An organization published an article stating that in any one-year period, approximately 9.6 percent of adults in a country 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. Conduct 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 population in the country. Part (a) Is this a test of one mean or proportion? O test of one mean O test of proportion Part (b) State the null and alternative hypotheses. ○ Ho: p = 0.096 Ha: p<0.096 ○ Ho: p < 0.096 Ha p=0.096 O Ho: p = 0.096 H: p > 0.096 O Ho: p>0.096 Ha: p = 0.096 O Ho: p=0.096 Hap = 0.096 Part (c) Is this a right-tailed, left-tailed, or two-tailed test? Oright-tailed test O left-tailed test O two-tailed test Part (d) What symbol represents the random variable for this test? OP ○ a Ox Ο σχ On Part (e) In words, define the random variable for this test. O the number of people in the survey O the proportion of people in the town surveyed not suffering from depression or a depressive illness ◇ the number of people in the town surveyed not suffering from depression or a depressive illness O the number of people in the town surveyed suffering from depression or a depressive illness ◇ the proportion of people in the town surveyed suffering from depression or a depressive illness Part (f) Calculate the following. (i) Enter your answer as a whole number. x= (ii) Enter your answer as a whole number. n = (iii) Enter your answer to two decimal places. p' = Calculate σx. (Round your answer to three decimal places.) Show the formula set-up. n pg n ○ σx = V n n P n pq Part (h) State the distribution to use for the hypothesis test. O normal hypergeometric O uniform O geometric O binomial Part (i) Find the p-value. (Round your answer to four decimal places.) Part (j) At a pre-conceived a 0.05, what are your following? (i) Decision: Do not reject the alternative hypothesis. Do not reject the null hypothesis. O Reject the null hypothesis Reject the alternative hypothesis. (ii) Reason for the decision: O p-value <α O p-value> α O p-value> α/2 O p-value = α O p-value = α/2 (iii) Conclusion: At the 5% level of significance, there is sufficient evidence to conclude that the proportion of people in the town with depression or depressive illness equal to 0.096. ○ At the 5% level of significance, there is insufficient evidence to conclude that the proportion of people in the town with depression or depressive illness is lower than 0.096. At the 5% level of significance, there is insufficient evidence to conclude that the proportion of people in the town with depression or depressive illness is higher than 0.904. At the 5% level of significance, there is insufficient evidence to conclude that the proportion of people in the town with depression or depressive illness is lower than 0.904. At the 5% level of significance, there is sufficient evidence to conclude that the proportion of people in the town with depression or depressive illness is higher than 0.096.