two-part question: (How to set up??) where do Istart? A clinical trial is planne
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two-part question: (How to set up??) where do Istart? A clinical trial is plannedtocomopare anexperimentalmedication designed to lower blood pressure to a placebo. Before starting the trial a piilot study is conductd involving 10participants. the objective o fth e study is toassess how systolicblood pressure changes untreated over time. Systolic bloodpressures are measured at baseling and again 4 weeks later. Computea 95% confidence interval for the mean difference in blood pressuerover 4 weeks. Baseline: 120 145 130 160 152 143 126 121 115 135 4 weeks: 122n 142 135 158 155 140 130 120 124 130 After the pilot study described above the main trail isconducted and involves a total of 200 patients. Patients areenrolled and randomized to receive either the experimentalmedication or the placebo. The data is Experimental Placebo (n=100) (n=100) %hypertensive 14% 22% collected at the end of the study after 6 weks on the asignedtreatment. Generate a 95% confidence interval for the difference inproportions of patients with hypertensionbetween groups. two-part question: (How to set up??) where do Istart? A clinical trial is plannedtocomopare anexperimentalmedication designed to lower blood pressure to a placebo. Before starting the trial a piilot study is conductd involving 10participants. the objective o fth e study is toassess how systolicblood pressure changes untreated over time. Systolic bloodpressures are measured at baseling and again 4 weeks later. Computea 95% confidence interval for the mean difference in blood pressuerover 4 weeks. Baseline: 120 145 130 160 152 143 126 121 115 135 4 weeks: 122n 142 135 158 155 140 130 120 124 130 After the pilot study described above the main trail isconducted and involves a total of 200 patients. Patients areenrolled and randomized to receive either the experimentalmedication or the placebo. The data is Experimental Placebo (n=100) (n=100) %hypertensive 14% 22% collected at the end of the study after 6 weks on the asignedtreatment. Generate a 95% confidence interval for the difference inproportions of patients with hypertensionbetween groups.Explanation / Answer
(a) First you start out by subtracting the List2 (4weeks)from List1 (Baseline). This will give you a list of differencesfrom which you can draw statistical numbers. With this list:2,-3,5,-2,3,-2,4,-1,9,-5 you can find the mean andstandard deviation, which is needed, for the confidence interval,CI. The formula for CI is CI= mean (+/-) (t*) ((standarddeviation)/(square root (n)) Form the list of differences, mean=.9 and standarddeviation=4.408325 and t* for a 95%CI with n=10, df=9 sot*=2.262. CI = .9 - (2.262)((4.408325)/(sqrt(10))) = -2.2533 CI = .9 + (2.262)((4.408325)/(sqrt(10))) = 4.0533 Therefore the 95% CI for the 4 week baseline study in differenceswill be (-2.2533,4.0533) (b) For this 95% CI, the equation is different due to it being atwo sample, Experimental vs Placebo and they are not matchedpairs. The equation is CI = ( E(p) - P(p)) (+/-) z* sqrt( ((E(p) (1-E(p)))/ n1) + ((P(p) (1-P(p)) /n2) ) Using E(p) = .14 P(p)=.22 n1=100 n2=100 z*= 1.96 CI= (.14-.22) - (1.96) sqrt( ((.14)(.86))/100 + ((.22)(.78))/100) )= -.185913 CI=(.14-.22) + (1.96) sqrt( ((.14)(.86))/100 + ((.22)(.78))/100) )= .025913 Therefore the 95% CI for the difference between the proportionchange in experimental vs placebo is (-.185913,.025913).
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