1.Easy
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 =
Chi-square tests worksheet with answers
2.Easy
A die is rolled 180 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 = 180k = 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 “students, bike”.
row total = 82column total = 59N = 204
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 = 1402 × 2
χ² =
5.Hard
A chi-square test of independence is carried out on a contingency table with 3 rows and 4 columns (not counting the totals). Using the table, find the critical value χ²crit at significance level α = 0.05.
α = 0.05
χ²crit =
6.Hard
A chi-square goodness-of-fit test compares observed counts in 4 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 = 0.01.
α = 0.01
χ²crit =
Answer key
- 1. χ² = 13.08
- 2. χ² = 12
- 3. E = 23.72
- 4. χ² = 13.5
- 5. χ²crit = 12.59
- 6. χ²crit = 11.35
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