Problem: (a) Assess ANOVA assumptions using the graph from PROC MIXED.

(b) Perform an ANOVA to determine if there is an interaction between the age group and

types of products; \(\alpha \) = 0:05

(c) If there is an interaction, create a profile plot for age group and product type and

provide an interpretation for the interaction

(d) If there is not an interaction, remove the interaction term, recompute the ANOVA

table, and determine if there are main effects of age group and product type; _ = 0:05

(e) Report significantly different pairs using Tukey's W and \(\alpha \) = 0:05; REMEMBER: if

there is an interaction present, we must account for that when performing post-hoc testing

Data from 15.10

1. Assess ANOVA assumptions using the graph from PROC MIXED.
2. Determine if there is a difference between gasoline blends using ANOVA for Latin
   Square; \(\alpha \) = 0:05
3. If there is a difference per part (b), use Tukey's W to determine the significantly
   different pairs; \(\alpha \) = 0:05
4. From part (c), which blend (or blends) gives the highest gas mileage?
5. Determine if there is a difference between gasoline blends using ANOVA for completely
   randomized designs (i.e., ignore the blocking factors); \(\alpha \) = 0:05
   (e) Compare the MSE from part (b) to the MSE from part (e) what happens when we
   ignore the blocking factors?
6. Which would you say is the appropriate analysis?

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