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. Commenton your findings.(d) Compute an approximate 95% CI for each effect. Compare your results with thosein part (a) and comment.(e) From your results in (a) and (b), build a model that relates the separation to thedesign factors.(f) From your model, determine the optimal settings to maximize the separation.