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

Without       24.6           28.3            18.9            23.7             15.4             29.5

With           26.3           31.7            18.2            25.3             18.3             30.9

a. Construct a 99% confidence interval for the mean μd of the population paired differences, where a paired difference is equal to the miles per gallon without the gasoline additive minus the miles per gallon with the gasoline additive.

b. Using the 2.5% significance level, can you conclude that the use of the gasoline additive increases the gasoline mileage? Assume that the population of paired differences is (approximately) normally distributed.