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
face123456observed355965463659

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
colourredorangeyellowgreenblueobserved10072505622claimed30%20%20%15%15%

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 300 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 300k = 5
χ² =
3.Medium
no defectminormajorTotalday shift15151040night shift15153060Total303040100

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 = 1002 × 3
χ² =
4.Medium
busbikecarTotalstudents18452184staff24421884Total428739168

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

row total = 84column total = 39N = 168
E =
5.Hard
passfailTotalline 1384280line 23169100line 34357100Total112168280dfα = 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 = 2803 × 2α = 0.01
χ² =
6.Hard
passfailTotalline 1233760line 28020100line 3413980Total14496240dfα = 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 = 2403 × 2α = 0.05
χ² =

Answer key

  1. 1. χ² = 16.48
  2. 2. χ² = 19.62
  3. 3. χ² = 6.25
  4. 4. E = 19.5
  5. 5. χ² = 5.625
  6. 6. χ² = 30.95

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