A car manufacturer concerned about two issues: rising cost of fuel and pollution from car emissions, decided to produce more fuel-efficient cars. He carried out an experiment to test a set of five prototypes of burners he designed, which were to be fitted to the new generation of cars he wished to produce. These burners were designated (A, B, C, D). He then added the old burner (E)

which had been in use, to compare them to see whether the new burners had improved fuel efficiency, and reduced the emission of pollutants. In his experiments, he planned to use five different drivers and five different cars.

He realized that the skills of the drivers could be different and suspected that cars could have effect on the fuel consumption and therefore decided to use a 5×5 Latin square design to study the efficiency of the burners. Randomization led to the following layout. Experiments were performed, changing the burners in each car in the order shown. Cars were driven on the same road, at the same speed for the same distance before fuel consumption was measured in miles per gallon. He recorded the consumption and the units of emission/gallon released.

Analyze the responses and determine whether the new burners have significant effect on the fuel.

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Driver Car 1 2 3 4 5 12345 E 54,10 A 76,6 C 60,6 D 59,6 B 60,7 D 57,6 E 50,12 B 69,8 C 54,6 A 70,6 C 53,5 D 66,8 A 75,5 B 59,8 E 50,13 B 60,6 C 60,5 E 53,12 A 64,5 D 60,6 A 64,6 B 70,7 D 69,8 E 51,13 C 56,5