A pharmaceutical manufacturer wants to investigate the bioactivity of a new drug. A completely randomized single-factor experiment was conducted with three dosage levels, and the following results were obtained.
a) Is there evidence to support a claim that the dosage level affects bioactivity? Use = 0.05. If so which dosage levels are responsible for the difference? Support your conclusion with the appropriate test statistics and graphs.
b) Analyze the residuals from this experiment and comment on model adequacy.
An experiment was performed to study the effects of three different types of 32-ounces bottles and three different shelf types (B) – smooth permanent shelves, end-aisle display with grilled shelves, and beverage coolers- on the time it takes to stock 12-bottle cases on the shelves. Three workers (factor C) were employed in the experiment, and two replicates of a 33 factorial design were run. The observed time data are shown in the following table. Analyze the data and draw conclusions.
Harry and Judy Peterson-Nedry 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 below, were originally studied in the experiment:
Variable Low Level (-) High level (+)
A = Pinot Noir Pommard Wadenswill
B = Oak type Allier Troncais
C = Age of barrel Old New
D = Yeast/skin contact Champagne Montrachet
E = Stems None All
F = Barrel toast Light Medium
G = Whole cluster None 10%
H = Fermentation temperature Low (75oF max) High (92oF max)
Harry and Judy decide to use a design with 16 runs. The wine was tasted by a panel of experts on March 8, 1986. Each expert ranked all 16 samples of wine tasted, with rank 1 being the best. The design and the taste-test panel results are shown below.
(a) What are the alias relationships in the design selected by Harry and Judy?
(b) Use the average ranks ( ) as a response variable. Analyze the data and draw conclusions.
(c) Use the standard deviations of the ranks (or some appropriate transformations such as log standard deviation s) as a response variable. What conclusions can you draw about the effects of the eight variables on variability in wine quality?
(d) After looking at the results Harry decide that one of the panel members (DCM) knows more about beer than he does about wine, so they decide to delete his ranking. What effect would have this have on the results and conclusions from parts (b) and (c)?
Consider the three variable central composite design shown below. Analyze the data and draw conclusions, assuming that we wish to maximize conversion (y1) with activity (y2) between 55 and 60. Perform a thorough analysis, including the response surface model for each variable. (Note need to do one variable at a time).
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