An experiment was carried out to investigate the effect of species (factor A, with I = 4) and grade (factor B, with J = 3) on breaking strength of wood specimens. One observation was made for each species-grade combination- resulting in SSA = 442.0, SSB = 428.6, and SSE = 123.4. Assume that an additive model is appropriate.

a. Test H0: a1 = a2 = a3 = a4 = 0 (no differences in true average strength due to species) versus Ha: at least one ai ( 0 using a level .05 test.

b. Test H0: b1 = b2 = b3 = 0 (no differences in true average strength due to grade) versus Ha: at least one βj ( 0 using a level .05 test?