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 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 =
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 = 1802 × 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, bus”.
row total = 94column total = 43N = 165
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 = 2003 × 2α = 0.01
χ² =
6.Hard
A chi-square test of independence is carried out on a contingency table with 3 rows and 3 columns (not counting the totals). How many degrees of freedom df does the test have?
3 × 3
df =
Answer key
- 1. χ² = 8.687
- 2. χ² = 5.067
- 3. χ² = 4.575
- 4. E = 24.5
- 5. χ² = 38.89
- 6. df = 4
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