leads to the model Xijk = + Ai + Bj + Cij + Uijk (i =

leads to the model Xijk = µ + Ai + Bj + Cij + Uijk (i = 1,...,a; j = 1, . . . ,

b, k = 1,...,n).

where the A’s, B’s, C’s, and U’s are independent normal with mean zero and variances σ2 A, σ2 B, σ2 C and σ2.

(i) Give an example of a situation in which such a model might be appropriate.

(ii) Reduce the model to a convenient canonical form along the lines of Section 7.4.

(iii) Determine UMP unbiased tests of

(a) H1 : σ2 B = 0;

(b) H2 : σ2 C = 0.