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_aabbobserved247667314claimed9/163/163/161/16

A dihybrid cross is expected to give offspring in the ratio 9 : 3 : 3 : 1. Among 400 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 = 400k = 4
χ² =
2.Easy
colourredgreenblueobserved472924claimed50%30%20%

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 100 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 100k = 3
χ² =
3.Medium
no defectminormajorTotalday shift9163762night shift12281454Total214451116

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

row total = 62column total = 51N = 116
E =
4.Medium
lowmediumhighTotalurban36341989rural9193260Total455351149

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 = 89column total = 51N = 149
E =
5.Hard

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). How many degrees of freedom df does the test have?

k = 5
df =
6.Hard
passfailTotalage 18–30152540age 31–503169100age 51+206080Total66154220dfα = 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 = 2203 × 2α = 0.05
χ² =

Answer key

  1. 1. χ² = 8.124
  2. 2. χ² = 1.013
  3. 3. E = 27.26
  4. 4. E = 30.46
  5. 5. df = 4
  6. 6. χ² = 2.071

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