Due Tue 02/27/2018 12:59 am The National Institute of Mental Health published an

Question

Due Tue 02/27/2018 12:59 am The National Institute of Mental Health published an article stating that in any one-year period, approximately 82% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 11.9% of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that city suffering from depression or a depressive illness is more than the 8.2% in the general adult American population. Test the relevant hypotheses using a 5% level of significance. Give answer to at least 4 decimal places. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) Select an answer Select an answer Based on the hypotheses, find the following: | Test Statistic = p-value Based on the above we choose to Select an answer The correct summary would be: Select an answor city suffering from depression or a depressive illness is more than the percent in the general adult American population that the true proportion of people in that of 8.2%. Submit

Explanation / Answer

H0: p <= 0.082
H1: p > 0.082

Test statistics,
z = (0.119 - 0.082)/sqrt(0.082*(1 - 0.082)/2000)
z = 6.0309

p-value = 0.0000 (using standard normal table)

Reject the null hypothesis. Because p-value is less than the significance level of 0.05.

We can conclude that the true proportion in the city suffering from depression or a depressive illness is more than the percent in the general adult american population of 8.2

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