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 0.05 level, what is the critical value of F used to test the hypothesis that the miles per gallon for all fuels are the same. Show your solution

Kilometers per liter

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

Answer:4.07

Explanation / Answer

Number of different brands (k) = 4

Total number of Observations (n) = 12

So,

Numerator degrees of freedom = k - 1 = 4 - 1 = 3

Denominator degrees of freedom = n - k = 12 - 4 = 8

Hence,

Critical value of F with 3 Numerator df and 8 denominator df at 0.05 significance level = 4.07

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