Question

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 = 449.0, SSB = 422.6, and SSE = 129.4. Assume that an additive model is appropriate.

(a) Test H₀: α₁ = α₂ = α₃ = α₄ = 0 (no differences in true average strength due to species) versus H_a: at least one α_i ≠ 0

using a level 0.05 test.

Calculate the test statistic. (Round your answer to two decimal places.)

f =

What can be said about the P-value for the test?

P-value > 0.100

0.050 < P-value < 0.100

0.010 < P-value < 0.050

0.001 < P-value < 0.010

P-value < 0.001

State the conclusion in the problem context.

Reject H₀. The data suggests that true average strength of at least one of the species is different from the others.

Reject H₀. The data does not suggest any difference in the true average strength due to species.    

Fail to reject H₀. The data does not suggest any difference in the true average strength due to species.

Fail to reject H₀. The data suggests that true average strength of at least one of the species is different from the others.

(b) Test H₀: β₁ = β₂ = β₃ = 0 (no differences in true average strength due to grade) versus

H_a: at least one β_j ≠ 0 using a level 0.05 test.

Calculate the test statistic. (Round your answer to two decimal places.)

f =

What can be said about the P-value for the test?

P-value > 0.100

0.050 < P-value < 0.100    

0.010 < P-value < 0.050

0.001 < P-value < 0.010

P-value < 0.001

State the conclusion in the problem context.

Reject H₀. The data does not suggest any difference in the true average strength due to grade.

Reject H₀. The data suggests that true average strength of at least one of the grades is different from the others.    

Fail to reject H₀. The data does not suggest any difference in the true average strength due to grade.

Fail to reject H₀. The data suggests that true average strength of at least one of the grades is different from the others.

Answer 1