12.45 Given the following data from a randomized block design,

Blocks 1 234 Treatment 1 9 10 2 7 Treatment 2 6 13 1 12 Treatment 3 9 16 9 14

(a) Decompose each observation yi j as yi j = y• • + ( yi• − y• • ) + ( y• j − y• • ) + ( yi j − yi• − y• j + y• • )

(b) Obtain the sums of squares and degrees of freedom for each array.

(c) Construct the analysis of variance table and test for differences among the treatments with α = 0.05.