A study to determine the effectiveness of a drug (serum) for arthritis resulted in the comparison of two groups, each consisting of 200 arthritic patients. One group was inoculated with the serum; the other received a placebo (an inoculation that appears to contain serum but actually is non active). After a period of time, each person in the study was asked to state whether his or her arthritic condition had improved. These are the results:

You want to know whether these data present sufficient evidence to indicate that the serum was effective in improving the condition of arthritic patients.
a. Use the chi-square test of homogeneity to compare the proportions improved in the populations of treated and untreated subjects. Test at the 5% level of significance.
b. Test the equality of the two binomial proportions using the two-sample z-test of Section 9.6. Verify that the squared value of the test statistic z2 = X2 from part a. Are your conclusions the same as in part a?

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Treated Untreated Improved Not Improved 83 74 126