3. [15 points] Ima Dunce performs a four factor factorial experiment with two replicates. Factor A is fixed and has two levels. Factors B, C, and D are random and each have three levels. Uncertain whether the choice of fixed or random factors makes a dierence in the analysis, she tests all interactions and main eects using MSE. Complete the table below and specify the appropriate MS to use in the denominator of each F-test in the right hand side of each item. If there is no single MS, simply indicate this by notation of . 4 4. [40 points] Harry and Judy Peterson-Nedry (two friends of the author) own a vineyard and winery in Newberg, Oregon. They grow several varieties of grapes and manufacture wine. Harry and Judy have used factorial designs for process and product development in the winemaking segment of their business. This problem describes the experiment conducted for their 1985 Pinot Noir. Eight variables, shown in Table 1, were originally studied in this experiment. Harry and Judy decided to use a design with 16 runs. The wine was tasted by a panel of experts on March 8, 1986. Each expert ranked the 16 samples of wine tasted, with rank 1 being the best. The design and the taste-test panel results are shown in Table 2. (a) [5 points] What type of design did the experimenters use? What is the benefit of such designs? (b) [5 points] What are the alias relationships in this design? (c) [5 points] What is the resolution of this design? What its corresponding statistical meaning? Is it possible to design a higher resolution design with the same numbers of runs and factors? (d) [10 points] Do any of the process variables aect average ranks ( y )? (e) [10 points] Do any of the process variables aect the variability in ranks (s)? (f) [5 points] What recommendations would you make for the levels of these eight factors? 5 Table 1: The factors Table 2: The design with observations 6