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
face123456observed201823261815

A die is rolled 120 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 = 120k = 6
χ² =
2.Easy
colourredgreenblueobserved87594claimed50%30%20%

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 150 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 150k = 3
χ² =
3.Medium
improvednot improvedTotalnew drug453580placebo6337100Total10872180

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 = 1802 × 2
χ² =
4.Medium
lowmediumhighTotalurban384443125rural244539108Total628982233

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

row total = 108column total = 62N = 233
E =
5.Hard
yesnoTotalline 1122840line 23466100line 383240Total54126180dfα = 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 = 1803 × 2α = 0.05
χ² =
6.Hard
yesnoTotalplant A421860plant B8020100plant C7327100Total19565260dfα = 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 = 2603 × 2α = 0.01
χ² =

Answer key

  1. 1. χ² = 3.9
  2. 2. χ² = 28.81
  3. 3. χ² = 0.8438
  4. 4. E = 28.74
  5. 5. χ² = 2.667
  6. 6. χ² = 2.347

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