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
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A die is rolled 300 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 = 300k = 6
χ² =
2.Easy
face123456observed111813121620

A die is rolled 90 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 = 90k = 6
χ² =
3.Medium
busbikecarTotalstudents187329120staff22174180Total409070200

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 = 2002 × 3
χ² =
4.Medium
no defectminormajorTotalday shift371845100night shift3240981Total695854181

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

row total = 100column total = 58N = 181
E =
5.Hard

A chi-square goodness-of-fit test checks whether counts in 7 categories follow a Poisson distribution whose mean is estimated from the same data. How many degrees of freedom df does the test have?

k = 7
df =
6.Hard

A chi-square goodness-of-fit test compares observed counts in 10 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 10
df =

Answer key

  1. 1. χ² = 19.12
  2. 2. χ² = 4.267
  3. 3. χ² = 30.52
  4. 4. E = 32.04
  5. 5. df = 5
  6. 6. df = 9

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