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 fail to reject H0,making a Type II error.
b. We fail to reject H0, making a Type I error.
c. We correctly reject H0.
d. We reject H0, making a Type I error.
e. We correctly fail to reject H0.

Answer 1

Answer:

a. We fail to reject H0,making a Type II error.

Step-by-step explanation:

H0: Null Hypothesis: p = 0.97  HA: Alternative Hypothesis: p > 0.97

P- Value = 0.102  if $\alpha$ = 0.05.  therefore P-value > $\alpha$ . we have therefore failed to reject the null hypothesis H0.

The following rule states that when we reject H0, H0 is true for Type I error and Ha is true for correct decision. When we fail to reject H0, H0 is true for correct decision and Ha is true for Type II error.

Based on the above and having failed to reject a false null hypotheses, Type II error is the failure to reject a false null hypothesis, thus making a Type II error. Therefore when we fail to reject H0, we make a Type II error.