1.Easy
A die is rolled 90 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 = 90k = 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 240 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 = 240k = 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 = 2402 × 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 “night shift, major”.
row total = 50column total = 34N = 125
E =
5.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 = 3003 × 2α = 0.01
χ² =
6.Hard
A chi-square test of independence is carried out on a contingency table with 3 rows and 4 columns (not counting the totals). How many degrees of freedom df does the test have?
3 × 4
df =
Answer key
- 1. χ² = 12.4
- 2. χ² = 216.5
- 3. χ² = 6.944
- 4. E = 13.6
- 5. χ² = 40.67
- 6. df = 6
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