A professor of statistics in Michigan State University wants to determine whether the average starting salaries among graduates of the 15 universities in Michigan are equal. A sample of 25 recent graduates from each university was randomly taken. The appropriate critical value for the ANOVA test is obtained from the F-distribution with degrees of freedom and is equal to:
A) 15 and 25
B) 14 and 360
C) 360 and 14
D) 25 and 15
E) 25 and 10

Question

Quizplus · Accepted Answer

In an ANOVA test, the degrees of freedom for the numerator (between groups) is calculated as the number of groups minus one, which is 15 - 1 = 14. The degrees of freedom for the denominator (within groups) is calculated as the total number of observations minus the number of groups, which is (25 graduates * 15 universities) - 15 = 375 - 15 = 360. Therefore, the correct degrees of freedom for the F-distribution are 14 and 360.

A Professor of Statistics in Michigan State University Wants to Determine