Question

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.

Answer 1

First sample : bare metal : n1=5322 , X1=841

Second sample : drug coated stents : n2=1120 , X2=134

The estimate of the sample proportions are ,

The pooled estimate is ,

The critical value is ,

; From Z-table

Therefore , the 98% confidence interval for the differencepX−pY is ,