MATH 483/567 Design of Experiments

Problem 3 (16 pts) The variance (52 of an individual observation can be estimated in a number of ways, depending on the situation. How many degrees of freedom are associated with the estimate .92 (of 0'2) in each of the following circumstances? 1 (a) (2 pts) A randomized unpaired comparison of two treatments A and B, where there are m, = 20 observations with A and n3 = 12 observations with B. (b) (2 pts) A completely randomized design with ve treatments, where 11,4 2 24, n3 2 15, nc = 12, up = 20, m; = 17. (c) (2 pts) A randomized block design with 6 blocks and 2 treatments. (d) (2 pts) A full factorial experiment with three factors (one with two levels, one with three levels and one with four levels) replicated twice. (e) (2 pts) A resolution IV 24'1 design (with I = ABCD) for estimating the main effects only (i.e., by ignoring all the interactions). (f) (2 pts) A 251 design of resolution V with 3 replicates per run. (g) (2 pts) A 23 design with two replicates per run for estimating all factorial effects. (11) (2 pts) A 22 design with ve center points for estimating the main effects and two-factor interaction only