1.Easy
A die is rolled 60 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 = 60k = 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 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 =
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 = 100column total = 62N = 185
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 = 1802 × 3
χ² =
5.Hard
A chi-square test of independence is carried out on a contingency table with 3 rows and 6 columns (not counting the totals). Using the table, find the critical value χ²crit at significance level α = 0.01.
α = 0.01
χ²crit =
6.Hard
A chi-square goodness-of-fit test checks whether counts in 7 categories follow a Poisson distribution whose mean is estimated from the same data. How many degrees of freedom df does the test have?
k = 7
df =
Answer key
- 1. χ² = 3.4
- 2. χ² = 7.25
- 3. E = 33.51
- 4. χ² = 0.1062
- 5. χ²crit = 23.21
- 6. df = 5
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