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? .
A)1.96
B)4.07
C)2.33
D)12.00

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?  .
A)1.96 
B)4.07 
C)2.33 
D)12.00

Quizplus · Accepted Answer

Since there are four grades of gasoline, we will need to use a one-way ANOVA test to determine if the means of each group are statistically different. At the 0.05 level, and with three degrees of freedom for both the numerator and denominator, the critical value for F is 4.07. Therefore, if the calculated F-value exceeds 4.07, we can reject the null hypothesis and conclude that there is a significant difference in the means of at least two of the gasoline grades.

Suppose That an Automobile Manufacturer Designed a Radically New Lightweight