A petroleum company was interested in comparing the miles per gallon achieved by four different gasoline blends

Question:

A petroleum company was interested in comparing the miles per gallon achieved by four different gasoline blends (A, B, C, and D). Because there can be considerable variability due to differences in driving characteristics and car models, these two extraneous sources of variability were included as blocking variables in the study. The researcher selected four different brands of cars and four different drivers. The drivers and brands of cars were assigned to blends in the manner displayed in the following table. The mileage (in mpg) obtained over each test run was recorded as follows.

a. Write a model for this experimental setting.
b. Estimate the parameters in the model.
c. Conduct an analysis of variance. Use Î± = .05.
d. What conclusions can you draw concerning the best gasoline blend?
e. Compute the relative efficiency of the Latin square design compared to a completely randomized design. Interpret this value. Were the blocking variables effective in reducing the variability in experimental units? Explain.
f. If future studies were to be conducted, would you recommend using both car model and driver as blocking variables? Explain.