Question

A supervisor of a manufacturing plant is interested in relating the average number of defects produced per day to two factors: the operator working the machine and the machine itself. The supervisor randomly assigns each operator to use each machine for three days and records the number of defects produced per day. Is there sufficient evidence to conclude that there is a significant difference among the average number of defects produced per day for the different machines?

Number of Defects Produced per Day

	Operator A	Operator B
Machine A	88	44
	88	22
	66	22
	44	66
Machine B	44	22
	88	77
	88	22
	44	66
Machine C	00	00
	55	77
	22	00
	00	11

ANOVA

Source of Variation	SSSS	dfdf	MSMS
Total	188.0000188.0000	2323
Machine	54.250054.2500	22	27.125027.1250
Operator	13.500013.5000	11	13.500013.5000
Interaction	10.750010.7500	22	5.37505.3750
Within	109.5000109.5000	1818	6.08336.0833

Step 1 of 2:

Find the value of the test statistic for testing the difference among the average number of defects produced per day for the different machines. Round your answer to two decimal places, if necessary.

Step 2 of 2:

Make the decision to reject or fail to reject the null hypothesis of equal average number of defects produced per day for the different machines and state the conclusion in terms of the original problem. Be sure to test for interaction first. Use α=0.05α=0.05.

Answer 1

Source of Variation	SS	df	MS	F	P-value	F crit
machine	54.25	2	27.125	4.46	0.0267	3.55
operator	13.5	1	13.5	2.22	0.1536	4.41
Interaction	10.75	2	5.375	0.88	0.4305	3.55
Within	109.5	18	6.0833
Total	188	23

step 1 of 2"

value of the test statistic for testing the difference among the average number of defects produced per day for the different machines =27.125/6.0833 =4.46

Step 2 of 2:

(Since for interaction :critical value is not less than test statistic , interaction is not significant)

for 0.05 level and (2,18) degree of freedom, critical value =3.55.

since test statistic is higher than critical value. we reject the null hypothesis of equal average number of defects produced per day for the different machines

And conclude that at least one machine has different mean from others,