Question 3: Consider a 25 factorial design. (a) How many factors and levels are considered in...

Question 3: Consider a 25 factorial design.
(a) How many factors and levels are considered in this factorial experiment?
(b) Show all the 32 treatment combinations using a, b, c, d, and e.
(c) Suppose you are not able to complete all 32 experiments in a day but you believe 16 experiments can be done in a day. How many blocks do you need under this situation?
(d) Revisiting part (c), which interaction effect would be confounded with the blocks? Using the sign method, assign optimal treatment combinations to each block.
(e) Revisiting part (c), now assign optimal treatment combinations to each block by using the defining contrast method. Note that the optimal treatment combinations you have found in parts (d) and (e) should be the same.

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