As director of the employee wellness and productivity program in your company,you are interested in comparing the effects of strength training,aerobic training,and yoga on decreasing rates of injury and absenteeism.The company has 9 divisions with roughly the same number of employees,and you randomly assign 3 divisions to participate in strength training,3 to aerobic training,and 3 to yoga.Analysis of the data yielded the following ANOVA table.
Using $\alpha$ = 0.05,the critical F value is ______.
A) 3.68
B) 3.74
C) 4.54
D) 4.60
E) 9.46

Question

As director of the employee wellness and productivity program in your company,you are interested in comparing the effects of strength training,aerobic training,and yoga on decreasing rates of injury and absenteeism.The company has 9 divisions with roughly the same number of employees,and you randomly assign 3 divisions to participate in strength training,3 to aerobic training,and 3 to yoga.Analysis of the data yielded the following ANOVA table.  
Using $\alpha$ = 0.05,the critical F value is ______.
A) 3.68 
B) 3.74 
C) 4.54 
D) 4.60 
E) 9.46

Quizplus · Accepted Answer

To find the critical F value, we need to look at the numerator and denominator degrees of freedom in the ANOVA table. From the table, we see that the numerator df is 2 (since there are three groups being compared) and the denominator df is 18 (since there are a total of 9 divisions involved, each contributing data to one of the three groups). Using a significance level of 0.05, we can look up the critical F value in an F-distribution table with these degrees of freedom to be 3.68 (rounded to two decimal places), which is closest to choice A. Therefore, the best choice is A, with an explanation as given above.

As Director of the Employee Wellness and Productivity Program in Your