Question

The manager of a warehouse monitors the volume of shipments made by the delivery team. The automated tracking system tracks every package as it moves through the facility. A sample of 25 packages is selected and weighed every day. On the basis of contracts with​ customers, the mean weight should be muμequals=22 pounds with sigmaσequals=5 pounds. Mark the statement below as True or False. If you believe that the statement is​ false, briefly say why you think it is false. A Type I error occurs if the mean weight muμ and standard deviation sigmaσ do not change. Choose the correct answer below. A. True B. ​False, a Type II error occurs if the mean weight muμ and standard deviation sigmaσ do not change. C. ​False, a Type I error occurs if the system signals a problem when none has occurred. D. ​False, a Type I error occurs if the system fails to detect a problem.

Answer 1

False. Generally type II error occurs in cases when a false null hypothesis is accpted. In this sense, the error is able to reject the alternative hypothesis. Hence in that case null hypothesis is false (which implies the shipment does not contain a problem) but it is detected by the system. In this sensem type I error will reject the true null hypothesis implying that there is a definite problem but it is not detected by the system.

Hence  Correct choice is D. ​False, a Type I error occurs if the system fails to detect a problem.