Dental claims experience was collected on 6480 policies. There were a total of 9720 claims on these policies. The following table shows the number of dental policies having varying numbers of claims.

Number of Claims	Number of Policies
0	1282
1	2218
2	1856
3	801
4	235
5	81
6 or more	7
Total	6480

Calculate the chi-squared statistic to test if a Poisson model with no predictors provides an adequate fit to the data.

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Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: C

The average number of claims on a policy is 9720/6480 = 1.5. Using this as the parameter of a Poisson distribution yields the following table of actual (given) and expected (calculated) policies with given numbers of claims:

Number of Claims	ActualNumber of Policies	Poisson Probability	ExpectedNumber of Policies	Chi-square
0	1282	0.2231	1445.69	18.53
1	2218	0.3347	2168.86	1.11
2	1856	0.2510	1626.48	32.39
3	801	0.1255	813.24	0.18
4	235	0.0471	305.21	16.15
5	81	0.0141	91.37	1.18
6 or more	7	0.0045	29.16	16.84
Total	6480	1.0000	6480.01	86.38

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.