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
face123456observed433847362848

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 =
2.Easy
phenotypeA_B_A_bbaaB_aabbobserved8835325claimed9/163/163/161/16

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 =
3.Medium
lowmediumhighTotalurban16194176rural37371387Total535654163

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

row total = 87column total = 53N = 163
E =
4.Medium
no defectminormajorTotalday shift41291989night shift41332195Total826240184

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 = 89column total = 82N = 184
E =
5.Hard

A chi-square goodness-of-fit test checks whether counts in 9 categories follow a Poisson distribution whose mean is estimated from the same data. How many degrees of freedom df does the test have?

k = 9
df =
6.Hard
yesnoTotalage 18–30293160age 31–5031940age 51+8020100Total14060200dfα = 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 = 2003 × 2α = 0.05
χ² =

Answer key

  1. 1. χ² = 7.15
  2. 2. χ² = 3.511
  3. 3. E = 28.29
  4. 4. E = 39.66
  5. 5. df = 7
  6. 6. χ² = 19.25

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