Type I & II errors

[megard]

A lathe is set to cut steel bars into lengths of 4 centimeters. The lathe is considered to be working properly if the average length of the bars it cuts is 4 centimeters. However, the operator of the lathe believes that the lathe is wearing out and the average length is no longer 4 centimeters. He plans to conduct a hypothesis test at the 0.05 level of significance, and if the results warrant, he will send the lathe to the repair shop; otherwise he will continue to use the lathe.

What are the Type I and type II errors in this situation, and what are the consequences of the errors, in terms of the use of the lathe?

[omega]

A type I error is made if we conclude that the lathe is wearing out and the average length is no longer 4 centimeters, when in fact it is working properly and the average length is 4 centimeters.

The consequence is that we would make unnecessary repair.

A type II error is made if we conclude that the lathe is working properly and the average length is 4 centimeters, when in fact it is wearing out and the average length is no longer 4 centimeters.

The consequence is that the lathe will continue to be used and the steel bars will be wasted. This is more serious than the consequence of a type I error.