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
colourbrownyellowredgreenobserved127614369claimed40%25%20%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 = 4
χ² =
2.Easy
face123456observed325148355222

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
no defectminormajorTotalday shift26382488night shift36173992Total625563180

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

row total = 92column total = 55N = 180
E =
4.Medium
no defectminormajorTotalday shift20211960night shift1092140Total303040100

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 =
5.Hard

A chi-square goodness-of-fit test compares observed counts in 11 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 11
df =
6.Hard

A chi-square test of independence is carried out on a contingency table with 2 rows and 4 columns (not counting the totals). How many degrees of freedom df does the test have?

2 × 4
df =

Answer key

  1. 1. χ² = 20.64
  2. 2. χ² = 18.55
  3. 3. E = 28.11
  4. 4. χ² = 4.41
  5. 5. df = 10
  6. 6. df = 3

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