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 trial runs on the test track using each of the four grades. 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?
A) 1.96
B) 4.07
C) 2.33
D) 12.00

Question

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 trial runs on the test track using each of the four grades. 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? 
A) 1.96 
B) 4.07 
C) 2.33 
D) 12.00

Quizplus · Accepted Answer

To test the hypothesis that the miles per gallon for each fuel are the same, we need to perform an analysis of variance (ANOVA) test. The critical value of F for a four-group ANOVA with two degrees of freedom in the numerator and eight degrees of freedom in the denominator, at the 0.05 level, is 4.07. Therefore, we choose option B, which is the only choice that matches this value.

Suppose an Automobile Manufacturer Designed a Radically New Lightweight Engine