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
colourbrownyellowredgreenobserved102582812claimed40%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 =
2.Easy
colourredorangeyellowgreenblueobserved382520134claimed30%20%20%15%15%

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 100 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 100k = 5
χ² =
3.Medium
busbikecarTotalstudents24243280staff16323280Total405664160

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 × 3
χ² =
4.Medium
busbikecarTotalstudents9283168staff882238Total173653106

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

row total = 38column total = 53N = 106
E =
5.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 =
6.Hard
passfailTotalage 18–3078280age 31–508911100age 51+93140Total17644220dfα = 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 = 2203 × 2α = 0.05
χ² =

Answer key

  1. 1. χ² = 21.73
  2. 2. χ² = 11.72
  3. 3. χ² = 2.743
  4. 4. E = 19
  5. 5. df = 6
  6. 6. χ² = 103

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