1.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 =
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 “urban, low”.
row total = 56column total = 54N = 148
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 = 2402 × 2
χ² =
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. How many degrees of freedom df does the test have?
k = 6
df =
6.Hard
The table shows observed counts. Test at α = 0.01 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 = 1403 × 2α = 0.01
χ² =
Answer key
- 1. χ² = 7.8
- 2. χ² = 187.1
- 3. E = 20.43
- 4. χ² = 10.55
- 5. df = 4
- 6. χ² = 12.27
Full step-by-step solutions: practise this topic on examproblems.com.