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

n = 100k = 5

χ² =

2.Easy

A dihybrid cross is expected to give offspring in the ratio 9 : 3 : 3 : 1. Among 192 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 = 192k = 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 = 85column total = 56N = 139

E =

4.Medium

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

row total = 105column total = 49N = 174

E =

5.Hard

A chi-square goodness-of-fit test compares observed counts in 6 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 = 0.05.

α = 0.05

χ²_crit =

6.Hard

A chi-square goodness-of-fit test compares observed counts in 9 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 9

df =

Answer key

1. χ² = 3.233
2. χ² = 19.7
3. E = 34.24
4. E = 29.57
5. χ²_crit = 11.07
6. df = 8

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