I am teaching Type I and Type II Errors Monday and wanted to get students thinking through the problem of balancing the probability of the two errors. I want them to understand the tension and realize they will not be able to eliminate either possibility. I plan to do this before actually introducing the names for the types of errors. I just wrote up these two “Would you rather?” scenarios. I would love some feedback or some other suggestions to use as follow up.

For the two scenarios below, decide which error would be worse. Clearly state your answer and your reasoning.

Scenario 1As a doctor, you see a large national study that 35.9% of Americans are now considered obese (). Alternatively, you think it may be possible that your patients are below the national average (). If you conduct a hypothesis test on a sample of your patients, which would be worse?

a.Rejecting the null hypothesis and stating that less than 35.9% of your patients are obese when in fact your patients are in line with the national average.

-or-

b. Failing to reject the null hypothesis that your patients match the national average, when in fact less than 35.9% of your patients are obese?

Scenario 2You are a researcher. Patients using the current treatment for lung cancer go into remission 55% of the time (). You believe that you have found an improved treatment (). Which would be worse?

a. Rejecting the null hypothesis and stating that your treatment is better when in fact it is not.

-or-

b. Failing to reject the null hypothesis that your treatment is equal to the current treatment, when in fact it is better.