The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.8% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 10.4% 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 9.8% 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? (Select the correct symbols and use decimal values not percentages.)H0: H1:  b. Based on the hypotheses, find the following:c. Test Statistic =  d. p-value =    e. Based on the above we choose to f. The correct summary would be: that the true proportion of people in that city suffering from depression or a depressive illness is more than the percent in the general adult American population of 9.8%.

Previous studies suggest that female teens are more likely than male teens to be depressed. Define the depression rates for the female and male teens as p1 and p2 respectively. The p-value of the hypothesis test is 0.061. What is the correct conclusion at the 5% significance level?

A Canadian study measuring depression level in teens (as reported in the Journal of Adolescence, vol. 25, 2002) randomly sampled 112 male teens and 101 female teens, and scored them on a common depression scale (higher score representing more depression). The researchers suspected that the mean depression score for male teens is higher than for female teens, and wanted to check whether data would support this hypothesis.The following hypotheses were tested:H0: μ1 = μ2Ha: μ1 > μ2The following is the (edited) output for the test:Which of the following is an appropriate conclusion based on the output? The data do not provide sufficient evidence to conclude that the mean depression score of male teens is larger than that of female teens. The data provide sufficient evidence to conclude that male and female teens do not differ in mean depression score. The data do not provide sufficient evidence to reject H0, so we accept it, and conclude that male and female teens do not differ in mean depression score. The data provide sufficient evidence to reject H0 and to conclude that the mean depression score for male teens is larger than that of female teens.

The following two hypotheses are tested:Ho: The proportion of U.S. adults who oppose same-sex marriage is roughly 50%.Ha: The proportion of U.S. adults who oppose same-sex marriage is above 50% (i.e., the majority oppose).Suppose a survey was conducted in which a random sample of 1,100 U.S. adults was asked about their opinions about same-sex marriage, and based on the data, the p-value was found to be .002.Use a .05 (5%) significance level.The fact that the p-value = .002 means that

(iv) Make a decision and conclusion for the hypothesis test in context. Use a significance level of 5% (α = 0.05).

Everything else remaining the same, is it easier to reject a null hypothesis with a 5% or 1% level of significance?