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
face123456observed223725322737

A die is rolled 180 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 = 180k = 6
χ² =
2.Easy
face123456observed202618261812

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
yesnoTotalmen6931100women7446120Total14377220

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 = 2202 × 2
χ² =
4.Medium
no defectminormajorTotalday shift17283176night shift18311059Total355941135

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

row total = 76column total = 41N = 135
E =
5.Hard

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

2 × 2
df =
6.Hard
passfailTotalline 1463480line 256460line 37822100Total18060240dfα = 0.05α = 0.0113.8416.63525.9919.21037.81511.34549.48813.277511.07015.086612.59216.812714.06718.475815.50720.090916.91921.6661018.30723.209

The table shows observed counts. Test at α = 0.05 whether the two variables are independent (no continuity correction). Compute the test statistic χ², then compare it with the critical value from the table.

N = 2403 × 2α = 0.05
χ² =

Answer key

  1. 1. χ² = 6.667
  2. 2. χ² = 7.2
  3. 3. χ² = 1.289
  4. 4. E = 23.08
  5. 5. df = 1
  6. 6. χ² = 24.3

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