Question

a manufacturer considers his production process to be out of control when defects exceed 5%. in a random sample of 67 items the defect rate is 5.4% but the manager claims that this is only a sample fluctuation and production is not really out of control. at the 7% level of significance use the o value method to test the manager's claim.

Answer 1

As we are testing here whether the proportion is more than 5%, therefore the hypothesized proportion value here is given as: P = 0.05

The test statistic here is computed as:

As this is a one tailed test, the p-value here is obtained from the standard normal tables as:
p = P(Z > 0.1502) = 0.4403

As the p-value here is 0.4403 > 0.07 which is the level of significance here, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence here that the defect rate is more than 5%.