IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit
A chi-square goodness-of-fit test checks whether the number of claims per policy follows a Poisson distribution whose mean is estimated from the data. After grouping, there are 6 categories. What is the degrees of freedom of the test statistic?
The degrees of freedom are 4. With six groups you lose one degree of freedom because the totals are fixed, and one more because the Poisson mean was estimated from the data, giving 6 − 1 − 1 = 4.
- A6
- B5
- C4Correct
- D3
- 2
Explanation
Degrees of freedom = number of groups − 1 − number of parameters estimated from the data. Here 6 − 1 − 1 = 4. Using 5 forgets the estimated Poisson mean.
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