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 180 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 = 180k = 6

χ² =

2.Easy

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 400 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 400k = 5

χ² =

3.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 = 1402 × 3

χ² =

4.Medium

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

row total = 93column total = 39N = 149

E =

5.Hard

A chi-square test of independence is carried out on a contingency table with 3 rows and 4 columns (not counting the totals). Using the table, find the critical value χ²_crit at significance level α = 0.05.

α = 0.05

χ²_crit =

6.Hard

The table shows observed counts. Test at α = 0.01 whether the two variables are independent (no continuity correction). Compute the test statistic χ², then compare it with the critical value from the table.

N = 1603 × 2α = 0.01

χ² =

Answer key

1. χ² = 24.8
2. χ² = 13.5
3. χ² = 2.204
4. E = 24.34
5. χ²_crit = 12.59
6. χ² = 11.28

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