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
colourredorangeyellowgreenblueobserved2918201320claimed30%20%20%15%15%

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 100 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 100k = 5
χ² =
2.Easy
face123456observed283338524148

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
busbikecarTotalstudents23361372staff32103880Total554651152

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

row total = 72column total = 51N = 152
E =
4.Medium
coughno coughTotalsmokers572380non-smokers211940Total7842120

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 = 1202 × 2
χ² =
5.Hard

A chi-square goodness-of-fit test compares observed counts in 6 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 6
df =
6.Hard

A chi-square test of independence is carried out on a contingency table with 3 rows and 4 columns (not counting the totals). How many degrees of freedom df does the test have?

3 × 4
df =

Answer key

  1. 1. χ² = 2.167
  2. 2. χ² = 10.15
  3. 3. E = 24.16
  4. 4. χ² = 4.121
  5. 5. df = 5
  6. 6. df = 6

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