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Inference for Categorical Data: Chi-Square — HS Statistics practice questions

14 multiple-choice questions and 5 flashcards on Inference for Categorical Data: Chi-Square, about 9% of the HS Statistics bank. Every one carries a written rationale.

Written and maintained by the CoStudy team · last updated 2026-10-02 · how we write and review questions

What this chapter covers

Inference for Categorical Data: Chi-Square is one of 7 chapters in CoStudy's HS Statistics bank, and it holds 14 of the bank's 150 multiple-choice questions — roughly 9% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.

Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.

Free Inference for Categorical Data: Chi-Square practice questions

3 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.

In a two-way table, a row total is 50, a column total is 40, and the grand total is 200. What is the expected count for that cell?

  1. 10
  2. 2,000
  3. 45
  4. 0.25

Answer: A — 10

A) Correct — (row total × column total)/grand total = 2000/200. B) Forgets to divide by the grand total. C) Averages the row and column totals. D) Divides the row total by the grand total only.

Separate random samples are taken from three schools, and each student's favorite subject is recorded. Which test compares the schools?

  1. A chi-square test of independence
  2. A chi-square test of homogeneity
  3. A goodness-of-fit test
  4. A two-sample t-test

Answer: B — A chi-square test of homogeneity

B) Correct — Several groups, one categorical variable. A) Is for one sample classified by two variables. C) Compares one group to a claimed distribution. D) Compares means, not category counts.

A category has observed count 15 and expected count 10. What is its contribution to χ²?

  1. 5
  2. 2.5
  3. 25
  4. 1.67

Answer: B — 2.5

B) Correct — (15 − 10)²/10 = 25/10. A) Uses O − E without squaring or dividing. C) Forgets to divide by E. D) Divides by O instead of E.

Inference for Categorical Data: Chi-Square flashcards

3 cards from the 5 in this chapter.

Chi-square independence?

Test if two categorical variables associated.

Expected count in a two-way table?

(row total × column total) / grand total. Condition for the test: every expected count is at least 5.

Chi-square degrees of freedom?

Goodness of fit: categories − 1. Two-way table: (rows − 1)(columns − 1).

Practise the full chapter

These are a sample. The full Inference for Categorical Data: Chi-Square chapter runs 19 items with per-chapter progress tracking, on the web and in the iOS app.

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