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The table below shows the quantity of watches made by a company for different plant layout...

The table below shows the quantity of watches made by a company for different plant layout and shift times.

Weekly quantity of wrist watches produced in a factory

Shifts (hours)

Layout

6

8

12

1

300

400

900

350

350

950

450

490

850

330

500

800

2

80

250

500

100

300

450

60

190

550

150

240

600

3

700

800

1200

600

900

1800

750

680

2000

800

720

2200

  1. What are the effects of layout and shift hours on quantity of watches produced? Explain your answer using the p-values.
  2. Plot an Interaction plot between layout and shifts.
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ReportAnswer #1

i) The output of two-way ANOVA is:

Anova: Two-Factor With Replication
SUMMARY 6 8 12 Total
1
Count 4 4 4 12
Sum 1430 1740 3500 6670
Average 357.5 435 875 555.8333
Variance 4225 5233.333 4166.667 60371.97
2
Count 4 4 4 12
Sum 390 980 2100 3470
Average 97.5 245 525 289.1667
Variance 1491.667 2033.333 4166.667 36390.15
3
Count 4 4 4 12
Sum 2850 3100 7200 13150
Average 712.5 775 1800 1095.833
Variance 7291.667 9433.333 186666.7 326644.7
Total
Count 12 12 12
Sum 4670 5820 12800
Average 389.1667 485 1066.667
Variance 72862.88 56990.91 368787.9
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 4053689 2 2026844 81.17901 3.8E-12 3.354131
Columns 3226106 2 1613053 64.60586 5.11E-11 3.354131
Interaction 757244.4 4 189311.1 7.582273 0.000313 2.727765
Within 674125 27 24967.59
Total 8711164 35

The p-value of the interaction is 0.000313. As the p-value<0.05, it means that the interaction between layout and shift hours is significant. This means that the production of a particular layout depends on the levels of shift hours as well.

ii) The interaction plot between layout and shifts can be made from the "average" data. The plot is:

Interaction Plot 2000 1800 1600 1400 1200 1000 Layout 1 800 Layout 2 600 Layout 3 400 200 0 6-hour 8-hour 12-hour Shifts Prod

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