Hypothesis Testing What is an example in which a It would be

Hypothesis Testing.

What is an example in which:

a.) It would be MORE IMPORTANT to keep the likliehood of a Type I Error low than to keep the likliehood of a Type II Error low.
b.) It would be MORE IMPORTANT to keep the likliehood of a Type II Error low than to keep the likliehood of a Type I Error low.

Solution

a)

A Type 1 Error occurs when we reject a true null hypothesis. Therefore, it is more important to be kept low when the hypothesis being true is very significant.

For example, let the null hypothesis be that a patient has cancer. Therefore, in this case, it is very important to keep the type 1 error low, as if the patient has cancer(null hypothesis true) but we conclude that is doesn\'t(reject null hypothesis), the result may be catastrophic for the patient.

b)

Type 2 error is the possibility of failing to reject a false null hypothesis.

It becomes more important to keep this low when the conclusion of the null hypothesis being true leads to a rather catastrophic result.

For example, if the null hypothesis is that a product being manufactured is good, and we fail to reject the null hypothesis even when it is false, the result may be that a defective product will be released into the market.