# 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.

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:

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