A machine shop has three machines used in precision grinding of cam rollers. Threemachinists are employed to grind rollers on the machines. In an experiment to determinewhether there are differences in output among the machines or their operators, each operatorworked on each machine on four different days. The outcome measured was the dailyproduction of parts that met specifications. With the operator as the row effect and themachine 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 ofthe 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.
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
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.
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