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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Name: ____________________   Date: ____________

1.Easy
phenotypeA_B_A_bbaaB_aabbobserved127485095claimed9/163/163/161/16

A dihybrid cross is expected to give offspring in the ratio 9 : 3 : 3 : 1. Among 320 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 = 320k = 4
χ² =
2.Easy
face123456observed272934312534

A die is rolled 180 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 = 180k = 6
χ² =
3.Medium
busbikecarTotalstudents27411987staff15233270Total426451157

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

row total = 87column total = 51N = 157
E =
4.Medium
no defectminormajorTotalday shift212950100night shift27191460Total484864160

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 = 1602 × 3
χ² =
5.Hard

A chi-square test of independence is carried out on a contingency table with 4 rows and 4 columns (not counting the totals). How many degrees of freedom df does the test have?

4 × 4
df =
6.Hard
passfailTotalplant A162440plant B166480plant C162440Total48112160dfα = 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 = 1603 × 2α = 0.05
χ² =

Answer key

  1. 1. χ² = 300.9
  2. 2. χ² = 2.267
  3. 3. E = 28.26
  4. 4. χ² = 13.96
  5. 5. df = 9
  6. 6. χ² = 7.619

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