Question: 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 \(\sigma_{1}=\sigma_{2}=1.0\) psi. From random samples of \(n_{1}=10\) and \(n_{2}=12\) we obtain \(\bar{y}_{1}=162.5\) and \(\bar{y}_{2}=155.0\). 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 \(\alpha=0.01\). Construct a 99 percent confidence interval on the true mean difference in breaking strength.

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