AP Statistics Chi-Square Tests Test with Point Values (PDF)

AP Statistics math test: Chi-Square Tests – Maths PDF

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This chi square test for AP Statistics covers chi-square tests (Common Core AP STAT 8.1, AP STAT 8.2, AP STAT 8.3, AP STAT 8.4, AP STAT 8.5, AP STAT 8.6, AP STAT 8.7), with a free PDF to print.

This 45-minute test covers goodness-of-fit tests, tests for homogeneity and independence, and choosing among inference procedures. Follow State, Plan, Do, Conclude and write each conclusion in context.

Time and points

About this test

Grade: AP Statistics
Chapter: Chi-Square Tests
Standards: AP STAT 8.1, AP STAT 8.2, AP STAT 8.3, AP STAT 8.4, AP STAT 8.5, AP STAT 8.6, AP STAT 8.7
Time: 45 minutes
Total: 20 points

Chi square test: questions

Question 1 – Goodness-of-fit test [5 pts]

Four categories, 80 observations.

A random sample of 80 observations is sorted into 4 categories. Test H0: all four categories are equally likely at alpha = 0.05. (Hypotheses 1, conditions 1, chi-square and df 1, p-value 1, conclusion 1)

Question 2 – Expected counts [3 pts]

Two-way table.

In the table, find the expected count in each cell and the degrees of freedom. (2 points for expected counts, 1 point for df)

Question 3 – Chi-square statistic [3 pts]

Compute the chi-square statistic and p-value for the table of Group X and Group Y. (3 points)

Question 4 – Which test [2 pts]

Name the chi-square test: (a) 150 students are each classified by grade and by whether they have a part-time job. (b) Random samples of 100 men and 100 women are each asked to choose a favorite pizza topping from five choices.

Question 5 – Conditions [2 pts]

Expected counts in a 3 by 3 table are 12, 8, 4, 10, 6, 14, 7, 9, 15. Is the chi-square condition met? Explain.

Question 6 – Interpretation [2 pts]

Interpreting chi-square.

A chi-square test for independence gives chi-square = 9.8, df = 2, p = 0.0074. State the conclusion in context when the variables are ‘type of music’ and ‘age group’.

Question 7 – Degrees of freedom [1 pt]

Find df for a test with 4 categories (goodness-of-fit) and for a 4 by 3 table.

Question 8 – Choose a procedure [2 pts]

Name the best procedure: (a) estimate the mean sleep time of all students in a school from a random sample, (b) compare the proportions of two treatment groups that recover.

Key facts behind this chi square test

Key facts

chi-square = sum of (O – E)^2 / E; right-tailed p-value; distribution skewed right.
Goodness-of-fit: one categorical variable; df = number of categories – 1.
Two-way table: E = row total x column total / grand total; df = (r – 1)(c – 1).
Conditions: random sample or random assignment, and all expected counts at least 5.
Homogeneity: compare distributions across groups; independence: two variables in one sample.

How to use this chi square test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All AP Statistics chapters: AP Statistics math.

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