Question: A chemical paste is made in batches and put into casks. Ten delivery batches were randomly selected for testing; then three casks were randomly selected from each delivery and the paste strength was measured twice, based on samples drawn from each sampled cask. The response was expressed as a percentage of fill strength. The collected data are given in the following table. Suppose we assume the normal regression model for these data with two categorical predictors.
(a) Produce a side-by-side boxplot for the data for each treatment.
(b) Produce a table of cell means.
(c) Produce a normal probability plot of the standardized residuals and a plot of the standardized residuals against each treatment combination (code the treatment combinations so there is a unique integer corresponding to each). Comment on the validity of the model.
(d) Construct the ANOVA table testing first for no interaction between Batch and Cask and, if necessary, no effect due to Batch and no effect due to Cask
(e) Based on the results of part (d), construct the appropriate table of means and plot the corresponding response curves.