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
colourbrownyellowredgreenobserved114877326claimed40%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
colourbrownyellowredgreenobserved1441106680claimed40%25%20%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 = 4
χ² =
3.Medium
no defectminormajorTotalday shift204852120night shift241858100Total4466110220

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
busbikecarTotalstudents9211646staff33302689Total425142135

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 = 46column total = 42N = 135
E =
5.Hard
passfailTotalage 18–30314980age 31–50142640age 51+33740Total48112160dfα = 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 = 0.05 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 = 1603 × 2α = 0.05
χ² =
6.Hard

A chi-square goodness-of-fit test compares observed counts in 7 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 7
df =

Answer key

  1. 1. χ² = 13.06
  2. 2. χ² = 11.72
  3. 3. χ² = 12.61
  4. 4. E = 14.31
  5. 5. χ² = 13.04
  6. 6. df = 6

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