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 90 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 = 90k = 6

χ² =

2.Easy

A dihybrid cross is expected to give offspring in the ratio 9 : 3 : 3 : 1. Among 160 offspring the counts shown are observed. Compute the chi-square goodness-of-fit statistic χ² for H₀: the ratio is 9 : 3 : 3 : 1.

n = 160k = 4

χ² =

3.Medium

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

row total = 99column total = 65N = 160

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 = 2002 × 3

χ² =

5.Hard

A chi-square test of independence is carried out on a contingency table with 2 rows and 4 columns (not counting the totals). How many degrees of freedom df does the test have?

2 × 4

df =

6.Hard

A chi-square goodness-of-fit test compares observed counts in 5 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 5

df =

Answer key

1. χ² = 7.867
2. χ² = 0.4444
3. E = 40.22
4. χ² = 10.78
5. df = 3
6. df = 4

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