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
colourredgreenblueobserved39201claimed50%30%20%

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 =
2.Easy
face123456observed463343463240

A die is rolled 240 times to test whether it is fair. The counts of each face are shown. Compute the chi-square goodness-of-fit statistic χ² for H₀: each face has probability 1/6.

n = 240k = 6
χ² =
3.Medium
no defectminormajorTotalday shift17262871night shift41301687Total585644158

The contingency table shows observed counts. For a chi-square test of independence, find the expected count E for the cell “night shift, no defect”.

row total = 87column total = 58N = 158
E =
4.Medium
coughno coughTotalsmokers132740non-smokers3664100Total4991140

The contingency table shows observed counts. Compute the chi-square statistic χ² for the test of independence between the row and column variables. Do not use a continuity correction.

N = 1402 × 2
χ² =
5.Hard

A chi-square goodness-of-fit test compares observed counts in 7 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 7
df =
6.Hard

A chi-square test of independence is carried out on a contingency table with 2 rows and 5 columns (not counting the totals). How many degrees of freedom df does the test have?

2 × 5
df =

Answer key

  1. 1. χ² = 13.01
  2. 2. χ² = 4.85
  3. 3. E = 31.94
  4. 4. χ² = 0.1538
  5. 5. df = 6
  6. 6. df = 4

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