Two types of plastic are suitable for use by an electronic calculator manufacturer. The breaking strength of this plastic is important. It is known that σ₁, = σ₂ = 1.0 psi. From random samples of n₁ = 10 and n₂ = 12 we obtain y̅₁ = 1623 and y̅₂ = 155.0. The company will not adopt plastic 1 unless its breaking strength exceeds that of plastic 2 by at least 10 psi. Based on the sample information, should they use plastic 1? In answering this question, set up and test appropriate hypotheses using α = 0.01. Construct a 99 percent confidence interval on the true mean difference in breaking strength.