Suppose that a manufacturer is testing one of its machines t

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 0.012. In reality, the machine is producing 97% good parts. What probably happens as a result of our testing?

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

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

c. We correctly reject H0.

d. We reject H0, making a Type I error.

e. We correctly fail to reject H0.

Solution

Since no level of significance is given so let us assume it 0.05. Since P-value is less than 0.05 so we reject the null hypothesis. In this case we reject the true null hypothesis so we made a type I error. Hence, option (d) is correct.

Note:

If level of significance is 0.01, the now P-value is not less than 0.01 so we fail to reject the null hypothesis. In this case we accept the true null hypothesis so we did not make any error. Hence, option (e) is correct.