Question: 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.