Question

2) (16 Marks in Total) To assess the relative of four different gasoline blends, researchers conducted an experiment using 24 automobiles of the same type, model, and engine size with six randomly assigned to one of the blends and the mileage per gallon was recorded for each car. Suppose all required assumptions are satisfied. The summary statistics and ANOVA for data are given in the following table:

1. (2 mark) Define a linear combination (a contrast) in terms of the 4 group means defined earlier to compare the overall average mileage effect of supplement x.
2. (2 mark) Define a linear combination (a contrast) in terms of the 4 group means defined earlier to compare the overall average mileage effect of supplement y.
3. (2 mark) Define a linear combination (a contrast) in terms
 of the 4 group means defined earlier to compare the overall average mileage effect of supplement x versus the overall average mileage effect of supplement y.
4. (5 marks) Use the Bonferroni method to calculate three simultaneous 94% confidence intervals for the contrast in parts (a), (b) and (c).
5. (5 marks) Using the Bonferroni method for simultaneous inference with family-wise confidence of 94%, summarize all significant differences. Also, what is the resulting individual confidence level for each interval? (Hint: You don’t have to construct all 6 confidence intervals. You can simply find E, the margin of errors (it will be the same for all pairs as we have equal sample sizes) and then find all pairs of sample means that differ by at least E. State clearly what E is and how it was calculated. Summarize.

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