Skip to content

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

For a likelihood ratio test comparing a Poisson model with a single rate (H0) against a model with separate rates for 4 independent risk groups (H1), −2 log Λ = 9.1. Using the asymptotic chi-square distribution, which is the correct degrees of freedom and conclusion at the 5% level? (Chi-square 5% points: 3 df 7.815; 4 df 9.488; 5 df 11.07)

Degrees of freedom are 4 minus 1, which is 3. The critical value 7.815 is below 9.1, so H0 of a common rate is rejected at 5 percent.

  1. A3 df; reject H0Correct
  2. B4 df; do not reject H0
  3. C3 df; do not reject H0
  4. D4 df; reject H0
  5. 5 df; do not reject H0

Explanation

H1 has 4 free parameters and H0 has 1, so df = 3. The critical value is 7.815 and 9.1 exceeds it, so reject H0. Using 4 df would wrongly give non-rejection.

Did you get it right without looking?

One question tells you little. A timed set on Hypothesis testing and goodness of fit shows your real accuracy, how long you take and where you lose marks.

Practise Hypothesis testing and goodness of fitFree diagnostic mock

More Hypothesis testing and goodness of fit questions