A major U.S. oil company has developed two blends of gasoline. Managers are interested in determining whether a difference in mean gasoline mileage will be obtained from using the two blends. As part of their study, they have decided to run a test using the Chevrolet Impala automobile with automatic transmissions. They selected a random sample of Impalas using Blend 1 and another Impalas using Blend 2. Each car was first emptied of all the gasoline in its tank and then filled with the designated blend of the new gasoline. The car was then driven 200 miles on a specified route involving both city and highway roads. The cars were then filled and the actual miles per gallon were recorded. The gathered sample data from each group is included in the Excel file. Assume that you know the standard deviation for each population (4.7 miles per gallon for Blend 1, 4.1 miles per gallon for Blend 2).

For this question, perform your calculation using the formulas do not use the Analysis Toolpak tools.

Part a) Calculate a 95% confidence interval for the difference between population means.

Part b) The company suspect that the population mean for Blend 1 is less than that for Blend 2. Perform a hypothesis test, using the p-value method, at a 90% confidence level. Show all parts of the hypothesis test, including your hypotheses, identification/calculation of the necessary values, your test-statistic calculation, your p-value calculation, and your conclusion.