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
colourredorangeyellowgreenblueobserved13994627728claimed30%20%20%15%15%

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
face123456observed423333282975

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
busbikecarTotalstudents12292364staff26243282Total385355146

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

row total = 64column total = 53N = 146
E =
4.Medium
no defectminormajorTotalday shift23174484night shift16263274Total394376158

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 = 74column total = 76N = 158
E =
5.Hard

A chi-square test of independence is carried out on a contingency table with 3 rows and 5 columns (not counting the totals). How many degrees of freedom df does the test have?

3 × 5
df =
6.Hard

A chi-square test of independence is carried out on a contingency table with 2 rows and 4 columns (not counting the totals). How many degrees of freedom df does the test have?

2 × 4
df =

Answer key

  1. 1. χ² = 31.39
  2. 2. χ² = 39.8
  3. 3. E = 23.23
  4. 4. E = 35.59
  5. 5. df = 8
  6. 6. df = 3

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