1.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 =
Chi-square tests worksheet with answers
2.Easy
A die is rolled 240 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 = 240k = 6
χ² =
3.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 = 2002 × 2
χ² =
4.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 = 39column total = 48N = 135
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. 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 6 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 = 38.8
- 2. χ² = 10.2
- 3. χ² = 2.083
- 4. E = 13.87
- 5. χ²crit = 9.488
- 6. χ²crit = 15.09
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