) between two independent groups (medication and placebo) that were created through random assignment in an experiment. The goal is to compare the proportions of success in these two groups. A two-sample z-test for a difference in proportions is the correct procedure for this purpose. A chi-square test for homogeneity could also be used, but the z-test is specifically designed to compare two proportions.

A popular brand of candy claims that the color distribution in its bags is 20% red, 20% blue, 25% green, 15% yellow, and 20% orange. A student buys a large bag of the candy, counts the number of candies of each color, and wants to test if the color distribution in their bag matches the company's claim. Which inference procedure should the student use?

A) A one-sample z-test for a proportion

B) A chi-square test for homogeneity

C) A two-sample z-interval for a difference in proportions

D) A chi-square goodness-of-fit test

Correct Answer: D

The student is comparing the observed distribution of a single categorical variable (color) with more than two categories from a single sample to a hypothesized or expected distribution. A chi-square goodness-of-fit test is designed specifically for this purpose, to see how well the observed sample distribution 'fits' the claimed population distribution.

A researcher wants to investigate whether there is an association between a person's preferred genre of music (Rock, Pop, Hip-Hop, Country) and their preferred social media platform (Platform X, Platform Y, Platform Z). The researcher takes a single random sample of 500 young adults and asks them to identify their preferences for both categories. Which of the following is the most appropriate inference method to analyze this data?

A) A chi-square test for homogeneity

B) A series of one-sample z-tests for each music genre

C) A chi-square test for independence

D) A two-sample z-test for a difference in proportions

Correct Answer: C

This study involves a single random sample from one population (young adults). For each individual in the sample, two different categorical variables (music genre and social media platform) are recorded. The research question is about the relationship or association between these two variables within that single population. Therefore, a chi-square test for independence is the correct procedure.

An education researcher is interested in comparing the distribution of after-school activities (Sports, Arts, Academics, Work) for high school students in urban and rural school districts. The researcher selects a random sample of 200 students from an urban district and a separate random sample of 150 students from a rural district. They then categorize each student based on their primary after-school activity. Which procedure is most appropriate for determining if the distribution of activities is the same for the two types of school districts?

A) A chi-square test for independence

B) A chi-square goodness-of-fit test

C) A two-sample z-test for a difference in proportions

D) A chi-square test for homogeneity

Correct Answer: D

This study involves two separate, independent samples taken from two distinct populations (urban students and rural students). The researcher is comparing the distribution of a single categorical variable (after-school activity) across these two populations. The appropriate procedure to test if the distribution of a categorical variable is the same across two or more populations is the chi-square test for homogeneity.

A city's transit authority wants to gauge public support for a new bus line. They survey a random sample of 400 city residents and find that 250 of them are in favor of the new line. They wish to create an interval to capture the true proportion of all city residents who support the new line. Which of the following is the most appropriate procedure?

A) A one-sample z-interval for a proportion

B) A one-sample z-test for a proportion

C) A two-sample z-interval for a difference in proportions

D) A chi-square goodness-of-fit test

Correct Answer: A

The goal is to estimate a population parameter (the true proportion of all residents in favor) rather than to test a specific hypothesis about it. The phrase 'create an interval to capture the true proportion' indicates that a confidence interval is needed. Since there is only one sample from one population, a one-sample z-interval for a proportion is the correct procedure.

A political analyst wants to know if the approval rating of the current mayor is different between registered Democrats and registered Republicans. They obtain a random sample of 100 registered Democrats and a separate random sample of 100 registered Republicans, asking each person if they approve of the mayor's performance. Which of the following is the most appropriate method to determine if a statistically significant difference exists?

A) A chi-square test for independence, because there are two categorical variables: party affiliation and approval status.

B) A chi-square test for homogeneity, because the analyst is comparing the distribution of approval status across two populations.

C) A one-sample z-test for a proportion, because the overall approval rating is the primary interest.

D) A chi-square goodness-of-fit test, because the analyst is checking if the observed counts fit a particular model.

Correct Answer: B

The analyst has taken two independent samples from two distinct populations (Democrats and Republicans) and wants to compare the distribution of a single categorical variable (approval: yes/no) between them. This is the classic setup for a chi-square test for homogeneity. While a two-sample z-test for a difference in proportions would also be appropriate and is mathematically equivalent in this 2x2 case, the chi-square test for homogeneity is the best description among the choices provided, especially as it generalizes to more than two populations or more than two categories. Option A is incorrect because the sampling method (two separate samples) defines it as a test of homogeneity, not independence.