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
phenotypeA_B_A_bbaaB_aabbobserved74373415claimed9/163/163/161/16

A dihybrid cross is expected to give offspring in the ratio 9 : 3 : 3 : 1. Among 160 offspring the counts shown are observed. Compute the chi-square goodness-of-fit statistic χ² for H₀: the ratio is 9 : 3 : 3 : 1.

n = 160k = 4
χ² =
2.Easy
face123456observed1213101177

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 =
3.Medium
no defectminormajorTotalday shift17443293night shift27172367Total446155160

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

row total = 67column total = 61N = 160
E =
4.Medium
yesnoTotalmen3268100women103040Total4298140

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 = 1402 × 2
χ² =
5.Hard

A chi-square goodness-of-fit test compares observed counts in 4 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 4
df =
6.Hard
yesnoTotalline 1411960line 236440line 3211940Total9842140dfα = 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 = 1403 × 2α = 0.05
χ² =

Answer key

  1. 1. χ² = 7.511
  2. 2. χ² = 3.2
  3. 3. E = 25.54
  4. 4. χ² = 0.6667
  5. 5. df = 3
  6. 6. χ² = 13.53

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