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
face123456observed495143442825

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 =
2.Easy
face123456observed655552615017

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 =
3.Medium
yesnoTotalmen2377100women253560Total48112160

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 = 1602 × 2
χ² =
4.Medium
no defectminormajorTotalday shift37124594night shift414429114Total785674208

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 = 114column total = 78N = 208
E =
5.Hard
passfailTotalplant A501060plant B602080plant C7030100Total18060240dfα = 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 = 0.01 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 = 0.01
χ² =
6.Hard
passfailTotalage 18–306337100age 31–5037340age 51+402060Total14060200dfα = 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 = 2003 × 2α = 0.05
χ² =

Answer key

  1. 1. χ² = 14.9
  2. 2. χ² = 29.28
  3. 3. χ² = 6.222
  4. 4. E = 42.75
  5. 5. χ² = 3.556
  6. 6. χ² = 12.29

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