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IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit

A chi-squared goodness-of-fit test is applied to 200 policies grouped into 6 cells, testing a Poisson distribution whose mean was estimated from the data. After merging cells so every expected count is at least 5, 5 cells remain. What are the degrees of freedom, and which critical value applies at 5% (chi-squared 5%: 1 df 3.841, 2 df 5.991, 3 df 7.815, 4 df 9.488)?

Degrees of freedom are the 5 remaining cells minus 1 minus the 1 estimated Poisson mean, giving 3. The 5% critical value for 3 degrees of freedom is 7.815. Forgetting to deduct the estimated parameter would wrongly give 4 degrees of freedom.

  1. A4 df; 9.488
  2. B3 df; 7.815Correct
  3. C2 df; 5.991
  4. D5 df; 11.07
  5. 1 df; 3.841

Explanation

Degrees of freedom = number of cells after merging minus 1 minus number of estimated parameters = 5 - 1 - 1 = 3. The 5% critical value for 3 df is 7.815. Using 4 df forgets the parameter estimated.

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