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
face123456observed1310137116

A die is rolled 60 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 = 60k = 6
χ² =
2.Easy
face123456observed222519241515

A die is rolled 120 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 = 120k = 6
χ² =
3.Medium
busbikecarTotalstudents163450100staff29292280Total456372180

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 = 1802 × 3
χ² =
4.Medium
busbikecarTotalstudents26293691staff444030114Total706966205

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

row total = 91column total = 70N = 205
E =
5.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 =
6.Hard

A chi-square goodness-of-fit test compares observed counts in 8 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 8
df =

Answer key

  1. 1. χ² = 4.4
  2. 2. χ² = 4.8
  3. 3. χ² = 12.98
  4. 4. E = 31.07
  5. 5. df = 4
  6. 6. df = 7

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