Question: A petroleum company is interested in comparing the miles per gallon achieved by four different gasoline blends \((\mathrm{A}, \mathrm{B}, \mathrm{C}\), and \(\mathrm{D})\). It implemented a \(4 \times 4\) Latin Square design using the amount of gasoline (in deciliters) needed to drive around a 15 -mile obstacle course as the response variable. The results of the experiment are presented below.

1. Why do you think a Latin Square design used for this experiment?
2. Given that \(\mathrm{SS}_{\mathrm{E}}=16.5\), test if there is a difference between the four gasoline blends. For full credit, show your work.
3. Construct the \(95 \%\) confidence interval for the difference in average deciliters between Blend D and Blend C. What does the confidence interval tell you?
4. This study was run on four different days. Each day, one driver drove all four cars (in a random order) around the course. Does this pose a problem with the interpretation of the study? Explain your answer.

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