Consider an experimental situation involving factors A, B, and C, where we assume a three way fixed effects model of the form IJijkl = ft. + ? _i + 0j + ? _k + (? ?) _{j k} + ? _{i j k l}. All other interactions arc considered to be nonexistent or negligible. The data are presented here.

(a) Perform a test of significance on the BC interaction at, ? = 0.05 level.

(b) Perform tests of significance on the main effects A, B, and C using a pooled mean square error at ? = 0.05 level.

B2 B, C C C C C2 C3 A1: 4.0 3.4 3.9 4.4 3.1 3.1 4.3 3.4 3.5 3.7 4.9 4.1 : 3.6 2.8 3.1 2.7 2.9 3.0 3.2 3.7 4.2 3.9 3.2 3.5 3.6 2.9 2.9 3.6 3.8 3.3 3.5 Ar. 4.8 3.3 3.7 3.8 4.2 3.6 : 3.6 3.2 3.9 3.2 3.4 2.2 3.5 2.9 3.2 2.8 4.3 4