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

Multiple Choice

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.