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 withσ = 70 psi. A random sample of 12 specimens has a mean ten-sile strength of x = 3450 psi.

(a) Test the hypothesis that mean strength is 3500 psi. Use α = 0.05.
(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 is 3470?
(d) Suppose that you wanted to reject the null hypothesis with probability at least 0.8 if mean strength μ = 3470. What sample size should be used?
(e) Explain how you could answer the question in part (a) with a two-sided confidence interval on mean tensile strength.