Tests for Two Sample Means 13. A pharmaceutical company implements a drug effectiveness trial for a "beta-blocker" intended to reduce the heart rate of patients during surgery. The subjects were divided at random into two groups of n=30 patients each. One group received the beta-blocker, the other a placebo. The pulse rate of each patient at a specific point in the surgery was recorded. The results of this study are as follows: For the treatment group, X T = 65.2 with ST = 6.8, and for the control (placebo) group X c= 70.2 with Sc = 9.3. Two patients in the placebo group died, so that ny =30 and no=28. Boxplots of the data distributions are modestly skewed, but with no outliers. Because the investigators were only interested in whether or not the drug reduces heart rate, a one-tailed test of significance was used. a. Given the available information, assess whether or not the Normality assumption for the two-sample t-test is likely to be valid. b. State the appropriate null and alternative hypotheses for this test. He: Ha : c. Based on the available information, which is the more appropriate test of significance, the pooled-variance t-test or the separate-variance t-test? Explain your answer. d. Based on your answer to part (c), compute the standard error of the difference S ( XT - x c. Note: Copy this value into the space provided in Question #14. Explain what this standard error value represents. e. Scale the X-axis of the sampling distribution of (XT - Xc ) under the assumption that Ho is true, and shade-in the area under the curve that corresponds to the p-value for the appropriate test of significance. E ( X T - XC) = S(XT - X) = f. Perform the appropriate two-sample t-test (compute the t-test statistic, determine the degrees of freedom and use the t-table to obtain the p-value)