IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit
Policy claim counts per year are grouped as 0, 1, 2, 3 or more, with observed numbers 60, 30, 8, 2 from 100 policies. The model fitted (parameters fully specified, not estimated) gives probabilities 0.55, 0.30, 0.12, 0.03. What is the chi-square statistic, to two decimals?
The statistic is about 2.12, found by summing (O-E)^2/E over the four cells using expected counts 55, 30, 12 and 3. The terms are 0.4545, 0, 1.3333 and 0.3333.
- A1.52
- B2.12Correct
- C2.61
- D3.18
- 0.88
Explanation
Expected counts are 55, 30, 12, 3. Terms: 25/55 = 0.4545; 0; 16/12 = 1.3333; 1/3 = 0.3333. Sum = 2.1212, about 2.12. Using observed counts in the denominator would give a different value.
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