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
colourredgreenblueobserved552619claimed50%30%20%

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 = 3
χ² =
2.Easy
phenotypeA_B_A_bbaaB_aabbobserved1595472115claimed9/163/163/161/16

A dihybrid cross is expected to give offspring in the ratio 9 : 3 : 3 : 1. Among 400 offspring the counts shown are observed. Compute the chi-square goodness-of-fit statistic χ² for H₀: the ratio is 9 : 3 : 3 : 1.

n = 400k = 4
χ² =
3.Medium
busbikecarTotalstudents222355100staff32311780Total545472180

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 = 1802 × 3
χ² =
4.Medium
lowmediumhighTotalurban422534101rural17201047Total594544148

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

row total = 47column total = 45N = 148
E =
5.Hard
yesnoTotalage 18–30453580age 31–50621880age 51+4951100Total156104260dfα = 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 = 2603 × 2α = 0.01
χ² =
6.Hard
dfα = 0.05α = 0.0113.8416.63525.9919.21037.81511.34549.48813.277511.07015.086612.59216.812714.06718.475815.50720.090916.91921.6661018.30723.209

A chi-square goodness-of-fit test compares observed counts in 10 categories with fully specified expected proportions (no parameters are estimated from the data). Using the table, find the critical value χ²crit at significance level α = 0.05.

α = 0.05
χ²crit =

Answer key

  1. 1. χ² = 1.083
  2. 2. χ² = 349.4
  3. 3. χ² = 21.13
  4. 4. E = 14.29
  5. 5. χ² = 15.72
  6. 6. χ²crit = 16.92

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