1. (13 points) In a randomized clinical trial comparing hydrochlorothiazide (HCTZ) to propranolol (PROP) for control of blood pressure, researchers were interested in whether blacks and whites differed in the rate of attaining goal blood pressure for each of the medications. The tables below provide demographic and blood pressure response data as well as other data from the study. Table 3.-Baseline Demographic Data and Prior Treatment Status" Propranolol Hydrochloride Hydrochlorothiazide N 340 343 Age, yr 49.619.0 49.89.9 Weight, kg 86.6+ 15.0 85.7 # 14.1 h Black 67.7 85.9 Prior treatment status, % No prior prescription 35.6 39. 1 Diuretic alone 17.9 18.7 Nondiuretic alone 6.2 3.2 Diuretic plus nondiuretic 38.2 35.6 Unknown medication 2.1 3.5Table 4.--Baseline Data and Effect of Treatment on Heart Rate and BP* Propranolol Hydrochloride Hydrochlorothiazide Heart rate, bom 76.9 + 10.4 76.7 11.5 E 80.9 10.0 79.4 $ 11.5 Systolic BP, mm Hg B 146.0 14,4 146.6+ 15.8 E 134.01 10.3 128 8+ 12.2 Diastolic BP, mm Hg B 101.8= 4.8 101.314.6 90.5 37.8 89.4 16.5 A Systolic BP, mm Ho -10.4 12.8 -18.1 13.6 W -13.2+ 13.1 -15.3+12.0 B -8,2+ 12 2 -20.3 + 14.3 & Diestolic BP. mm Hg -10.8 =7.0 -12.016.5 W -12.6=6.6 -10.95.7 -0.5+7.0 -13.047.0 6 reaching goal 67.0 64.1 $% whites at goal 61.7 65.3 9% blacks at goal 53.3 71.3 % $140 mm Hg systolict 65.8 84.9 while $140 mm Ho systolet 60.0 81.6 "h black $ 140 mm Hg cystoliat 84.1 87.7a. Complete the following 2 by 2 table. (4 points) Reached Goal BP BP Medication Yes No Hydrochlorothiazide Propranolol b. Calculate the 95% confidence interval for po (the proportion attaining goal BP on hydrochlorothiazide among Blacks). Note Zo.025 = 1.96. (4 points)c. Calculate the 95% confidence interval for p1 (the proportion attaining goal BP on propranolol among Blacks). (4 points) d. Explain and compare the 95% confidence intervals of pland pa by writing one on top of another. Are these two intervals overlapping? (1 point)