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 dihybrid cross is expected to give offspring in the ratio 9 : 3 : 3 : 1. Among 240 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 = 240k = 4

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. For a chi-square test of independence, find the expected count E for the cell “staff, bike”.

row total = 42column total = 47N = 115

E =

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 = 86column total = 51N = 181

E =

5.Hard

A chi-square goodness-of-fit test compares observed counts in 4 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 4

df =

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). Using the table, find the critical value χ²_crit at significance level α = 0.01.

α = 0.01

χ²_crit =

Answer key

1. χ² = 10.92
2. χ² = 27.72
3. E = 17.17
4. E = 24.23
5. df = 3
6. χ²_crit = 9.21

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