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
face123456observed241424221620

A die is rolled 120 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 = 120k = 6
χ² =
2.Easy
colourbrownyellowredgreenobserved29231434claimed40%25%20%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 = 4
χ² =
3.Medium
improvednot improvedTotalnew drug5763120placebo51960Total10872180

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 = 1802 × 2
χ² =
4.Medium
busbikecarTotalstudents314328102staff11421871Total428546173

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

row total = 102column total = 42N = 173
E =
5.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 test of independence is carried out on a contingency table with 2 rows and 11 columns (not counting the totals). Using the table, find the critical value χ²crit at significance level α = 0.05.

α = 0.05
χ²crit =
6.Hard

A chi-square goodness-of-fit test checks whether counts in 6 categories follow a Poisson distribution whose mean is estimated from the same data. How many degrees of freedom df does the test have?

k = 6
df =

Answer key

  1. 1. χ² = 4.4
  2. 2. χ² = 29.05
  3. 3. χ² = 23.44
  4. 4. E = 24.76
  5. 5. χ²crit = 18.31
  6. 6. df = 4

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