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
colourredgreenblueobserved50228claimed50%30%20%

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 80 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 80k = 3
χ² =
2.Easy
colourbrownyellowredgreenobserved88443533claimed40%25%20%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 = 4
χ² =
3.Medium
yesnoTotalmen253560women6337100Total8872160

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
busbikecarTotalstudents13343380staff28371883Total417151163

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

row total = 80column total = 51N = 163
E =
5.Hard
passfailTotalline 1265480line 24357100line 3192140Total88132220dfα = 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 = 2203 × 2α = 0.01
χ² =
6.Hard

A chi-square goodness-of-fit test checks whether counts in 8 categories follow a Poisson distribution whose mean is estimated from the same data. How many degrees of freedom df does the test have?

k = 8
df =

Answer key

  1. 1. χ² = 6.667
  2. 2. χ² = 2.445
  3. 3. χ² = 6.896
  4. 4. E = 25.03
  5. 5. χ² = 3.188
  6. 6. df = 6

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