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

A chi-square goodness of fit test on 8 classes, with 2 parameters estimated from the data, gives a statistic of 9.2. The 5% critical value for 5 degrees of freedom is 11.07, and for 7 degrees of freedom is 14.07. Which conclusion is correct?

Do not reject the fit. Degrees of freedom are 8 - 1 - 2 = 5, the critical value is 11.07, and the statistic of 9.2 is below it, so there is insufficient evidence against the model.

  1. AReject the fit, since 9.2 exceeds the 5% value for 5 degrees of freedom
  2. BDo not reject the fit, since 9.2 is below 11.07 on 5 degrees of freedomCorrect
  3. CDo not reject the fit, since 9.2 is below 14.07 on 7 degrees of freedom
  4. DReject the fit, since the number of estimated parameters is too large
  5. The test is invalid because the statistic is not an integer

Explanation

Degrees of freedom = 8 - 1 - 2 = 5. The critical value is 11.07 and 9.2 is less than this, so there is no evidence against the fitted model. Using 7 degrees of freedom ignores the estimated parameters.

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