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
colourredorangeyellowgreenblueobserved12184856347claimed30%20%20%15%15%

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 400 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 400k = 5
χ² =
2.Easy
colourredgreenblueobserved604941claimed50%30%20%

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 150 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 150k = 3
χ² =
3.Medium
improvednot improvedTotalnew drug4951100placebo7129100Total12080200

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 = 2002 × 2
χ² =
4.Medium
no defectminormajorTotalday shift12451067night shift8164064Total206150131

The contingency table shows observed counts. For a chi-square test of independence, find the expected count E for the cell “day shift, no defect”.

row total = 67column total = 20N = 131
E =
5.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 =
6.Hard
passfailTotalplant A4258100plant B334780plant C295180Total104156260dfα = 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 = 2603 × 2α = 0.01
χ² =

Answer key

  1. 1. χ² = 3.488
  2. 2. χ² = 7.389
  3. 3. χ² = 10.08
  4. 4. E = 10.23
  5. 5. df = 3
  6. 6. χ² = 0.6875

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