An engineer studying the tensile strength of a composite material knows that tensile strength is approximately...
An engineer studying the tensile strength of a composite material knows that tensile strength is approximately normally distributed with σ = 60 psi. A random sample of 20 specimens has a mean tensile strength of 3450 psi.
(a) Test the hypothesis that the mean tensile strength is 3500 psi, using α = 0.01
(b) What is the smallest level of significance at which you would be willing to reject the null hypothesis?
(c) What is the β error for the test in part (a) if the true mean tensile strength is 3470 psi?
(d) Suppose that you wanted to reject the null hypothesis with probability of at least 0.8 if mean strength μ = 3470 psi. What sample size would be necessary?
(e) Explain how you would answer the question in part (a) with a two sided CI on mean tensile strength.
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