An engineer who is studying the tensile strength of a

QUESTION:

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 \(\sigma=60\) psi. A random sample of 12 specimens has a mean tensile strength of \(\bar{x}=3450\) psi.
(a) Test the hypothesis that mean strength is 3500 psi. Use \(\alpha=0.01\).
(b) What is the smallest level of significance at which you would be willing to reject the null hypothesis?
(c) What is the \(\beta\)-error for the test in part (a) if the true mean is

(d) Suppose that you wanted to reject the null hypothesis with probability at least  if mean strength \(\mu=3470\). 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.

Equation Transcription:

Text Transcription:

sigma=60

x bar=3450

alpha=0.01

beta

mu=3470