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 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 =

2.Easy

A dihybrid cross is expected to give offspring in the ratio 9 : 3 : 3 : 1. Among 320 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 = 320k = 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 “day shift, no defect”.

row total = 75column total = 43N = 144

E =

4.Medium

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

row total = 82column total = 54N = 160

E =

5.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 =

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 = 1603 × 2α = 0.05

χ² =

Answer key

1. χ² = 3.573
2. χ² = 4.167
3. E = 22.4
4. E = 27.68
5. χ²_crit = 9.21
6. χ² = 10.14

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