2. Testing for food safety. A food safety inspector is called upon to investigat

Question

2. Testing for food safety. 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. (a) Write the hypotheses in words. (b) What is a Type 1 error in this context? (c) What is a Type 2 error in this context? (d) Which error is more problematic for the restaurant owner? Why? e) Which error is more problematic for the diners? Why? (f) As a diner, would you prefer that the food safety inspector requires strong evidence or very strong 2 evidence of health concerns before revoking a restaurant's license? Explain your reasoning

Explanation / Answer

Solution:

(a) Write the hypotheses in words.

( H0 ): The regulations are being met (e.g. the true mean of the number of violations is some threshold)

(H1): The regulations are not being met (e.g. the true mean of the number of violations is > the threshold)

(b) What is a Type 1 error in this context?

The restaurant is meeting the regulations but the evidence suggests otherwise (e.g. from sampling variation).

(c) What is a Type 2 error in this context?

The restaurant is not meeting the regulations but the evidence is insufficient to conclude otherwise.

(d) Which error is more problematic for the restaurant owner? Why?

A Type I error is more problematic for the restaurant owner since s/he is meeting the sanitation standards but are about to be punished for not meeting them.

(e) Which error is more problematic for the diners? Why?

A Type II error is more problematic for the diners since they will expect to be eating in a clean environment, but in fact the restaurant should be subject to health regulation enforcement.

(f) As a diner, would you prefer that the food safety inspector requires strong evidence or very strong evidence of health concerns before revoking a restaurant's license? Explain your reasoning.

As a diner, I'd prefer that the food safety inspector requires strong evidence of health concerns before revoking a restaurant's license (rather than very strong evidence). That way I can be confident about the cleanliness of the establishment when I learn that it passed inspection. On the other hand, if standards are too strict, many good restaurants (including clean ones!) will have to close when they get violation notices based on weak evidence. A proper balance is probably necessary. Perhaps a first test with very strong evidence can certify most restaurants as in compliance and a second test (with more observations) could be run for restaurants that fail the first test. This would give good, clean, restaurants an opportunity to avoid punishment.

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