"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

the pilot will be out $1,500 unnecessarily.

Explanation:

In statistics a type 1 error is defined as a rejection of a false positive finding or conclusion (true null hypothesis).

For example if a null hypothesis is that a person performed a task while the alternative is that he did not do it. Type 1 error is assuming that the person did not perform the task and sanctioning him, whereas he actually performed the task.

In this scenario the mechanic's theory is 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.

The cost of rejecting this hypothesis will be to tear the engine down at a cost of $1,500. If it is a type 1 error this cost is unnecessary

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