The National Institute of Mental Health published an article...

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. $H_{0}$: _____ b. $H_{a}$ :____

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Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to decide whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. It involves setting the null and alternative hypotheses, choosing a significance level, and using test statistics to make a decision.

One-Sided Test

A one-sided test is used when the research hypothesis predicts a specific direction of the effect, such as the true proportion being lower than a known value. It focuses on deviations in only one direction, making the test more powerful for detecting differences in that specified direction.

Alternative Hypothesis

The alternative hypothesis is a statement that contradicts the null hypothesis, proposing that the parameter is not equal to the specified value in a particular direction. In a one-sided test, it specifically suggests that the true percentage is either lower or higher than the stated value.

Null Hypothesis

The null hypothesis is a statement of no effect or no difference, asserting that the parameter (in this case, the proportion of individuals suffering from depression) is equal to a specified value. It represents the status quo or a baseline assumption that any observed deviation in sample data is due to random chance.

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