Four drivers volunteer to drive their car in a study of mileage obtained under four different brands of gasoline. Each driver uses each brand in 100 miles of driving (over a set course, at fixed speeds, etc.) The mileage per gallon was calculated for each run, giving the following: Brand of Gasoline Driver A B C D 1 12.6 10.9 11.3 13.2 2 16.4 16.1 17.6 17.9 3 13.0 10.6 11.8 12.6 4 19.2 18.0 18.9 19.9 a. Write out the additive linear model for the above study assuming 'driver' as a fixed treatment. (Note: Does not matter which representation of model you use)

b. In context of your model in (a), state both all the null and associated alternative hypotheses of interest.

c. Use the following data to compute the appropriate ANOVA table for your model in a. Copy and paste the output. data Brand; input Driver @@; do brand='A','B','C','D'; input mpg @@; output; end; datalines; 1 12.6 10.9 11.3 13.2 2 16.4 16.1 17.6 17.9 3 13.0 10.6 11.8 12.6 4 19.2 18.0 18.9 19.9 ;

d. Based on the SAS output, and the associated p-value from ANOVA, make the decision and the conclusion regarding the hypotheses stated in (b).

e. Based on your conclusion in d, share your thoughts about how you will further investigate the significant effect(s). (Note: No need to use SAS here, only share thoughts) f. If it is possible to implement your thoughts in (e) based on the materials covered, implement it. Otherwise state why it is not possible to implement your thoughts. I believe this will be due to the amount of materials covered, so state where your knowledge lacks. (Note: Implementing thoughts mean testing the comparisons you thought in e)