AP Statistics Flashcards: Skills Focus: Selecting an Appropriate Inference Procedure for Categorical Data
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
How do you distinguish between one-variable and two-variable categorical data scenarios when selecting a test?
One-variable scenarios, which use a goodness-of-fit test, involve a single categorical variable from one sample. Two-variable scenarios involve either two variables from one sample (independence test) or one variable from two or more samples (homogeneity test).
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How do you distinguish between one-variable and two-variable categorical data scenarios when selecting a test?
One-variable scenarios, which use a goodness-of-fit test, involve a single categorical variable from one sample. Two-variable scenarios involve either two variables from one sample (independence test) or one variable from two or more samples (homogeneity test).
When can a two-sample z-test for proportions and a chi-square test for homogeneity both be used?
When comparing the proportions of a categorical variable with only two outcomes across two independent groups, both tests are mathematically equivalent and will yield the same conclusion. The chi-square test is more versatile as it can handle more than two categories or groups.
When is a one-sample z-test for a proportion used for categorical data?
This test is used when you want to test a claim about a single population proportion based on data from one sample, where the categorical variable has only two possible outcomes.
A national survey asked a random sample of 1,000 adults their favorite season (Winter, Spring, Summer, Fall) to see if preferences are equally distributed. What test should be used?
A chi-square test for goodness of fit is appropriate to compare the observed distribution of favorite seasons to a hypothesized uniform distribution (25% for each season).
What is the key difference between a chi-square test for homogeneity and a chi-square test for independence?
A test for homogeneity compares the distribution of one categorical variable across two or more populations, while a test for independence assesses if there is an association between two categorical variables within a single population.
A researcher wants to know if the proportion of students who prefer online classes is different between undergraduate and graduate students. What is the most appropriate inference procedure?
A two-sample z-test for a difference in proportions should be used, as it compares a proportion between two independent groups (undergraduates and graduates).
To see if the distribution of car types (Sedan, SUV, Truck) is the same in the North and South regions of a country, random samples of car registrations are taken from each region. What test is appropriate?
A chi-square test for homogeneity is used because it compares the distribution of a single categorical variable (car type) across two different populations (North and South regions).
What is the purpose of a chi-square test for goodness of fit?
It is used to determine if the observed distribution of a single categorical variable from one sample matches a hypothesized or claimed distribution.
A survey of 500 randomly selected high school students asks about their grade level and whether they have a part-time job. What test determines if having a part-time job is associated with grade level?
A chi-square test for independence should be used to determine if there is a statistically significant association between two categorical variables (grade level and job status) within a single sample.
What is the 'Large Counts' condition for chi-square tests?
The condition requires that all expected counts must be at least 5. This ensures that the sampling distribution of the chi-square statistic is well-approximated by a chi-square distribution.