Question

Required information

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 1124 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.

The 98% confidence interval is (  ,  ).

Answer 1

Solution :

Given that,

₁ = x₁ / n₁ = 0.1580

₂ = x₂ / n₂ = 0.1192

1) Point estimate of difference between two proportions

= ₁ -  ₂

= 0.1580 - 0.1192

= 0.0388

2)

Our aim is to construct 98% confidence interval.

= 2.326 (use z table)

Margin of error =   *

=  

= 0.0255

3) Required interval is

Point estimate   Margin of error

0.0388    0.0255

(0.0388 - 0.0255 , 0.0388 +  0.0255)

( 0.0133 , 0.0643 )

The 98% confidence interval is ( 0.0133 , 0.0643 )