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
colourredgreenblueobserved873924claimed50%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 =
2.Easy
face123456observed102013121223

A die is rolled 90 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 = 90k = 6
χ² =
3.Medium
lowmediumhighTotalurban14162555rural453538118Total595163173

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

row total = 55column total = 63N = 173
E =
4.Medium
no defectminormajorTotalday shift3492568night shift2983168Total631756136

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

row total = 68column total = 56N = 136
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
passfailTotalplant A281240plant B411960plant C5149100Total12080200dfα = 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 = 2003 × 2α = 0.05
χ² =

Answer key

  1. 1. χ² = 3.92
  2. 2. χ² = 9.067
  3. 3. E = 20.03
  4. 4. E = 28
  5. 5. df = 6
  6. 6. χ² = 6.778

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