Reference no: EM131551858

Question: Refer to the NASA Polymer II case in problem 16.

(a) Find the residuals and plot them against the cell means (that serve as fitted values in this context). Does it appear that response variability is consistent from treatment combination to treatment combination? Why or why not?

(b) Normal plot the residuals found in (a). Does this plot suggest problems with the basic "normal distributions with a common variance" model? Why or why not?

(c) Transform each response using y = arcsin (y/100), where y is a percent (between 0 and 100) as given in problem 16. Compute the four sample means for the transformed values.

(d) Find residuals for the transformed data from (c). Plot these against the sample means from (c). Does it appear that variability in transformed response is consistent from treatment combination to treatment combination? Normal plot these residuals. Does this plot suggest problems with the basic "normal distributions with a common variance" model for the transformed response? Why or why not?

(e) Transform each response in problem 16 using y = ln (y). Answer (c) and (d) with the newly transformed data.

(f) Which version of the data (the original, the arcsin transformed, or the log transformed) seems best described by the "normal distributions with a common variance" model? Why?

Problem: NASA Polymer II. In a preliminary investigation, Sutter, Jobe, and Crane designed a weight loss study that was to be balanced (with an equal number of specimens per polymer resin/oven position combination). Polymer resin specimens of a standard size were supposed to be randomly allocated (in equal numbers) to each of two positions in the oven. The following percent weight loss values were in fact obtained.

(a) The lack of balance in the data set above resulted from a misunderstanding of how the experiment was to be conducted. How would you respond to a colleague who says of this study "Well, since an equal number of specimens were not measured for each polymer resin/oven position combination, we do not have a balanced experiment so a credible analysis cannot be made"?

(b) How many experimental factors were there in this study? Identify the numbers of levels for each of the factors.

(c) Write a model equation for the "normal distributions with a common variance" description of this study. Give the numeric ranges for all subscripts.

(d) Find the fitted main effect for each level of each factor.

(e) Find the fitted interactions for all combinations of polymer resin and oven position.

(f) Use the model from (c) and find a 99 % two-sided confidence interval for the interaction effect for Avimid-N and position 1. Are intervals for the other interaction effects needed? Why or why not?

(g) Use the model from (c) and find 95 % two-sided confidence intervals for each of the main effects.

(h) Use the model from (c) and find a 90 % two-sided confidence interval for the difference in oven position main effects.

(i) Use the model from (c) and find a 90 % confidence interval for the difference in polymer resin main effects.