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

n = 400k = 5

χ² =

2.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 =

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 = 88column total = 48N = 183

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 = 69column total = 53N = 155

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 = 0.01.

α = 0.01

χ²_crit =

6.Hard

A chi-square test of independence is carried out on a contingency table with 3 rows and 3 columns (not counting the totals). How many degrees of freedom df does the test have?

3 × 3

df =

Answer key

1. χ² = 11.18
2. χ² = 5
3. E = 23.08
4. E = 23.59
5. χ²_crit = 15.09
6. df = 4

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