Part B - Worked Problems

Show all of your work and necessary steps for full marks. Each question is worth 10 points.

1. The manufacturer of a gasoline additive claims that the use of this additive increases gasoline mileage. A random sample of 6 cars was selected, and these cars were driven for one week without the gasoline additive and then for one week with the additive. The following table gives the mileage (in miles per gallon) for these cars with and without the additive:

Car

1

2

3

4

5

6

Mileage Without Additive

24.6

28.3

18.9

23.7

15.4

29.5

Mileage With Additive

26.3

31.7

18.2

25.3

18.3

30.9

Asuming mileages are normally distributed, can you conclude that the use of the gasoline additive increases mileage at the 2.5% significance level?