Question 1151950: Researchers are interested in estimating difference in drug therapy adherence among subjects with depression who received usual care and those who received care in a collaborative care model. The collaborative care model emphasized the role of clinical pharmacists in providing drug therapy management and treatment follow-up. Of the 50 subjects receiving usual care, 34 adhered to the prescribed drug regimen, while 34 out of 74 subjects in the collaborative care model adhered to the drug regimen. Construct a 95% confidence interval for the difference in adherence proportions for the populations of subjects represented by these two samples and interpret the result
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! the half-interval is z*sqrt (p1(1-p1)/n1+p2(1-p2)/n2))
(34/50) =p1=0.68
(34/74)=p2=0.459
SE=sqrt ((0.68*0.32/50+0.459*0.541/74))=sqrt(0.00771)=0.088
z=1.96
z*SE=0.172
95% CI of difference is 0.221 +/- 0.172
or (0.049, 0.383)
Because the CI of the difference does NOT contain 0, there is statistical support for a true difference in means between these two proportions, and there is a difference in adherence proportions.
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