Question

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be? (Note = refer to top of page 508 for format and appropriate equality and non-equality symbols, respectively)a. H0 :______b. Ha :______

Answer 1

a)
`H_(0) = 9.5`

b)
`H_(a) < 9.5`

Explanation:

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness.

At the null hypothesis, we test if the value we find is equal to the expected value, that is:

`H_(0) = 9.5`

Test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population

Lower, which means that the alternate hypothesis, we test if the value we find is lower than the expected value, that is:

`H_(a) < 9.5`