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Consider a balanced incomplete block design (BIBD) with k treatments of effects 71,..., TK , n blocks, each treatment appearing in p blocks, s treatments observed in each block, and 1. pairs of treatments available in each block. The null hypothesis is Ho : 71 = . .. =t . (a) Let D denote the Durbin-Skillings-Mack test statistic for general alternatives in BIBD. Prove E[ D] = k -1. [8] (b) The following table presents the data { X, } in a BIBD: Treatment Block - 2 3 4 5 21 15 17 28 2 25 19 35 32 W 39 32 35 44 A 22 16 24 30 5 38 34 45 42 Test Ho against general alternatives by the p-value of the test based on D. [8] (c) Decide the differences between treatment effects 71,..., 75 based on the data in part (b) by the Skillings-Mack two-sided all-treatment multiple comparison procedure for BIBD with a =0.1, using R to find relevant 90.1 - [4]