(Solution) - A study was conducted to compare automobile gasoline mileage for -(2025 Original AI-Free Solution)

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A study was conducted to compare automobile gasoline mileage for three formulations of gasoline. Four automobiles, all of the same make and model, were used in the experiment, and each formulation was tested in each automobile. Using each formulation in the same automobile has the effect of eliminating (blocking out) automobile- to-automobile variability. The data (in miles per gallon) follow.

a. Do the data provide sufficient evidence to indicate a difference in mean mileage per gallon for the three gasoline formulations?
b. Is there evidence of a difference in mean mileage for the four automobiles?
c. Suppose that prior to looking at the data, you had decided to compare the mean mileage per gallon for formulations A and B. Find a 90% confidence interval for this difference.
d. Use an appropriate method to identify the pairwise differences, if any, in the average mileages for the three formulations.