The National Institute of Mental Health published an article stating that in any

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?

(a) null hypothesis

H0: p < 9.5H0: p = 0.095   

H0: p = 9.5H0: p < 0.095H0: p 0.095

(b) alternative hypothesis

Ha: p = 0.095Ha: p < 0.095   

Ha: p 0.095Ha: p < 9.5Ha: p 9.5

Explanation / Answer

a)

Assumption is , approximately, 9.5% of American adults suffer from depression or a depressive illness.

This is null hypothesis.

H0: p = 0.095

b)

Claim is , Proportion of people in that town suffereing from depression or depressive illness is lower.

This is alternative(Claim) hypothesis.

Ha: p < 0.095

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