Suppose that an automobile manufacturer designed a radically new lightweight eng
ID: 3363602 • Letter: S
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 0.05 level, what is the critical value of F used to test the hypothesis that the miles per gallon for each fuel is the same. Show your work.
Miles Per Gallon
Regular: Below Regular Premium Super Premium
$39.31 36.69 38.99 40.04
39.87 40.00 40.02 39.89
39.87 41.01 39.99 39.93
.) 3.49
B.) 4.07
C.) 2.33
D.) 3.86
E.) 3.26
Explanation / Answer
Ans is 4.07
B option
You could do the same mental exercise for a 2 x 3 design, but it is tedious for me to write up, so I am going to give you the general rule. Every variable in your design has a certain number of levels. Variable 1 in the 2 x 3 design has 2 levels, variable 2 has 3 levels. You get df1 when you multiply the levels of all variables with each other, but with each variable, subtract one level. So in the 2 x 3 design, df1 would be (2 – 1) x (3 – 1) = 2 degrees of freedom. Back to the 2 x 2 design, df1 would be (2 – 1) x (2 – 1) = 1 degrees of freedom. Now let’s see what happens with a 2 x 2 x 2 design: (2 – 1) x (2 – 1) x (2 – 1) = still 1 degrees of freedom. A 3 x 3 x 4 design (I hope you’ll never have to analyze that one): (3 – 1) x ( 3 – 1) x (4 -1) = 2 x 2 x 3 = 12 degrees of freedom.
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