1.Easy
A die is rolled 300 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 = 300k = 6
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 = 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 = 1002 × 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 “night shift, major”.
row total = 71column total = 80N = 179
E =
5.Hard
A chi-square test of independence is carried out on a contingency table with 3 rows and 6 columns (not counting the totals). How many degrees of freedom df does the test have?
3 × 6
df =
6.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 = 2803 × 2α = 0.01
χ² =
Answer key
- 1. χ² = 35.16
- 2. χ² = 3.532
- 3. χ² = 14.84
- 4. E = 31.73
- 5. df = 10
- 6. χ² = 17.25
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