Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than $97 \%$ good parts $\left( \mathrm { H } _ { 0 } : p = 0.97 \right.$ and $\left. \mathrm { H } _ { \mathrm { A } } : p 0.97 \right)$. The test results in a $P$-value of $0.122$. Unknown to the manufacturer, the machine is actually producing $99 \%$ good parts. What probably happens as a result of the testing?
A) They correctly reject $\mathrm { H } _ { 0 }$.
B) They fail to reject $\mathrm { H } _ { 0 }$, making a Type I error.
C) They correctly fail to reject $\mathrm { H } _ { 0 }$.
D) They fail to reject $\mathrm { H } _ { 0 }$, making a Type II error.
E) They reject $\mathrm { H } _ { 0 }$, making a Type I error.

Question

Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than $97 \%$ good parts $\left( \mathrm { H } _ { 0 } : p = 0.97 \right.$ and $\left. \mathrm { H } _ { \mathrm { A } } : p > 0.97 \right)$. The test results in a $P$-value of $0.122$. Unknown to the manufacturer, the machine is actually producing $99 \%$ good parts. What probably happens as a result of the testing?
A) They correctly reject $\mathrm { H } _ { 0 }$.
B) They fail to reject $\mathrm { H } _ { 0 }$, making a Type I error.
C) They correctly fail to reject $\mathrm { H } _ { 0 }$.
D) They fail to reject $\mathrm { H } _ { 0 }$, making a Type II error.
E) They reject $\mathrm { H } _ { 0 }$, making a Type I error.

Quizplus · Accepted Answer

The P-value of 0.122 is greater than typical significance levels (e.g., 0.05), so they fail to reject $ H_0 $. Since the true proportion is 0.99, failing to reject $ H_0 $ is a Type II error.

Suppose That a Manufacturer Is Testing One of Its Machines 97%97 \%97%

Suppose That a Manufacturer Is Testing One of Its Machines $97 \%$