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
face123456observed4444393536102

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
face123456observed131110191324

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
lowmediumhighTotalurban1233853rural8351255Total206820108

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 = 55column total = 68N = 108
E =
4.Medium
busbikecarTotalstudents134047100staff1983360Total324880160

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 × 3
χ² =
5.Hard

A chi-square test of independence is carried out on a contingency table with 3 rows and 6 columns (not counting the totals). How many degrees of freedom df does the test have?

3 × 6
df =
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 8 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 = 0.05.

α = 0.05
χ²crit =

Answer key

  1. 1. χ² = 66.36
  2. 2. χ² = 9.733
  3. 3. E = 34.63
  4. 4. χ² = 15.9
  5. 5. df = 10
  6. 6. χ²crit = 14.07

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