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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
face123456observed171612181413

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 =
2.Easy
colourredorangeyellowgreenblueobserved7147402715claimed30%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
improvednot improvedTotalnew drug4951100placebo233760Total7288160

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 =
4.Medium
lowmediumhighTotalurban31321982rural1081634Total414035116

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

row total = 82column total = 41N = 116
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 goodness-of-fit test compares observed counts in 3 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 =
6.Hard
passfailTotalplant A382260plant B271340plant C33740Total9842140dfα = 0.05α = 0.0113.8416.63525.9919.21037.81511.34549.48813.277511.07015.086612.59216.812714.06718.475815.50720.090916.91921.6661018.30723.209

The table shows observed counts. Test at α = 0.01 whether the two variables are independent (no continuity correction). Compute the test statistic χ², then compare it with the critical value from the table.

N = 1403 × 2α = 0.01
χ² =

Answer key

  1. 1. χ² = 1.867
  2. 2. χ² = 11.04
  3. 3. χ² = 1.724
  4. 4. E = 28.98
  5. 5. χ²crit = 9.21
  6. 6. χ² = 4.365

Full step-by-step solutions: practise this topic on examproblems.com.