Exam MAS-I Practice Question 166
Study guide: Exam MAS-I
Mean claim severity (in $000) is compared across six territories with 5 claims each. The one-way ANOVA gives \hat\sigma^2 = 4.0 on 24 degrees of freedom, and its F test rejects equal means. After looking at the six sample means, the actuary notices that territories B and E differ most, by \bar y_B - \bar y_E = 4.0, and wants a statement about this difference that holds with 95% family-wise confidence.
These percentiles are available:
| Quantity | Value |
|---|---|
t, two-sided area 0.05, 24 df |
2.064 |
t, two-sided area 0.05/15 = 0.00333, 24 df |
3.258 |
Studentized range q_{0.05;\,6,\,24} |
4.373 |
F_{0.05;\,5,\,24} |
2.621 |
Part a (1 point)
Calculate the half-width of the Scheffé interval for \mu_B - \mu_E at 95% family-wise confidence. Give your answer to two decimal places.
Part b (1 point)
The actuary wants an interval that keeps the 95% family-wise guarantee for this comparison and, among such intervals, is the narrowest. Which interval should be used, and what does it conclude about \mu_B - \mu_E?
- A) The ordinary
tinterval; the difference is significant - B) Bonferroni for all 15 pairwise differences; the difference is not significant
- C) Tukey's interval; the difference is significant
- D) Scheffé's interval; the difference is not significant
Part c (1 point)
Explain why the ordinary t interval is not acceptable here, and why Tukey's interval is preferred to the Bonferroni and Scheffé intervals.
Answer this question and see the worked solution