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 die is rolled 300 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 = 300k = 6

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 “rural, medium”.

row total = 66column total = 41N = 160

E =

5.Hard

A chi-square goodness-of-fit test checks whether counts in 5 categories follow a Poisson distribution whose mean is estimated from the same data. How many degrees of freedom df does the test have?

k = 5

df =

6.Hard

The table shows observed counts. Test at α = 0.05 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 = 2203 × 2α = 0.05

χ² =

Answer key

1. χ² = 7
2. χ² = 8.96
3. χ² = 13.53
4. E = 16.91
5. df = 3
6. χ² = 8.391

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