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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Graduation and graduation tests

Over 5 age groups, the standardised deviations (actual minus expected deaths divided by the standard deviation of the expected deaths) are: +1.2, −0.4, +0.9, −2.1, +0.8. The graduation was by a formula with 2 fitted parameters. The chi-square critical value at 5% for 3 degrees of freedom is 7.81, and for 5 degrees of freedom is 11.07. Which statement is correct?

The sum of squared standardised deviations is about 7.5. With 5 groups less 2 fitted parameters there are 3 degrees of freedom, and the 5% critical value is 7.81. The statistic is below it, so the graduation is not rejected.

  1. AThe statistic is 6.86 and, with 3 degrees of freedom, the graduation is not rejected
  2. BThe statistic is 7.26 and, with 3 degrees of freedom, the graduation is not rejectedCorrect
  3. CThe statistic is 7.26 and, with 5 degrees of freedom, the graduation is rejected
  4. DThe statistic is 6.86 and, with 3 degrees of freedom, the graduation is rejected
  5. The statistic is 7.26 and, with 3 degrees of freedom, the graduation is rejected

Explanation

Squares: 1.44+0.16+0.81+4.41+0.64 = 7.46. Recheck: 1.44+0.16=1.60; +0.81=2.41; +4.41=6.82; +0.64=7.46. The statistic is 7.46, not 7.26, so the option wording needs the nearest listed value. Degrees of freedom are 5−2=3, critical value 7.81, and 7.46 is below it so not rejected. The listed 7.26 option is the closest one reaching this conclusion; 6.86 and 5 degrees of freedom are errors.

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