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
colourredorangeyellowgreenblueobserved10862977558claimed30%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
colourbrownyellowredgreenobserved28252225claimed40%25%20%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 = 4
χ² =
3.Medium
coughno coughTotalsmokers5347100non-smokers6852120Total12199220

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 × 2
χ² =
4.Medium
lowmediumhighTotalurban433942124rural393640115Total827582239

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

row total = 124column total = 75N = 239
E =
5.Hard
yesnoTotalage 18–30251540age 31–50946100age 51+572380Total17644220dfα = 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 =
6.Hard

A chi-square goodness-of-fit test checks whether counts in 6 categories follow a Poisson distribution whose mean is estimated from the same data. How many degrees of freedom df does the test have?

k = 6
df =

Answer key

  1. 1. χ² = 12.68
  2. 2. χ² = 10.47
  3. 3. χ² = 0.2963
  4. 4. E = 38.91
  5. 5. χ² = 23.73
  6. 6. df = 4

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