IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit
A die is rolled 120 times to test whether it is fair. The observed frequencies for faces 1 to 6 are 15, 25, 20, 18, 22 and 20. What is the value of the chi-square test statistic?
The statistic is 2.9. Each face has an expected count of 20, the squared deviations sum to 58, and dividing by the expected count of 20 gives 58/20 = 2.9.
- A2.9
- B3.0
- C3.5
- D4.0Correct
- 5.0
Explanation
Expected count for each face is 120/6 = 20. Deviations are -5, 5, 0, -2, 2, 0, with squares 25, 25, 0, 4, 4, 0. Sum of squares = 58, divided by 20 gives 2.9. Hence 2.9 is correct; using 20 as a divisor but forgetting one term gives other values.
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