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 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 = 4

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 × 2

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, high”.

row total = 63column total = 22N = 151

E =

5.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 = 2003 × 2α = 0.01

χ² =

6.Hard

A chi-square test of independence is carried out on a contingency table with 2 rows and 3 columns (not counting the totals). How many degrees of freedom df does the test have?

2 × 3

df =

Answer key

1. χ² = 11.85
2. χ² = 8.36
3. χ² = 1.273
4. E = 9.179
5. χ² = 0.96
6. df = 2

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