Two types of plastic are suitable for an electronics component manufacturer to use. The breaking strength of this plastic is important. It is known that σ₁ = σ₂ = 1.0 psi. From a random sample of size n₁ = 10 and n₂ = 12, you obtain x₁ = 162.5 and x₂ = 155.0. The company will not adopt plastic 1 unless its mean breaking strength exceeds that of plastic 2 by at least 10 psi.

(a) Based on the sample information, should it use plastic 1? Use α = 0.05 in reaching a decision. Find the P-value.

(b) Calculate a 95% confidence interval on the difference in means. Suppose that the true difference in means is really 12 psi.

(c) Find the power of the test assuming that α = 0.05.

(d) If it is really important to detect a difference of 12 psi, are the sample sizes employed in part (a) adequate in your opinion?