1.Easy
A sweet manufacturer claims the colour proportions shown in the table. A random sample of 60 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.
n = 60k = 3
χ² =
Chi-square tests worksheet with answers
2.Easy
A die is rolled 300 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 = 300k = 6
χ² =
3.Medium
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 = 75column total = 62N = 171
E =
4.Medium
The contingency table shows observed counts. For a chi-square test of independence, find the expected count E for the cell “urban, low”.
row total = 85column total = 65N = 164
E =
5.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 =
6.Hard
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. χ² = 3.339
- 2. χ² = 11.28
- 3. E = 27.19
- 4. E = 33.69
- 5. df = 4
- 6. χ² = 9.75
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