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
colourredorangeyellowgreenblueobserved7440393413claimed30%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 =
2.Easy
face123456observed181111181319

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 =
3.Medium
lowmediumhighTotalurban113356100rural225543120Total338899220

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 = 2202 × 3
χ² =
4.Medium
lowmediumhighTotalurban27363093rural18391370Total457543163

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 = 93column total = 75N = 163
E =
5.Hard

A chi-square goodness-of-fit test compares observed counts in 3 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 3
df =
6.Hard
dfα = 0.05α = 0.0113.8416.63525.9919.21037.81511.34549.48813.277511.07015.086612.59216.812714.06718.475815.50720.090916.91921.6661018.30723.209

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). Using the table, find the critical value χ²crit at significance level α = 0.01.

α = 0.01
χ²crit =

Answer key

  1. 1. χ² = 13.46
  2. 2. χ² = 4.667
  3. 3. χ² = 9.131
  4. 4. E = 42.79
  5. 5. df = 2
  6. 6. χ²crit = 11.35

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