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

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

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

Question 1 of 7

A school administrator wants to estimate the proportion of students who are satisfied with the cafeteria's lunch options. A random sample of 150 students is surveyed, and each student is asked whether they are satisfied or not. Which of the following is the most appropriate inference procedure to construct a 95% confidence interval for the proportion of all students who are satisfied?

All Questions (7)

A school administrator wants to estimate the proportion of students who are satisfied with the cafeteria's lunch options. A random sample of 150 students is surveyed, and each student is asked whether they are satisfied or not. Which of the following is the most appropriate inference procedure to construct a 95% confidence interval for the proportion of all students who are satisfied?

A) A one-sample t-interval for a mean

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

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

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

Correct Answer: B

The data collected is categorical (satisfied or not satisfied), and the goal is to estimate a single population proportion from one random sample. Therefore, a one-sample z-interval for a proportion is the correct procedure. A t-interval is used for quantitative data (means), a two-sample interval is for comparing two groups, and a chi-square test is for analyzing counts across multiple categories, not for creating a confidence interval for a single proportion.

A pharmaceutical company has developed a new drug designed to lower blood pressure. To test its effectiveness, 80 patients with high blood pressure are recruited. Each patient's blood pressure is measured before they start the medication and again one month after starting the medication. The company wants to determine if there is convincing evidence that the drug lowers blood pressure. Which is the most appropriate statistical test?

A) A two-sample t-test for a difference of means

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

C) A paired t-test for a mean difference

D) A t-test for the slope of a regression line

Correct Answer: C

This is a matched pairs design because two measurements (before and after) are taken on each of the 80 subjects. The data are not independent samples. The data are quantitative (blood pressure readings). The appropriate procedure is to analyze the differences in blood pressure for each patient and perform a paired t-test for a mean difference. A two-sample t-test would be appropriate if there were two independent groups of patients (one receiving the drug, one a placebo).

A biologist wants to compare the average wingspan of a certain bird species in two different geographic regions. She collects a random sample of 40 birds from Region A and a separate random sample of 45 birds from Region B and measures their wingspans. Which of the following procedures should be used to determine if there is a significant difference in the mean wingspans between the two regions?

A) A paired t-test for a mean difference

B) A two-sample t-test for a difference of means

C) A chi-square test for homogeneity

D) A one-sample t-test for a mean

Correct Answer: B

The biologist is comparing a quantitative variable (wingspan) between two independent groups (birds from Region A and birds from Region B). The samples are independent because the selection of birds in one region does not affect the selection in the other. Therefore, a two-sample t-test for a difference of means is the most appropriate procedure. A paired t-test is incorrect because the data are not paired. A chi-square test is for categorical data.

A market research firm wants to know if there is an association between a person's preferred type of coffee (brewed, espresso, iced, blended) and their age group (18-30, 31-50, 51+). The firm surveys a single random sample of 500 coffee drinkers and records their preference and age group. Which inference procedure is most appropriate for this investigation?

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

B) A chi-square test for homogeneity

C) A chi-square test for independence

D) A two-sample t-test for a difference of means

Correct Answer: C

The study involves a single random sample from one population (coffee drinkers) and measures two categorical variables (preferred coffee type and age group). The goal is to determine if there is an association between these two variables. This is the definition of a chi-square test for independence. A test for homogeneity would be used if independent random samples were taken from each age group and their coffee preferences were compared. A goodness-of-fit test is used for one categorical variable from one sample.

A car manufacturer claims that its new hybrid model has a fuel efficiency distribution of 50% for city driving, 30% for highway driving, and 20% for mixed driving conditions. To test this claim, a consumer advocacy group randomly selects 200 owners of this model and records the primary type of driving they do. Which statistical test is most appropriate to determine if the observed driving type distribution is different from the one claimed by the manufacturer?

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

B) A chi-square test for homogeneity

C) A chi-square test for independence

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

Correct Answer: D

This scenario involves one sample (200 owners) of one categorical variable (primary driving type) and the goal is to compare the observed distribution of this variable to a hypothesized or claimed distribution (50%, 30%, 20%). This is the classic setup for a chi-square goodness-of-fit test. A test for homogeneity would compare distributions across multiple populations, and a test for independence would examine the association between two variables within one population.

A real estate agent wants to investigate if there is a significant linear relationship between the size of a house (in square feet) and its selling price (in dollars). The agent collects data on square footage and selling price for a random sample of 50 recently sold houses in a particular suburb. What is the most appropriate inference procedure to test the agent's hypothesis?

A) A two-sample t-test for a difference of means

B) A chi-square test of independence

C) A t-test for the slope of the regression line

D) A paired t-test for a mean difference

Correct Answer: C

The agent is examining the relationship between two quantitative variables (square footage and selling price) from a single sample of houses. The goal is to determine if the linear relationship is statistically significant. The appropriate procedure for this is a t-test for the slope of the regression line. A two-sample t-test would compare the means of two independent groups, and a chi-square test is for categorical data.

A sociologist is studying educational attainment levels in two different cities. They want to determine if the distribution of the highest level of education completed (High School, Bachelor's Degree, Master's Degree, Doctorate) is the same for the adult residents of City A and City B. They collect a random sample of 400 adults from City A and a separate random sample of 500 adults from City B. Which procedure should be used?

A) A chi-square test for independence

B) A chi-square test for homogeneity

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

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

Correct Answer: B

This study involves comparing the distribution of a single categorical variable (highest level of education) across two independent populations (City A and City B). The data are collected from two separate random samples. This is the correct setup for a chi-square test for homogeneity. A test for independence would be used if one sample was taken and two categorical variables were measured. A two-sample z-test would only be appropriate if the categorical variable had only two outcomes (e.g., has a degree vs. does not).