1.Easy
A sweet manufacturer claims the colour proportions shown in the table. A random sample of 200 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.
n = 200k = 5
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, medium”.
row total = 82column total = 73N = 160
E =
4.Medium
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 × 3
χ² =
5.Hard
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
A chi-square goodness-of-fit test compares observed counts in 9 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?
k = 9
df =
Answer key
- 1. χ² = 23.72
- 2. χ² = 17.12
- 3. E = 37.41
- 4. χ² = 16.82
- 5. χ² = 60.01
- 6. df = 8
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