1.Easy
A die is rolled 120 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 = 120k = 6
χ² =
Chi-square tests worksheet with answers
2.Easy
A sweet manufacturer claims the colour proportions shown in the table. A random sample of 300 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.
n = 300k = 4
χ² =
3.Medium
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 = 38column total = 30N = 78
E =
4.Medium
The contingency table shows observed counts. For a chi-square test of independence, find the expected count E for the cell “rural, low”.
row total = 86column total = 52N = 121
E =
5.Hard
A chi-square test of independence is carried out on a contingency table with 3 rows and 5 columns (not counting the totals). How many degrees of freedom df does the test have?
3 × 5
df =
6.Hard
A chi-square goodness-of-fit test checks whether counts in 4 categories follow a Poisson distribution whose mean is estimated from the same data. Using the table, find the critical value χ²crit at significance level α = 0.01.
α = 0.01
χ²crit =
Answer key
- 1. χ² = 2.4
- 2. χ² = 17.22
- 3. E = 14.62
- 4. E = 36.96
- 5. df = 8
- 6. χ²crit = 9.21
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