Angioplasty is a medical procedure in which an obstructed blood vessel is widened. In some cases, a wire mesh tube, called a stent, is placed in the vessel to help it remain open. An article presents the results of a study comparing the effectiveness of a bare metal stent with one that has been coated with a drug designed to prevent re-blocking of the vessel. A total of 5322 patients received bare metal stents, and of these, 841 needed treatment for re-blocking within a year. A total of 1120 received drug coated stents and 134 of them required treatment within a year.
Let p_{X} represent the population proportion of patients with bare metal stents who needed treatment and let p_{Y} represent the population proportion of patients with drug coated stents who needed treatment. Find a 98% confidence interval for the differencepX−pYpX−pY . Round the answers to four decimal places.
Bare Metal | Drug Coated | |
x= | 841 | 134 |
n = | 5322 | 1120 |
p̂=x/n= | 0.1580 | 0.1196 |
estimated diff. in proportion=p̂_{1}-p̂_{2}= | 0.0384 | |
Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) = | 0.0109 |
for 98 % CI value of z= | 2.326 | from excel:normsinv((1+0.98)/2) | |
margin of error E=z*std error = | 0.025382 | ||
lower bound=(p̂1-p̂2)-E= | 0.0130 | ||
Upper bound=(p̂1-p̂2)+E= | 0.0638 | ||
from above 98% confidence interval for difference in population proportion =(0.0130 <p1-p2<0.0638) |
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