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.

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 a 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.

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With24.6 28.3 18.9 23.7 5.4 29.5 With 26.3 31.7 18.2 25.3 18.3 30.9