Question

Construct a confidence interval for p 1 minus p 2 at the given level of confidence. x 1 equals 398​, n 1 equals 528​, x 2 equals 434​, n 2 equals 585​, 90 ​% confidence The researchers are _____ ​% confident the difference between the two population​ proportions, p 1 minus p 2 ​, is between _____ and ____ .

Answer 1

Sol;

p1^=x1/n1=398/528=0.7537879

p2^=x2/n2=434/585=0.7418803

z crit for 90%=1.645

90% confidence interval for difference in proportions is

p1^-p2^+-z*sqrt(p1^(1-p1^/n1+p2^*(1-p2^)/n2)

(0.7537879-0.7418803)+-1.645*sqrt(0.7537879*(1-0.7537879)/528+0.7418803*(1-0.7418803)/585)

0.0119076-0.04285973,0.0119076+0.04285973

-0.03095213,0.05476733

The researchers are __90___ ​% confident the difference between the two population​ proportions, p 1 minus p 2 ​, is between -0.0309 and 0.0548.