E O CONFIDENCE INTERVALS AND HYPOTHESIS TESTING Hypothesis test for a population proportion Kimberl An antidepressant has historically been known to relieve depression for 80% of patients who use the drug. The drug's formula was changed recently to include a smaller dose of its main, active ingredient. Due to this change, a medical researcher suspects that among all people with depression who use the new version of the drug, the proportion, p, of people who find relief is lower than 80%. A random sample of 190 patients who use the new version is selected by the researcher, and 144 of them find relief from depression. Based on these data, can we support the researcher's claim at the 0.01 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H. P Ho : 0 X S p H :0 (b) Determine the type of test statistic to use. (Choose one) 0=0 OSO 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) * 00 0 (d) Find the critical value. (Round to three or more decimal places.) X 5 ? 0 (e) Can we support the claim that the proportion of people who find relief from depression using the new version of the drug is lower than 80%? O Yes O No