Question: A bottle cap manufacture with four machines and three operators wants to see if variation in hourly production is due to the machines and/or the operators or an interaction effect of machine and operator. Each operator is assigned to each machine and the production of caps from 3 randomly selected hours is recorded. The analysis shows the following Analysis of Variance table.
|
Source
|
Sum of Squares
|
df
|
Mean Square
|
|
Machines
|
114
|
|
|
|
Operators
|
115
|
|
|
|
Interaction
|
100
|
|
|
|
Error
|
54
|
|
|
|
Total
|
383
|
|
|
Answer these questions.
What are the degrees of freedom for the machines, operators, interaction and error?
What is the critical value of F for the machine effect at the 1% level of significance?
What is the mean square for machines, operators, interaction and error?
What is the computed value of F for the machines?
What is the computed value of F for the operators?
Using a 1% significance level, what is the decision for the machines?