Question

4. Many drivers of cars that can run on regular gas actually buy premium gas in the belief that they will get better gas mileage. To test that belief, a consumer research group evaluated the use of 9 cars in a company fleet in which all the cars run on regular gas. Each car was filled first with either regular or premium gasoline, decided by a coin toss, and the mileage for that tankful was recorded. Then the mileage was recorded again for the same cars for a tankful of the other kind of gasoline. The consumer research group did not let the drivers know about this experiment. Here are the results (miles per gallon): Car No.234579 Regular 16 20 21 22 23 22 27 27 27 Premium 922 242425 2526 28284* Diff-P-R323 2 2311 Regular: Σ x = 205 Σx2-4781 Premium: Σx = 221 Σ x2-5491 Diff. Σχ 16 Σ x2-42- a) Is there evidence that the car gets better gas mileage by running on premium gas? Test the appropriate hypotheses at a- 0.05. < ed b) Suppose that research group did not use 9 cars but used 18 cars, 9 with the regular gas and 9 with premium gas. Using this design and a -0.05 to test the appropriate hypotheses.<

Answer 1

Conclusion: The estimated P-value is 0.693 and greater than 0.05 level of significance. Hence, we retain the null hypothesis and conclude that there is no evidence that the car gets better gas mileage by running on premium gas.