A petroleum company was interested in comparing the miles per gallon achieved by four different gasoline blends (I, II, III, IV). Because there can be considerable variability due to differences in drivers and car models, these two extraneous sources of variability were included as blocking variables in the following Latin square design. Each driver drove each car model over a standard course with the assigned gasoline blend using a Latin square design. However, when driver 3 was operating a model 4 car using blend II gasoline, there was a malfunction of the car's carburator that invalidated the data. This malfunction was not discovered until well after the completion of the study, and hence the data could not be replaced. The miles per gallon data are given here.
a. Run an analysis of variance by estimating the missing value. Use a = .05.
b. Make treatment comparisons by using Fisher's least significant difference, with a = .05.