3) Suppose Joe was considering a romantic encounter. However, the widely reporte

Question

3) Suppose Joe was considering a romantic encounter. However, the widely reported increase in the spread of AIDS has given him justifiable concern in his romantic liaisons. Life can be unkind. In these times, falling victim to sweet circumstance could mean falling victim to the HIV virus. How does Joe want to construct his hypotheses? a) formulation A: Ho Potential companion has AIDS against H Potential companion does not have AIDs; b) formulation B: H, Potential companion does not have AIDS against H Potential companion has AIDS Describe the Type I and Type II errors in each case. If you were Joe, which formulation do you prefer and why ?

Explanation / Answer

Formulation B is quite correct as we are testing the presence of AIDS in the potential companion. The statement to be tested becomes the alternative hypothesis. Thus the statement that Potential companion has AIDS becomes the alternative hypothesis HA . Formulation B is preferred as it is actually testing the presence of AIDS.

Type 1 error = P(H0 is Rejected given H0 is True) i.e P(H0 is Rejected H0 is True)

Type 2 error = P(H0 is not Rejected given H0 is False) i.e P(H0 is not Rejected H0 is False)

So in case a) the type 1 error indicates probability of detecting NO AIDS while the companion actually had AIDS and the the type 2 error indicates probability of detecting AIDS while the companion actually had NO AIDS.

Similarly in Case b) the type 1 error indicates probability of detecting AIDS while the companion actually had NO AIDS and the the type 2 error indicates probability of detecting NO AIDS while the companion actually had AIDS.

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