Two types of plastic are suitable for use by an electronics component manufacturer. 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, we obtain x1 = 162.5 and x2 = 155.0. The company will not adopt plastic 1 unless its mean breaking strenght 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?