Question

A medical examination tests the presence of viruses in human bodies. Here,

H0: The viral load equals zero (i.e., virus not present) and

Ha: The viral load is larger than zero (i.e., virus present).

3.1 What would be a Type I error?  

3.2 What would be a Type II error?

3.3 Two methods of testing are available: Test A sets the bar to reject the null high (i.e.,

harder to reject), whereas Test B sets the bar to accept the null high. Assuming the virus

is highly infectious and potentially deadly, which test would you choose, and why?

Answer 1

3.1

Type 1 error : Probability of rejecting the null hypothesis when actually it is true.

Mathematically, P[ reject H0 | H0 is true]

Type 1 error would occur when we conclude that we reject H0 means accept H1 when actually H0 is true.

In words it can be written as type 1 error will occur when we conclude that the viral load is larger than zero that means the viral is present when actually the virus load equals zero that means it is not present .

So type 1 error is concluding that the virus is present when actually it is not present.

3.2

Type 2 error : Probability of accepting null hypothesis when it is false.

Mathematically, P[ accept H0 | H1 is true]

Type 2 error would occur when we conclude that we accept H0 that means reject H1 when actually H1 is true

In words it can be written as type 2 error will occur when we conclude that the virus load is zero that means the virus is not present when actually the virus load is larger than zero that means the virus is present.

So type 2 error is concluding that the virus is not present when actually it is present.

Here type 2 error will affect a life of individual very badly.Here type 2 error is a serious issue.

3.3

Test A sets the bar to reject the null high ( harder to reject) , reframing the sentence as the "test A sets the bar harder to reject the null hypothesis" . Here harder to reject means "to not to reject" thats means "to accept" .So in test A we are accepting the null hypothesis. That means here we conclude that the virus is not present .

Test B sets the bar to accept the null high ( harder to accept), reframing the sentence as the "test B sets the bar harder to accept the null hypothesis ". Here harder to accept means "to not to accept" that means "to reject" . So in test B we are rejecting the null hypothesis that means we accept the alternative hypothesis. Concluding that the virus is present.

As mentioned, the virus is highly infectious and potentially deadly , we should choose test B because it concludes that the virus is present .

Explaination: Because in test B , it is better to say that the virus is present and take medication though it is not present than as in test A ,remaining unaware of the fact that the virus is present and concluding it is not present and not taking the medications.

As in test A when we conclude that the virus is not present , this will be a serious mistake if the virus is actually present . But in test B it will be safe to initially conclude that the virus is present though it is not.

Eg.If a patient has a virus and we conclude that he doesn't have the virus so he will not take medication , which will affect his health very badly . This is test A.

If a patient does not have a virus and we conclude he does has a virus so he will take medications, so this will be safe and will not affect his health that badly . This is type B.

So we choose type B