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 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 =

2.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 = 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, car”.

row total = 50column total = 49N = 111

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, minor”.

row total = 110column total = 54N = 190

E =

5.Hard

A chi-square goodness-of-fit test compares observed counts in 11 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 2 rows and 11 columns (not counting the totals). How many degrees of freedom df does the test have?

2 × 11

df =

Answer key

1. χ² = 8.517
2. χ² = 5.035
3. E = 22.07
4. E = 31.26
5. χ²_crit = 23.21
6. df = 10

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