1. A stud},r to determine the effectiveness of a drug, or serum. for the treatment of arthritis resulted in the comparison of two groups1 each consisting of 400 arthritic patients. lCivic group was inoculated with the serum, whereas the other received a placebo [an inoculation that appears to contain serum hut actuallf,r is not active}. After a period of time, each person in the stud}r was asl-red whether their arthritic condition had improved, and the observed results are presented in the accompanying table. The question of interest is: Do these data present evidence to indicate that the proportion of arthritic individuals who improved difers depending on whether or not they received the drug? Condition Treated Untreated Improved 234 143 Not improved 166 252 {a} Conduct a hypothesis test using the X: test statistic. with or = .05. Report {1} the null and alternative hypotheses: {ii} the expected cell counts; [iii] the test statistic: {iv} the critical value: [vi the p-value; and {vi} the conclusion. {h} Using the 3-statistic1 test the hypothesis that the proportion of treated persons who improved is equal to the proportion of untreated persons who improved. with o = .05. Hint: Express each proportion as a mean. See Section 1133 of the textbook for a refresher. Report [1] the null and alternative hypotheses; {ii} the test statistic; {iii} the critical value; {iv} the p-value; and {v} the conclusion. {c} Prove that [assuming a is the same for both tests} the x2 statistic X2 is equivalent to the square ofthe test statistic 2 {22}. In other words, prove that the 12 test used in part {a} is equivalent to the two-tailed Ztest used in part [h]. Hint: Use the Z statistic