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 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. For a chi-square test of independence, find the expected count E for the cell “students, car”.
row total = 84column total = 23N = 156
E =
4.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 = 103column total = 77N = 193
E =
5.Hard
A chi-square test of independence is carried out on a contingency table with 3 rows and 5 columns (not counting the totals). How many degrees of freedom df does the test have?
3 × 5
df =
6.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 = 2003 × 2α = 0.05
χ² =
Answer key
- 1. χ² = 21.32
- 2. χ² = 329.2
- 3. E = 12.38
- 4. E = 41.09
- 5. df = 8
- 6. χ² = 5.31
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