11.5 Suppose you are consulted to help design an esperiment involving two factors at two levels each. A sufficient number of blocks of size two are available for the experiment. The investigator wishes to obtain equal information on the main effects and the two-factor interaction. (i) Give the name of the method used for constructing a suitable experimental design. (ii) Write out explicitly the design for this study and explain how you obtained it. (iii) Outline the ANOVA table for the design given in (ii), including source of variation, d.f., and sums of squares. (iv) Suppose only 6 blocks of size 2 are available for the experiment. What method could one use to construct the design. Explain and give the design. What kind of design is this?