Skip to content

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

A test of whether claim sizes follow a fitted distribution produces expected frequencies of 30.0, 25.0, 18.0, 4.0 and 3.0 for five classes. Following the standard rule that every expected frequency should be at least 5, what is the best step before applying the chi-square test?

Combine the last two classes into one with expected frequency 7.0. This fixes the shortfall below 5 with minimal loss of information, whereas discarding classes or leaving them unchanged would distort the chi-square approximation.

  1. ADiscard the last two classes and reduce the sample size accordingly
  2. BCombine the last three classes into one class with expected frequency 25.0
  3. CCombine the last two classes into one class with expected frequency 7.0Correct
  4. DApply Yates' continuity correction to the last two classes
  5. Proceed unchanged because the total expected frequency exceeds 5

Explanation

Only the classes with expected 4.0 and 3.0 are below 5. Merging them gives 7.0, which satisfies the rule and loses the least information. Merging three classes is unnecessary, and discarding data biases the test.

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