Question

2. (40 points) in clinical trials of the drug Lipitor, 270 subjects were given a placebo and 7 of them had an allergic reaction. Among 863 subjects treated with 10 mg of Lipitor, 18 of them experienced an allergic reaction. Construct two 95% confidence interval estimates of the percentages of allergic reactions. Show all formulas and substitutions, even if you do the work on your calculator. Compare the results. What do you conclude? Answer in complete sentences.

Answer 1

Given data, 1= 240 subjects Let x be represents the no. of subiect who were given a placebo and have alleggic reaction X=7 and Ộ be the proportion of subiect who were given a placebo and have alleggic reaction in a sample of 940 subjects, P= 0.0259 (1-x) % - 95% |-x=0.95 &=1-0195 50105 % =0.025 28/2 = 20.095 24 = 1.96 270 95% confidence interval estimates of the percentages of all allogic reaction in placebo :subject is given of § +2/12, C1-B) 010259 4.96 10.0259 C1-0.0259) V 270 0.02593 1,96 0.0259 X0.9741 V 270 0.0299 +1.96 0.0952 V270 0.0259 +1.96 X0.0097 0.0259 +0.0190 0.0069, 010449)

Now, 'ne 563 reated . Let X' be, represent the noi of subjects. foe song of lip Htoo and have the allergic reaction, X = 18 and Ộ be the proportion of subjects treated with long of lipitor and have the allergic reaction in a sample of 863 subject, Þ= * = 0.0208 (1) % - 95% 1-4 = 0.95 x=1-0.95 =0.05 -0.025 24/2 =20,025 20444 =1.96 95% confidence interval estimates of the percentages of all allergie reaction in a treatment of 10 mg lipitos is given by, - Å2 24/2/P(12) 0.0208 + 1.96 0.0208 (1-0.0208) V 863 0.02.08 £1.96 0.0208 X0.9792 863 n 010208 31.96 0.0204. 0.0208 +1.96 %0.0049 0.0208 +0.0096 10.0112, 0.0304)

When we compare both the confidence that confidence inteove mpare both the confidence interval we find confidence interval estimate of the percentage of all allergic reaction in placebo subject is narrow than the confidence interval estimates of the percentages of all reaction in a treatment of io ng lipitos,
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