Suppose 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, economy, premium, and super premium. The test car made three runs on the test track using each of the four different grades of gasoline (i.e there were a total of 12 test runs). The miles per gallon were recorded for each grade. 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 are the same
The sample size is 12. The number of treatments is 4. Thus, the degrees of freedom associated with the sum of square error is 8 which is sample size minus number of treatments. The degree of freedom is 3 which is number of treatments minus 1. The theoretical F value is determined by entering the F table (pp.723-24) at 3 degrees of freedom for the numerator and 8 degrees of freedom for the denominator for the level of significance given which in this case is 0.05.
