Chi-square tests worksheet with answers

Free printable Chi-square tests worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A die is rolled 120 times to test whether it is fair. The counts of each face are shown. Compute the chi-square goodness-of-fit statistic χ² for H₀: each face has probability 1/6.

n = 120k = 6

χ² =

2.Easy

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 150 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 150k = 3

χ² =

3.Medium

The contingency table shows observed counts. For a chi-square test of independence, find the expected count E for the cell “students, bus”.

row total = 58column total = 43N = 157

E =

4.Medium

The contingency table shows observed counts. Compute the chi-square statistic χ² for the test of independence between the row and column variables. Do not use a continuity correction.

N = 1002 × 3

χ² =

5.Hard

A chi-square goodness-of-fit test compares observed counts in 7 categories with fully specified expected proportions (no parameters are estimated from the data). Using the table, find the critical value χ²_crit at significance level α = 0.05.

α = 0.05

χ²_crit =

6.Hard

A chi-square test of independence is carried out on a contingency table with 3 rows and 6 columns (not counting the totals). How many degrees of freedom df does the test have?

3 × 6

df =

Answer key

1. χ² = 6.2
2. χ² = 13.55
3. E = 15.89
4. χ² = 3.056
5. χ²_crit = 12.59
6. df = 10

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