STAT 5132: Montgomery Chapter 3 Assignment

Reminder:
DO NOT hand in unedited SAS output/code.
ONLY include the results required
Answer questions IN ORDER; Include question number; Label graphs
Include SAS input for questions at the end of the entire homework as Appendix
SAVE your SAS code, since you may be asked to continue problems on successive homework
Reading: Montgomery Chapter 3
1. You want to compare 5 treatments using a one-way fixed effects model. You want enough
replication so that the F test has at least 80% power (at the 5% significance level) when
the largest difference between means is 4 units. Suppose that 2 = 9. How large must
n be (assuming balanced experiment, i.e., ni = n)? Make sure you show your software
inputs or hand calculations to receive full credits.
2. Recall Exercise 5 in Lecture 9. There were a = 6 randomly chosen schools each with
n = 5 teachers.
a. How much power does this study have if the true variances were such that 22=2? Make sure you show your software inputs or hand calculations to receive full
credits.
b. In a random effects situation you can either increase a and/or n to increase the power.
You investigate different combinations and find the following:
a = 11, n = 5, 81:6% power
a = 9, n = 6, 82:2% power
a = 8, n = 7, 83:7% power
a = 7, n = 8, 83:6% power
If it costs $20 in time and resources to evaluate each teacher once at a school and $100 in
time and resources to access a school, which of these options would you choose? Explain your
answer.

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