Metalworks, a supplier of fabricated industrial parts, wants to determine if the average output rate for a particular component is the same across the three work shifts. However, since any of four machines can be used, the machine effect must be controlled for within the sample. The accompanying table shows output rates (in units) for the previous day.

MachineShift (Factor A)

(Factor B)..............1..........................2..........................3

A........................1392........................1264........................1334

B........................1228........................1237........................1107

C........................1173........................1108........................1186

D.....................1331.....................1342.....................1387

a. Use Excel to generate the appropriate ANOVA table at the 5% significance level.

b. At the 5% significance level, can you conclude that the average output rate differs across the work shifts?

c. At the 5% significance level, can you conclude that the average output rate differs across the machines?

d. If significant differences exist across the machines, use Tukey's HSD method at the 5% significance level to determine which machines have different average output rates.