High Fuel Company markets a gasoline additive for automobiles that it claims will increase a car’s miles per gallon (mpg) performance. In an effort to determine whether High Fuel’s claim is valid, a consumer testing agency randomly selected eight makes of automobiles. Each car’s tank was filled with gasoline and driven around a track until empty. Then the car’s tank was refilled with gasoline and the additive, and the car was driven until the gas tank was empty again. The miles per gallon were measured for each car with and without the additive. The results are reported in the file High Fuel.
The testing agency is unwilling to accept the assumption that the underlying probability distribution is normally distributed, but it would still like to perform a statistical test to determine the validity of High Fuel’s claim.
a. What statistical test would you recommend the testing agency use in this case? Why?
b. Conduct the test that you believe to be appropriate. Use a significance level of 0.025.
c. State your conclusions based on the test you have just conducted. Is High Fuel’s claim supported by the test’s findings?