final - STAT 8260 Final Exam Thursday May 1 2008 SHOW ALL...

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STAT 8260 Final Exam – Thursday, May 1, 2008 SHOW ALL WORK Name: 1. Consider a randomized complete block design in which two blocks are used with four treatments per block. The four treatments are combinations of two factors: factor A (with levels A1 and A2), and factor B (with levels B1 and B2). Let y ijk be the response in the i th block, at the j th level of A combined with the k th level of B. The design and data can be represented schematically as follows: 111 y 112 y 211 y 212 y 121 y 122 y 221 y 222 y The classical model for such a design would be y ijk = μ + τ i + α j + β k +( αβ ) jk + e ijk . However, we will consider a model in which we assume that factors A and B do not interact. That is, consider the model y ijk = μ + τ i + α j + β k + e ijk , i = 1 , 2; j = 1 , 2; k = 1 , 2; with the usual assumption of independent errors where E( e ijk ) = 0, var( e ijk ) = σ 2 for all i, j, k . Here τ i , α j and β k are effects for blocks, levels of factor A, and levels of factor B, respectively.
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