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_aabbobserved86394324claimed9/163/163/161/16

A dihybrid cross is expected to give offspring in the ratio 9 : 3 : 3 : 1. Among 192 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 = 192k = 4
χ² =
2.Easy
face123456observed416048536038

A die is rolled 300 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 = 300k = 6
χ² =
3.Medium
improvednot improvedTotalnew drug7941120placebo114960Total9090180

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 = 1802 × 2
χ² =
4.Medium
busbikecarTotalstudents441444102staff818935Total523253137

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

row total = 35column total = 32N = 137
E =
5.Hard

A chi-square goodness-of-fit test checks whether counts in 6 categories follow a Poisson distribution whose mean is estimated from the same data. How many degrees of freedom df does the test have?

k = 6
df =
6.Hard
passfailTotalage 18–307624100age 31–506733100age 51+392160Total18278260dfα = 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 = 2603 × 2α = 0.05
χ² =

Answer key

  1. 1. χ² = 18.09
  2. 2. χ² = 8.76
  3. 3. χ² = 36.1
  4. 4. E = 8.175
  5. 5. df = 4
  6. 6. χ² = 2.857

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