Question

Scenario C. The flu shot changes every year, and some years it is more effective at preventing the flu than others. A group of researchers wants to compare the effectiveness of the flu shot this year to the flu shot last year.

What would be a type I error for this scenario?

What would be a type II error for this scenario?

Answer 1

First we construct the null and alternative hypothesis

The null hypothesis is the hypothesis of no difference, that is we say that there is no difference in effectiveness between this year and last year . The alternative hypothesis is the opposite of null hypothesis .

The null and alternative hypothesis

H0: effectiveness of flu shot this year is same as that of last year

Ha: effectiveness of flu shot this year is more than  that of last year

Type I error is the error of rejecting the null hypothesis when it is true  

That is on the basis of the test , we reject H0 and conclude that this year's shot is more effective than last year , when in reality there is no difference in effectiveness. The health department takes measures to introduce the new flu shot, which was not necessary.

Type II error is the error of accepting the null hypothesis when it is false .

That is on the basis of the test , we fail to reject H0 and conclude that there is no difference in effectiveness between this year and last year , when in reality this  year's shot is more effective than last year . The new shot will not be introduced , which would have been better in combating fight against flu.