The National Institute of Mental Health published an article stating that in any two-year period, approximately 10.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 150 people in a certain town, eight 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?
The National Institute of Mental Health published an article stating that in any two-year period, approximately 10.5
percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 150 people in a certain town, eight 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?
Let P be the true proportion of American adults suffer from depression or depressive illness.
Here we have to test the hypothesis that the true proportion of American adults who suffers from depression or depressive illness is lower than the proportion given in the article.
The National Institute of Mental Health published article states that this percentage is 10.5, that means 0.105 proportion.
Hence null and alternative hypothesis are,
Null hypothesis H0 : P = 0.105
Alternative hypothesis, H1 : P < 0.105
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