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 80 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 80k = 3

χ² =

2.Easy

A dihybrid cross is expected to give offspring in the ratio 9 : 3 : 3 : 1. Among 400 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 = 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 = 1602 × 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 “staff, car”.

row total = 96column total = 42N = 174

E =

5.Hard

A chi-square goodness-of-fit test compares observed counts in 10 categories with fully specified expected proportions (no parameters are estimated from the data). Using the table, find the critical value χ²_crit at significance level α = 0.01.

α = 0.01

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 = 2603 × 2α = 0.01

χ² =

Answer key

1. χ² = 2.004
2. χ² = 128.2
3. χ² = 16.81
4. E = 23.17
5. χ²_crit = 21.67
6. χ² = 27.96

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