Question

The National Institute of Mental Health published an article stating that in any one-year period, approximately $9.5$a 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?

localid="1650439913140" $a.H_0$__________

$b.H_a$ __________

Short answer

a.$H_0:p=0.095$

b.$H_a:p<0.095$

Step-by-step solution

Given Information

$9.5$percent of adults in the United States are depressed or have a depressive disease. The goal is to see if the genuine number of people suffering from depression or a depressive disease is less than $9.5$percent.

Explanation part a

The Null Hypothesis is:

• $H_0$: The true number of persons who suffer from depression or mental disease is $9.5$percent.
• The Null Hypothesis ($H_0$): It's a declaration that there's no difference between sample means or proportions, or between a sample mean or proportions and a population mean or proportion.

Explanation part b

An Alternative Hypothesis is:

• $H_a$: The genuine proportion of people suffering from depression or a depressive disease is less than $9.5$
• The alternate hypothesis is as follows: It is the population assertion that contradicts $H_0$, and it is what we conclude when we reject $H_0$

Step 4: Conclusion 

For the above data, the null and alternative hypotheses are provided by:

$H_0:p=0.095$

$H_a:p<0.095$