many drivers of cars run on regular gas actually buy premium in the belief that they will get better gas mileage. to test that belief, we use 10cars from a company fleet in which all the cars run on regular gas. each car is filled first with either regular or premium gasoline, decided by a coin toss and the mileage for that tankful is recorded. then the mileage is recorded again for the same cars for a tankful of the other kind of gasoline. we don't let the drivers know about this experiment.

a. is there evidence that cars get significantly better fuel economy with premium gasoline?

b. how big might that difference? check 90% confidence interval.

c. even if the difference is significant, why might the company choose to stick with regular gasoline?

d. suppose u have done a "bad thing".( we are sure you didn't) suppose you had mistakenly treated these data as two independent samples instead of matched pairs. what would the significance test have found? carefully explain why the results are so different.