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
face123456observed404852333631

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
face123456observed616339564536

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
lowmediumhighTotalurban13163160rural19263176Total324262136

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

row total = 60column total = 62N = 136
E =
4.Medium
improvednot improvedTotalnew drug5070120placebo142640Total6496160

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 =
5.Hard
passfailTotalage 18–30251540age 31–50301040age 51+172340Total7248120dfα = 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 = 1203 × 2α = 0.01
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 9 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 = 8.85
  2. 2. χ² = 13.36
  3. 3. E = 27.35
  4. 4. χ² = 0.5556
  5. 5. χ² = 8.958
  6. 6. χ²crit = 20.09

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