Many drivers of cars that can run on regular gas buy premium in the belief that they will get better gas mileage. To test this belief, 10 cars were selected from a company fleet in which all thecars run on regular gas. Each car was filled with either regular or premium gasoline, which was decided by a coin toss, and the mileage for that tankful was recoded. Then the same car was filled with the other type of gasoline and the mileage recorded for the tankful. None of the drivers were informed on the type of gasoline in the vehicle. Car # 1 2 3 4 5 6 7 8 9 10 Regular 16 20 21 22 23 22 27 25 27 28 Premium 19 22 24 24 25 25 26 26 28 32 difference ? ? ? ? ? ? ? ? ? ? a. Write a null and alternative hypothesis. b. Calculate the difference between observations. c. Is there evidence that cars get significantly better fuel mileage with premium gasoline? (Perform a paired t-test) d How big might that difference be? (Construct a 90% confidence interval) e. Even if the difference is significant, why might the company choose to stick with regular gasoline?
Many drivers of cars that can run on regular gas buy premium in the belief that they will get
better gas mileage. To test this belief, 10 cars were selected from a company fleet in which all thecars run on regular gas. Each car was filled with either regular or premium gasoline, which was decided by a coin toss, and the mileage for that tankful was recoded. Then the same car was filled with the other type of gasoline and the mileage recorded for the tankful. None of the drivers were informed on the type of gasoline in the vehicle.
Car # 1 2 3 4 5 6 7 8 9 10
Regular 16 20 21 22 23 22 27 25 27 28
Premium 19 22 24 24 25 25 26 26 28 32
difference ? ? ? ? ? ? ? ? ? ?
a. Write a null and alternative hypothesis.
b. Calculate the difference between observations.
c. Is there evidence that cars get significantly better fuel mileage with premium gasoline?
(Perform a paired t-test)
d How big might that difference be? (Construct a 90% confidence interval)
e. Even if the difference is significant, why might the company choose to stick with regular
gasoline?
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