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 = 4
χ² =
Chi-square tests worksheet with answers
2.Easy
A sweet manufacturer claims the colour proportions shown in the table. A random sample of 60 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.
n = 60k = 3
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 × 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 “staff, bus”.
row total = 122column total = 71N = 234
E =
5.Hard
A chi-square goodness-of-fit test compares observed counts in 11 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?
k = 11
df =
6.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. Using the table, find the critical value χ²crit at significance level α = 0.01.
α = 0.01
χ²crit =
Answer key
- 1. χ² = 1.577
- 2. χ² = 0.6889
- 3. χ² = 5.04
- 4. E = 37.02
- 5. df = 10
- 6. χ²crit = 15.09
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