An oil company tested four different blends of gasoline for fuel efficiency according to a Latin square design in order to control for the variability of four different drivers (1, 2, 3, 4) and four different models of cars (I, II, III, IV). Fuel efficiency was measured in miles per gallon (mpg) after driving cars over a standard course. The results for the fuel efficiencies (mpg) for 4 blends of gasoline (A, B, C, D) are given

	Car model
Driver	I	II	III	IV
1	D 15.5	B 33.9	C 13.2	A 29.1
2	B 16.3	C 26.6	A 19.4	D 22.8
3	C 10.8	A 31.1	D 17.1	B 30.3
4	A 14.7	D 34.0	B 19.7	C 21.6

Because this experiment was done by an oil company it is reasonable to assume that the main issue is whether there are differences among the four blends and higher mpg is desirable. (You do not have to analyze the residuals for this problem.)

a. Carry out the analysis of variance. Are there any differences between the blends in
regards to fuel efficiency? If yes, which blend would you recommend? Why?
b. Would you conclude that there is an effect due to the driver? Why?
c. Would you conclude that there is an effect due to model of the car? Why?
d. Redo all analyses above at = 0.01. Which, if any, of your conclusions would be different?
e. Suppose we had ignored the fact that the car model and the driver might contribute to observed mpg. Carry out a one-way ANOVA with the blend of gasoline as the only
effect to be tested (i.e. ignore which driver/car model was used for each observation). What would you conclude in this case? Use = 0.05.