1.Easy
A sweet manufacturer claims the colour proportions shown in the table. A random sample of 150 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.
n = 150k = 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 320 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 = 320k = 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 “day shift, minor”.
row total = 95column total = 80N = 184
E =
5.Hard
A chi-square goodness-of-fit test checks whether counts in 7 categories follow a Poisson distribution whose mean is estimated from the same data. How many degrees of freedom df does the test have?
k = 7
df =
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 = 2.056
- 2. χ² = 7.333
- 3. χ² = 3.647
- 4. E = 41.3
- 5. df = 5
- 6. χ²crit = 9.21
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