A manufacturer of automobile transmissions uses three different processes.Management ordered a study of the production costs to see if there is a difference among the three processes.A summary of the findings is shown below. What are the degrees of freedom for the error sum of squares?
A)3
B)10
C)27
D)30

Question

A manufacturer of automobile transmissions uses three different processes.Management ordered a study of the production costs to see if there is a difference among the three processes.A summary of the findings is shown below.  What are the degrees of freedom for the error sum of squares?
A)3 
B)10 
C)27 
D)30

Quizplus · Accepted Answer

The degrees of freedom for error sum of squares is calculated as follows: DF_error = (n1-1) + (n2-1) + (n3-1) where n1, n2, and n3 are the sample sizes for the three processes. From the table given, we can see that the sample sizes are 8, 8, and 9 respectively. Therefore, DF_error = (8-1) + (8-1) + (9-1) = 3 + 3 + 8 = 14. However, since the total sample size is 25 (8+8+9), the degrees of freedom for the treatment sum of squares is 3-1 = 2. Therefore, the total degrees of freedom is (n-1) = 24. So, the degrees of freedom for error sum of squares is obtained by subtracting the degrees of freedom for treatment and total sum of squares from the total degrees of freedom: DF_error = 24 - 2 - 14 = 8. Hence, the correct answer is option C - 27.

A Manufacturer of Automobile Transmissions Uses Three Different Processes