Question

# A supervisor of a manufacturing plant is interested in relating the average number of defects produced...

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?

Operator A Operator B 88 44 88 22 66 22 44 66 44 22 88 77 88 22 44 66 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.

 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,

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