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 evidence of health concerns before revoking a restaurant's license? Explain your reasoning

Explanation / Answer

(a)

Null Hypothesis : H0 : The regulation is being met

Alternative Hypothesis : Ha : The regulation is not being met.

(b)

Type 1 error occurs when we reject the null hypothesis but its true. Thus in this context a type 1 error would be when license is revoked as the evidence suggests that regulations are not being met although in actuality the regulations are being met.

(c)

Type 2 error occurs when we fail to reject a null hypothesis when it is false. Thus in this context it would mean that although the regulations are not being met, the evidence suggests that the regulations are being met and thus the license is not revoked.

(d)

For the restaurant owner the problematic case would be when although the regulations are being met the evidence will suggest otherwise and his license would be revoked. This will occur in type 1 error.

(e)

For the diners the problematic situation will be when the evidence suggests that the regulations are being met whereas in actuality the regulations are not being met. This would occur in type 2 error.

(f)

As a diner, I would prefer that food safety inspector requires strong evidence of health concerns before revoking a restaurant's license. Since for me the safety of the food is paramount I would try to reduce the type 2 error and thus stronger evidence would welcome.

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