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
colourredorangeyellowgreenblueobserved7451745150claimed30%20%20%15%15%

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 300 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 300k = 5
χ² =
2.Easy
colourredorangeyellowgreenblueobserved5644492922claimed30%20%20%15%15%

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 200 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 200k = 5
χ² =
3.Medium
busbikecarTotalstudents9181340staff11272260Total204535100

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 = 1002 × 3
χ² =
4.Medium
busbikecarTotalstudents28412089staff33401588Total618135177

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

row total = 88column total = 61N = 177
E =
5.Hard

A chi-square goodness-of-fit test compares observed counts in 4 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 4
df =
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 = 8.817
  2. 2. χ² = 4.858
  3. 3. χ² = 0.3274
  4. 4. E = 30.33
  5. 5. df = 3
  6. 6. df = 2

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