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
face123456observed111218141421

A die is rolled 90 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 = 90k = 6
χ² =
2.Easy
phenotypeA_B_A_bbaaB_aabbobserved140443719claimed9/163/163/161/16

A dihybrid cross is expected to give offspring in the ratio 9 : 3 : 3 : 1. Among 240 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 = 240k = 4
χ² =
3.Medium
improvednot improvedTotalnew drug174360placebo3169100Total48112160

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 × 2
χ² =
4.Medium
no defectminormajorTotalday shift1838864night shift44331794Total627125158

The contingency table shows observed counts. For a chi-square test of independence, find the expected count E for the cell “day shift, no defect”.

row total = 64column total = 62N = 158
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 test of independence is carried out on a contingency table with 2 rows and 2 columns (not counting the totals). Using the table, find the critical value χ²crit at significance level α = 0.01.

α = 0.01
χ²crit =
6.Hard
passfailTotalplant A5842100plant B36440plant C71980Total16555220dfα = 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 = 2203 × 2α = 0.01
χ² =

Answer key

  1. 1. χ² = 4.8
  2. 2. χ² = 2.696
  3. 3. χ² = 0.127
  4. 4. E = 25.11
  5. 5. χ²crit = 6.635
  6. 6. χ² = 28.28

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