A food safety inspector is called upon to investigate a restaurant with a few customer reports of poor sanitation practices. The food safety inspector uses a hypothesis testing framework to evaluate whether regulations are not being met. If he decides the restaurant is in gross violation, its license to serve food will be revoked.

What is a Type 1 Error in this context?

P (Type I Error) = P (Revokes the license | Restaurant is not in gross violation)

Step-by-step explanation:

A type I error occurs when we reject a true null hypothesis (H₀). It is the probability of rejecting the null hypothesis when the null hypothesis is true.

The type I error is also known as the level of significance. It is denoted by α.

P (Type I Error) = P (Rejecting H₀ | H₀ is true) = α.

In this case, the food inspector uses a hypothesis testing framework to evaluate whether regulations are not being met.

He decides the the restaurant's license to serve food will be revoked if the restaurant is in gross violation.

So the hypothesis is defined as:

H₀: The restaurant is not in gross violation.

Hₐ: The restaurant is in gross violation.

The type I error will be committed by the food inspector if he concludes that the the restaurant is in gross violation and revokes their license, when in fact the restaurant is not in gross violation.

α = P (Revokes the license | Restaurant is not in gross violation)