Statistical and mathematical questions

1. An experiment was designed to identify a better ultrafiltration membrane for 

separating proteins and peptide drugs from fermentation broth. Two levels of 

an additive PVP (% wt) and time duration (hours) were investigated to 

determine the better membrane. The separation values (measured in %) 

resulting from these experimental runs are as follows:

(a) Compute the estimates of the effects and their standard errors for this design. 

(b) Construct two-factor interaction plots and comment on the interaction of the factors. 

(c) Use the t ratio to determine the significance of each effect with α = 0.05. Comment

on your findings.

(d) Compute an approximate 95% CI for each effect. Compare your results with those

in part (a) and comment.

(e) From your results in (a) and (b), build a model that relates the separation to the

design factors.

(f) From your model, determine the optimal settings to maximize the separation.