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 dihybrid cross is expected to give offspring in the ratio 9 : 3 : 3 : 1. Among 400 offspring the counts shown are observed. Compute the chi-square goodness-of-fit statistic χ² for H₀: the ratio is 9 : 3 : 3 : 1.
n = 400k = 4
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 = 1402 × 3
χ² =
4.Medium
The contingency table shows observed counts. For a chi-square test of independence, find the expected count E for the cell “students, bus”.
row total = 116column total = 80N = 210
E =
5.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 = 2203 × 2α = 0.05
χ² =
6.Hard
A chi-square goodness-of-fit test checks whether counts in 9 categories follow a Poisson distribution whose mean is estimated from the same data. How many degrees of freedom df does the test have?
k = 9
df =
Answer key
- 1. χ² = 3.8
- 2. χ² = 47.31
- 3. χ² = 0.96
- 4. E = 44.19
- 5. χ² = 3.663
- 6. df = 7
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