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
colourbrownyellowredgreenobserved1681155760claimed40%25%20%15%

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 400 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 400k = 4
χ² =
2.Easy
face123456observed433635334449

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 shift23164180night shift19261560Total424256140

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
lowmediumhighTotalurban18243577rural423628106Total606063183

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

row total = 106column total = 63N = 183
E =
5.Hard
passfailTotalline 1291140line 2354580line 36832100Total13288220dfα = 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 = 2203 × 2α = 0.05
χ² =
6.Hard

A chi-square test of independence is carried out on a contingency table with 2 rows and 3 columns (not counting the totals). How many degrees of freedom df does the test have?

2 × 3
df =

Answer key

  1. 1. χ² = 9.262
  2. 2. χ² = 4.9
  3. 3. χ² = 12.23
  4. 4. E = 36.49
  5. 5. χ² = 14.07
  6. 6. df = 2

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