Question: A manufacturer of commercial fishing nets produces the net material on a large number of machines. The company would like the machines to be as homogeneous as possible in order to produce netting that has a very uniform strength. The company is concerned that there is considerable amount of material that must be discarded, reworked, or downgraded to a lower quality product. This results in loss of revenue to the company. The process engineer, after examining the maintenance records of the machines, suspects that there may be a larger variation in material strength between machines relative to the usual variation in material produced from the same machine. The two sources of variation are measured by \(\sigma_{M}^{2}\), the detectable variation between machines, referred to as the "Special Cause " variability, the variability due to Machine Differences. The second source of variability is measured by \(\sigma^{2}\), the background noise or variability in the process, referred to as the "Common Cause" variability. The engineer decides to run a small pilot study by randomly selecting four machines at random and then selecting five samples of material from each of the selected machines for strength determinations. The 20 samples of material were then analyzed in random order. The results are given here.

1. What type of design is this? Write down the model with all the assumptions.
2. Find the values for A, B and C in the ANOVA table below.
   
3. Is there significant variability due to variability due to Machine Differences (use a = 0.05)?
4. Estimate all variance components.
5. The overall goal of the company is to produce net with strength measurements mean of at least 123. Test if the overall mean strength measurements is larger than 123.
6. If there is another manufacturer who produces the same net material for commercial fishing nets and the same study was conducted. Describe a possible way to compare the overall means between the two manufacturer. (Assume that the setting is the same \(\mathrm{a}=4, \mathrm{n}=5\) also \(\mathrm{MSE}_{B}=\) \[2.3,MST{{r}_{B}}=34.2\] and B=126.5. Explain your steps - (some extra points will be given here)-

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