Additive a was randomly assigned to 15 of the cars and additive b was randomly assigned to the other 15 cars. the gas tank of each car was filled with gasoline and the assigned additive. the cars were again run under the same driving conditions until the tanks were empty. the distance traveled was recorded and the difference in the distance with the additive minus the distance without the additive for each car was calculated.
the following table summarizes the calculated differences. note that negative values indicate less distance was traveled with the additive than without the additive.
additive values below q1 q1 median q3 values above q3
a −10, −8, −2 1 3 4 5, 7, 9
b −5, −3, −3 −2 1 25 35, 37, 40
(a) two ways that the effectiveness of a gasoline can be evaluated are by looking a either:
o the proportion of cars that have increased gas mileage when the additive is used in those cars or
o the mean increase in gas mileage when the additive is used in those cars.
1. which additive, a or b, would you recommend if the goal is to increase gas mileage in the highest proportion of cars? explain your choice.
2. which additive, a or b, would you recommend if the goal is to have the highest mean increase in gas mileage? explain your choice.