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 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 =

2.Easy

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 60 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 60k = 3

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 = 42column total = 47N = 135

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, medium”.

row total = 85column total = 58N = 150

E =

5.Hard

A chi-square test of independence is carried out on a contingency table with 2 rows and 11 columns (not counting the totals). 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 checks whether counts in 7 categories follow a Poisson distribution whose mean is estimated from the same data. How many degrees of freedom df does the test have?

k = 7

df =

Answer key

1. χ² = 53.11
2. χ² = 12.67
3. E = 14.62
4. E = 32.87
5. χ²_crit = 18.31
6. df = 5

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