Question

1. Hypothesis Testing (4 pts) The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.4% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 11.4% 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 9.4% in the general adult American population. Test the relevant hypotheses using a 5% level of significance. Give answer to at least 4 decimal places. a) What are the correct hypotheses? Draw a picture of your p-value, including the mean, standard deviation, and shaded region b) Using Geogebra, calculate the following p-value- c)

Answer 1

Dear student, please post the question one at a time.

1)

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho:p 0.094 Ha: p>0.094 This corresponds to a right-tailed test, for which a z-test for one population proportion needs to be used 2) Rejection Region Based on the information provided, the significance level is α-0.05, and the critical value for a right-tailed test is ze 1.64. The rejection region for this right-tailed test is R- z:1.64) The z-statistic is computed as follows: p -Po 0.114-0.094 Po(1 Po)/n 0.094(10.094)/2000 (4) Decision about the null hypothesis Since it is observed that z 3.065>ze 1.64, it is then concluded that the null hypothesis is rejected. using the P-value approach: The p-value is p = 0.0011, and since p concluded that the null hypothesis is rejected. 0.0011 < 0.05, it is It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion p is greater than Po, at the α-0.05 significance level.

Hence we have evidence that the true proportion of people in the city suffering from depression or depressive illness is more than 9.4% in general adult American population

Z-Test Results: t-stats-3.065, p-value -0.0011 0.40 0.35 0.30 0.25 0.20 О. 15 0.10 0.05 0.00 4.0-3.5 -3.0-2.5 -2.0-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0