Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (H? : p = 0.97 and HA : p 0.97) . The test results in aP-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 reject H0, making a Type I error.
B) They correctly reject H0.
C) They fail to reject H0, making a Type I error.
D) They fail to reject H0, making a Type II error.
E) They correctly fail to reject H0.

Question

Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (H? : p = 0.97 and HA : p > 0.97) . The test results in aP-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 reject H0, making a Type I error.
B) They correctly reject H0.
C) They fail to reject H0, making a Type I error.
D) They fail to reject H0, making a Type II error.
E) They correctly fail to reject H0.

Quizplus · Accepted Answer

Since the p-value is 0.122, which is typically higher than the common alpha level of 0.05, the manufacturer will likely fail to reject the null hypothesis (H0: p = 0.97). However, because the machine actually produces 99% good parts, which is greater than 97%, the correct decision would have been to reject H0. Failing to reject H0 when it is false constitutes a Type II error.

Suppose That a Manufacturer Is Testing One of Its Machines