Suppose that an automobile manufacturer designed a radically new lightweight eng

Question

Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline that will have the best fuel economy. The four grades are: regular, below regular, premium, and super premium. The test car made three trial runs on the test track using each of the four grades and the miles per gallon recorded. At the 0.23 level, what is the critical value of F used to test the hypothesis that the miles per gallon for each fuel is the same?

Kilometers per liter   Regular Below Regular Premium Super Premium 39.31    36.39        38.99    40.04        39.87    40.00        40.02    39.89        39.87    41.01        39.99    39.93       

Explanation / Answer

The degree of freedom df1=4-1=3

The degree of freedom df2= 4*3-3=9

Given a=1-0.23=0.77, F(0.77, df1=4-1=3, df2=12-3=9) =1.730891 (from F table)

Answer: 1.77

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