1.Easy
A sweet manufacturer claims the colour proportions shown in the table. A random sample of 80 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.
n = 80k = 3
χ² =
Chi-square tests worksheet with answers
2.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 = 5
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 = 1602 × 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 “staff, car”.
row total = 74column total = 41N = 134
E =
5.Hard
A chi-square goodness-of-fit test compares observed counts in 6 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 =
6.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. Using the table, find the critical value χ²crit at significance level α = 0.05.
α = 0.05
χ²crit =
Answer key
- 1. χ² = 18.04
- 2. χ² = 3.2
- 3. χ² = 10.31
- 4. E = 22.64
- 5. χ²crit = 15.09
- 6. χ²crit = 9.488
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