An engineer who is studying the tensile strength of a steel alloy (intended for use in golf club shafts) wants to test the following hypotheses: " role="presentation" style="display: inline-block;...

An engineer who is studying the tensile strength of a steel alloy (intended for use in golf club shafts) wants to test the following hypotheses:" role="presentation" style="display: inline-block; line-height: 0; font-size: 19.36px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">




H




0




:


μ


=


3500




versus" role="presentation" style="display: inline-block; line-height: 0; font-size: 19.36px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">




H




a




:


μ


≠


3500




at" role="presentation" style="display: inline-block; line-height: 0; font-size: 19.36px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">


α




= 0.01. He knows that tensile strength is approximately normally distributed with" role="presentation" style="display: inline-block; line-height: 0; font-size: 19.36px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">


σ




= 60 psi. A random sample of 50 specimens has a mean tensile strength of" role="presentation" style="display: inline-block; line-height: 0; font-size: 19.36px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">







¯




x









= 3450 psi.

a. What is the power of the test if the true mean strength is" role="presentation" style="display: inline-block; line-height: 0; font-size: 19.36px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">


μ




= 3470?

b. Suppose that you wanted to reject the null hypothesis with a probability of 0.9 if the true mean strength was" role="presentation" style="display: inline-block; line-height: 0; font-size: 19.36px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">


μ




= 3470. What sample size would be required?