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
colourbrownyellowredgreenobserved1727310154claimed40%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
face123456observed624363413556

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
lowmediumhighTotalurban21123467rural40133891Total612572158

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

row total = 67column total = 25N = 158
E =
4.Medium
yesnoTotalmen384280women265480Total6496160

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 =
5.Hard

A chi-square goodness-of-fit test compares observed counts in 8 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 8
df =
6.Hard

A chi-square test of independence is carried out on a contingency table with 2 rows and 5 columns (not counting the totals). How many degrees of freedom df does the test have?

2 × 5
df =

Answer key

  1. 1. χ² = 14.3
  2. 2. χ² = 14.08
  3. 3. E = 10.6
  4. 4. χ² = 3.75
  5. 5. df = 7
  6. 6. df = 4

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