Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (H0: p = 0.97 and HA: p 0.97). The test results in a P-value of 0.102. In reality, the machine is producing 99% good parts. What probably happens as a result of our testing?
A) We correctly fail to reject H0.
B) We correctly reject H0.
C) We reject H0, making a Type I error.
D) We fail to reject H0, making a Type I error.
E) We fail to reject H0, making a Type II 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 (H0: p = 0.97 and HA: p > 0.97). The test results in a P-value of 0.102. In reality, the machine is producing 99% good parts. What probably happens as a result of our testing?
A) We correctly fail to reject H0.
B) We correctly reject H0.
C) We reject H0, making a Type I error.
D) We fail to reject H0, making a Type I error.
E) We fail to reject H0, making a Type II error.

Quizplus · Accepted Answer

Given the P-value of 0.102, we fail to reject the null hypothesis (H0: p = 0.97) because the P-value is greater than the common alpha level of 0.05. However, in reality, the machine is producing 99% good parts, which means it is actually performing better than the null hypothesis suggests. Failing to reject H0 when HA is true (the machine produces more than 97% good parts) leads to a Type II error.

Suppose That a Manufacturer Is Testing One of Its Machines