Question: Five machines were designed to produce steel pipes with a diameter of 4.0 cm. To test the machines,

a random selection of six pipes are selected from each machine and their diameters are measured. The

data are as follows.

Machine 1 Machine 2 Machine 3 Machine 4 Machine 5

3.8 3.9 3.9 4.1 4.1

3.9 3.8 4.2 3.9 4.2

3.9 4.0 4.1 4.0 4.3

3.8 4.0 4.0 4.1 4.1

3.9 4.0 3.8 4.0 4.0

3.8 3.7 4.2 3.9 3.8

1. Use ANOVA to determine if there is a difference between the five machines. Include the ANOVA
   table in your write up.
2. Use Tukey's post-hoc test to determine which pairs of machines are significantly different.
3. Suppose that Machine 1 is considered the \gold standard" in steel pipe production. Use Dunnett's
   post-hoc test to determine if the other four machines are significantly different than Machine 1.
4. Use the Kruskal-Wallis to determine if there is a difference between the five machines.
5. Use the Kruskal-Wallis-based approach to post-hoc testing to determine which pairs of machines
   are significantly different.
6. Use PROC MIXED in SAS to construct the plots necessary to assess ANOVA assumptions for
   the model in part (a).
7. Comment on each of the plots as they relate to the corresponding ANOVA assumptions.
8. Use the BFL test to formally determine if the five variances can be assumed equal.
9. Which analysis would you present to the company that commissioned this project? Use your

responses to parts (f) through (h) to formulate your response.

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