1.Easy
A sweet manufacturer claims the colour proportions shown in the table. A random sample of 100 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.
n = 100k = 3
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 160 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 = 160k = 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 “day shift, major”.
row total = 91column total = 68N = 172
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 = 1602 × 2
χ² =
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 = 1803 × 2α = 0.01
χ² =
6.Hard
A chi-square goodness-of-fit test compares observed counts in 3 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 = 30.33
- 2. χ² = 34.73
- 3. E = 35.98
- 4. χ² = 19.39
- 5. χ² = 0.86
- 6. χ²crit = 9.21
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