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 60 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 = 60k = 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 = 4

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 = 1802 × 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 “day shift, no defect”.

row total = 94column total = 57N = 181

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 = 1603 × 2α = 0.01

χ² =

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 = 1803 × 2α = 0.05

χ² =

Answer key

1. χ² = 2.2
2. χ² = 12.56
3. χ² = 5.818
4. E = 29.6
5. χ² = 4.643
6. χ² = 38.77

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