Question

It has been reported that the proportion of college seniors who have student loans is 72%. The state senate feels that the proportion of college seniors in their state who have student loans is much less than this and tests the following hypotheses: H0 : p=0.72 H1 : p<0.72 In this situation, explain the meaning of a Type II error.

Answer 1

Given -

Proportion of college seniors who have student loans is 72% .

We have to test hypotheses:

H0 : p=0.72

H1 : p<0.72

Now Type II error is a statistical term referring to the non-rejection of a false null hypothesis. type II error describes the error that occurs when one fails to reject a null hypothesis that is actually false . i.e we accept null hypothesis but in fact it is false

Thus Type II Error is = Pr ( Accept H0 | H1 is True )

So In this situation, the meaning of a Type II error is that we accept the claim that proportion of college seniors who have student loans is 72% , but in fact it is false and proportion is much less than 72% .