AP Statistics Chi-Square Tests Worksheet (PDF)

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

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This chi square worksheet 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.

These 20 problems practice AP Statistics topics 8.1 to 8.7. You will compute expected counts, chi-square statistics, degrees of freedom, and p-values, carry out goodness-of-fit and two-way table tests, and choose the right procedure for categorical data.

AP Statistics · Common Core State 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

Chi square worksheet: exercises 1 to 10

Exercise 1 – Expected counts for GOF

A company claims that its candy mix is 30% red, 30% blue, 20% green, and 20% yellow. In a random bag of 200 candies, find the expected count of each color under the claim.

Exercise 2 – Degrees of freedom

Find the degrees of freedom: (a) goodness-of-fit with 6 categories; (b) a two-way table with 3 rows and 4 columns; (c) a 2 by 2 table.

Exercise 3 – Compute chi-square

Candy colors.

The observed counts in the bag are red 68, blue 56, green 42, yellow 34. Compute the chi-square statistic.

Exercise 4 – p-value

Right-tail p-value.

For chi-square = 2.333 with df = 3, find the p-value and state a conclusion at alpha = 0.05.

Exercise 5 – Largest contribution

In the candy test, which color contributes most to chi-square?

Exercise 6 – Hypotheses

Write the null and alternative hypotheses for a goodness-of-fit test of whether a die is fair, in context.

Exercise 7 – Check conditions

A random sample of 40 people is classified into 5 categories with claimed proportions 0.35, 0.30, 0.20, 0.10, 0.05. Is the condition for a chi-square test met?

Exercise 8 – Fair die

120 rolls of a die.

A die is rolled 120 times: 14, 21, 17, 22, 19, 27 for faces 1 to 6. Test whether it is fair at alpha = 0.05.

Exercise 9 – Expected counts in a table

Observed counts of study location by class (two-way table).

Using the observed table of study location by class, find the expected count for sophomores who study in the library.

Exercise 10 – Chi-square for the table

Observed (expected) counts. Expected = row total times column total over grand total.

Compute chi-square for the study location table using the expected counts shown, and find df.

Exercises 11 and up

Exercise 11 – Conclusion for the table

The p-value for the study location test is 0.0126. State the conclusion at alpha = 0.05.

Exercise 12 – Homogeneity

Poll results by region.

Independent random samples of 100 voters from each of three regions were asked about a proposal. Test whether the distribution of opinion is the same in all three regions (alpha = 0.05).

Exercise 13 – Independence or homogeneity?

Choosing the test.

Name the test: (a) 300 randomly chosen adults are classified by age group and favorite social media app. (b) Three random samples of 100 students each from three schools are asked their favorite subject.

Exercise 14 – Missing expected count

Three categories, 100 observations.

In a goodness-of-fit test with 100 observations, the null proportions are 0.30, 0.30, and 0.40. Find the expected counts, chi-square, and df.

Exercise 15 – Wrong test

A teacher gives a pretest and a posttest to 30 students, recording pass/fail on each. A student runs a chi-square test on the 2 by 2 table. Why is it inappropriate?

Exercise 16 – Small expected counts

A 2 by 2 table has expected counts 12.4, 3.6, 9.6, 2.4. Is a chi-square test appropriate? What could be done?

Exercise 17 – 2 by 2 table

Streaming by age group.

In a random sample of 200 adults, streaming habits were recorded for two age groups. Test for an association at alpha = 0.01.

Exercise 18 – Which procedure?

Choose the procedure: (a) compare the mean heights of two randomly chosen groups; (b) test whether a coin gives equal chances of heads and tails in 200 flips; (c) estimate the proportion of students who own a bike; (d) test whether grade level and club membership are related in one sample.

Exercise 19 – Multi-step

A random sample of 90 teens reports their favorite season: spring 15, summer 36, fall 24, winter 15. Test whether all four seasons are equally popular at alpha = 0.05, and name the season with the biggest contribution.

Exercise 20 – Interpret the p-value

A chi-square test for independence has p-value 0.02. Interpret it in context for variables ‘class level’ and ‘car type’.

Key facts behind this chi square worksheet

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 worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the chi square worksheet as a PDF with the button below and keep it with your notes.

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