An engineer who is studying the tensile strength of a steel alloy intended for use in golf club shafts knows that tensile strength is approximately normally distributed with σ = 60 psi. A random sample of 12 specimens has a mean tensile strength of psi.
(a) Test the hypothesis that mean strength is 3500 psi. Use a = 0.01.
(b) What is the smallest level of significance at which you would be willing to reject the null hypothesis?
(c) Explain how you could answer the question in part (a) with a two-sided confidence interval on mean tensile strength.