Design a factorial experiment whose three factors have 2, 3, and 4 levels, respectively.
(a) List the factors and their levels.
(b) Assuming that all interactions are to be included in the analysis of variance, what is the minimum number of replicates required for the degrees of freedom for error to be at least 30?
(c) What would the degrees of freedom for error be if all three-factor interactions are assumed to equal zero, and there are no replications.