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
face123456observed131099109

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
colourredorangeyellowgreenblueobserved11177695093claimed30%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 =
3.Medium
lowmediumhighTotalurban14123460rural22241460Total363648120

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 = 1202 × 3
χ² =
4.Medium
lowmediumhighTotalurban9102847rural8294077Total173968124

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

row total = 77column total = 39N = 124
E =
5.Hard
yesnoTotalage 18–3055560age 31–50481260age 51+473380Total15050200dfα = 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 =
6.Hard
dfα = 0.05α = 0.0113.8416.63525.9919.21037.81511.34549.48813.277511.07015.086612.59216.812714.06718.475815.50720.090916.91921.6661018.30723.209

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). Using the table, find the critical value χ²crit at significance level α = 0.01.

α = 0.01
χ²crit =

Answer key

  1. 1. χ² = 1.2
  2. 2. χ² = 22.12
  3. 3. χ² = 14.11
  4. 4. E = 24.22
  5. 5. χ² = 20.96
  6. 6. χ²crit = 21.67

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