"I believe your airplane's engine is sound," states the mechanic. "I've been over it carefully, and can't see anything wrong. I'd be happy to tear the engine down completely for an internal inspection at a cost of $1,500. But I believe that roughness you heard in the engine on your last flight was probably just a bit of water in the fuel, which passed harmlessly through the engine and is now gone." As the pilot considers the mechanic's hypothesis, the cost of Type I error is:
A)the pilot will experience the thrill of no-engine flight.
B)the pilot will be out $1,500 unnecessarily.
C)the mechanic will lose a good customer.
D)impossible to determine without knowing α.

Question

Quizplus · Accepted Answer

The cost of a Type I error (rejecting a true null hypothesis) in this context would be taking an unnecessary action based on the belief that there is a problem when there isn't one. Therefore, if the pilot opts for the engine teardown based on the mechanic's offer, despite the engine being sound, the unnecessary cost incurred would be $1,500.

"I Believe Your Airplane's Engine Is Sound," States the Mechanic