A machine shop has three machines used in precision grinding of cam rollers. Three machinists are employed to grind rollers on the machines. In an experiment to determine whether there are differences in output among the machines or their operators, each operator worked on each machine on four different days. The outcome measured was the daily production of parts that met specifications. With the operator as the row effect and the machine as the column effect, the following sums of squares were observed: SSA = 3147.0, SSB = 136.5, SSAB = 411.7, SSE = 1522.0.

a. How many degrees of freedom are there for the operator effect?

b. How many degrees of freedom are there for the machine effect?

c. How many degrees of freedom are there for interactions?

d. How many degrees of freedom are there for error?

e. Construct an ANOVA table. You may give ranges for the P-values.

f. Is the additive model plausible? Provide the value of the test statistic and the P-value.

g. Is it plausible that the main effects of operator are all equal to 0? Provide the value of the test statistic and the P-value.

h. Is it plausible that the main effects of machine are all equal to 0? Provide the value of the test statistic and the P-value.