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_aabbobserved71352925claimed9/163/163/161/16

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
face123456observed324238353657

A die is rolled 240 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 = 240k = 6
χ² =
3.Medium
no defectminormajorTotalday shift403129100night shift304640Total703535140

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 × 3
χ² =
4.Medium
no defectminormajorTotalday shift45272799night shift1643867Total617035166

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

row total = 67column total = 35N = 166
E =
5.Hard
dfα = 0.05α = 0.0113.8416.63525.9919.21037.81511.34549.48813.277511.07015.086612.59216.812714.06718.475815.50720.090916.91921.6661018.30723.209

A chi-square goodness-of-fit test compares observed counts in 7 categories with fully specified expected proportions (no parameters are estimated from the data). Using the table, find the critical value χ²crit at significance level α = 0.05.

α = 0.05
χ²crit =
6.Hard
dfα = 0.05α = 0.0113.8416.63525.9919.21037.81511.34549.48813.277511.07015.086612.59216.812714.06718.475815.50720.090916.91921.6661018.30723.209

A chi-square test of independence is carried out on a contingency table with 2 rows and 6 columns (not counting the totals). Using the table, find the critical value χ²crit at significance level α = 0.01.

α = 0.01
χ²crit =

Answer key

  1. 1. χ² = 27.38
  2. 2. χ² = 10.05
  3. 3. χ² = 14.28
  4. 4. E = 14.13
  5. 5. χ²crit = 12.59
  6. 6. χ²crit = 15.09

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