A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars were selected and were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X1 and X2 as given in the table. Consequently, D = X1 – X2. Test the effectiveness of the octane booster at α=0.05. Assume that the normality assumption is satisfied. Gasoline Mileage
Without booster, X1
(mpg)
Gasoline Mileage without booster, X1 (mpg) Gasoline Mileage With booster, X2(mpg)
21.2 23.8
25.4 25.6
20.9 22.4
27.6 28.3
22.8 24.5
27.3 28.8
23.4 25.2
1. What critical value should be used at a = 0.05?
2. Determine the mean of the differences.
3. State the alternative hypothesis?
4. Compute the standard deviation of the differences.