Free forever Calculate score
AP Stats · Unit 8 Progress Check

AP Statistics Unit 8 Progress Check Inference for Categorical Data: Chi-Square walkthrough.

AP Statistics Unit 8 is chi-square inference, and the Unit 8 Progress Check MCQ tests whether you can pick the right one of three chi-square tests and check its conditions. This walkthrough covers what the questions ask, the traps, and how to reason through them. Explanations only — no AP Classroom answer keys.

Updated August 2026Written by Mahmudul HasanFree · No signup

What Unit 8 covers

Unit 8 is Inference for Categorical Data: Chi-Square. Inference: chi-square is roughly 2–5% of the AP Statistics exam but a common free-response topic.

The chi-square statistic
Σ(observed − expected)²/expected, and what it measures.
Goodness-of-fit test
Comparing one categorical variable’s distribution against a claimed model.
Test for independence
Testing whether two categorical variables are associated within one sample.
Test for homogeneity
Comparing the distribution of one variable across several populations.
Expected counts
Computing them, and the condition that all be at least 5.
Degrees of freedom
Different formula for each of the three tests.

The Progress Check MCQ: what each question type tests

These are the question patterns that recur on this Progress Check, and what each one is really asking.

Which chi-square test?
One variable against a model is goodness-of-fit; two variables in one sample is independence; one variable across groups is homogeneity.
Compute expected counts
For a two-way table, row total times column total divided by grand total.
Degrees of freedom
Goodness-of-fit: categories minus 1. Two-way tables: (rows minus 1)(columns minus 1).
Condition checking
All expected counts at least 5, plus random and independence conditions.
Interpret the result
A large statistic and small P-value are evidence against the null of no difference or no association.

The Progress Check FRQ

Unit 8 free response gives a table and asks you to run the appropriate chi-square test. Points come from choosing the right test, computing expected counts, checking that all are at least 5, calculating the statistic and degrees of freedom, and stating a conclusion in context linked to the P-value.

Where students lose the most points

Picking the wrong chi-square test
The three are distinguished by how the data were collected, not by the numbers.
Using observed counts to check the condition
The condition is about expected counts being at least 5.
Wrong degrees of freedom
Goodness-of-fit and two-way tables use different formulas.
Confusing independence and homogeneity
Independence is one sample and two variables; homogeneity is several samples and one variable.
Concluding causation
A significant chi-square shows association, not cause.

How to work through this unit

Before any chi-square question, decide the test from how the data were collected: one sample and one variable, one sample and two variables, or several samples. The design picks the test.

Once you have finished the Progress Check, put your raw score into our AP Statistics Calculator to see roughly where that pace puts you on the 1–5 scale, and use the AP Statistics Review for the full exam format and study plan.

Frequently asked questions

Quick answers — written by humans, not a chatbot.

What does the AP Statistics Unit 8 Progress Check cover?

Chi-square inference: the chi-square statistic, the goodness-of-fit test, the test for independence, the test for homogeneity, expected counts, and degrees of freedom.

How do I choose between the three chi-square tests?

By the study design. One variable compared to a model is goodness-of-fit, two variables from one sample is a test for independence, and one variable compared across several samples is a test for homogeneity.

What is the condition for a chi-square test?

All expected counts must be at least 5, along with the random and independence conditions. The condition is about expected counts, not observed counts.

Do you publish AP Statistics Unit 8 answer keys?

No. We publish walkthroughs of the reasoning and traps rather than AP Classroom answers.

Related

Keep going.

Scroll to Top