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
face123456observed181413201510

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
face123456observed413650323348

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
lowmediumhighTotalurban172380120rural314940120Total4872120240

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 = 2402 × 3
χ² =
4.Medium
no defectminormajorTotalday shift1391638night shift27191056Total40282694

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

row total = 56column total = 28N = 94
E =
5.Hard
yesnoTotalage 18–30443680age 31–5059160age 51+471360Total15050200dfα = 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 = 2003 × 2α = 0.01
χ² =
6.Hard

A chi-square test of independence is carried out on a contingency table with 2 rows and 4 columns (not counting the totals). How many degrees of freedom df does the test have?

2 × 4
df =

Answer key

  1. 1. χ² = 4.267
  2. 2. χ² = 7.35
  3. 3. χ² = 26.81
  4. 4. E = 16.68
  5. 5. χ² = 34.84
  6. 6. df = 3

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