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
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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
colourredgreenblueobserved311811claimed50%30%20%

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 60 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 60k = 3
χ² =
3.Medium
lowmediumhighTotalurban43113387rural12101537Total552148124

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 = 87column total = 48N = 124
E =
4.Medium
lowmediumhighTotalurban394220101rural384129108Total778349209

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

row total = 101column total = 83N = 209
E =
5.Hard

A chi-square goodness-of-fit test compares observed counts in 3 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 3
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 5 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 = 2.4
  2. 2. χ² = 0.1167
  3. 3. E = 33.68
  4. 4. E = 40.11
  5. 5. df = 2
  6. 6. χ²crit = 9.488

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