Solution Found!
An engineer who is studying the tensile strength of a
Chapter 9, Problem 46E(choose chapter or problem)
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
Questions & Answers
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
ANSWER:
Step 1 of 7
Given,
Sample size, n = 8
The sample mean,
The standard deviation,
Using the given values let’s determine the following: