Exam MAS-I Practice Question 172
Study guide: Exam MAS-I
An actuary plans a one-way ANOVA at the 5% level to test whether mean log-severity differs across three territories, with n = 5 claims from each. Log-severity is normal with standard deviation \sigma = 0.5 in every territory, and the true territory means are 8.1, 8.1 and 8.7. Under these true means the F statistic has a noncentral F-distribution with 2 and 12 degrees of freedom.
Part a (1 point)
Calculate the noncentrality parameter \theta of the F statistic's distribution. Give your answer to two decimal places.
Part b (1 point)
The number of territories and the number of claims per territory stay fixed, so the F statistic keeps 2 and 12 degrees of freedom and the same critical value. Which of the following changes to the situation above would give the test the highest power?
- A) Every true territory mean is 0.3 higher: 8.4, 8.4 and 9.0
- B) The standard deviation falls from 0.5 to 0.45, with the true means unchanged
- C) The true means are 7.9, 8.3 and 8.7, with
\sigma = 0.5 - D) The true means are 8.0, 8.6 and 8.6, with
\sigma = 0.5
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