Question

Construct a confidence interval for p 1 minus p 2 at the given level of confidence.

x 1 equals378​, n 1 equals522​, x 2 equals426​, n 2 equals563​, 95​% confidence

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

Answer 1

Answer:

Given,

To determine the confidence interval

For the 95% confidence interval, z value is 1.96

x1 = 378

n1 = 522

x2 = 426

n2 = 563

p1^ = x1/n1

substitute values

p1^ = 378/522

p1^ = 0.7241

p2^ = x2/n2

substitute values

= 426/563

p2^ = 0.7567

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

substitute the values

= (0.7241 - 0.7567) +/- 1.96*sqrt(0.7241(1-0.7241)/522 + 0.7567(1-0.7567)/563)

= - 0.0326 +/- 0.0522

= (- 0.0326 - 0.0522 , - 0.0326 + 0.0522)

= ( - 0.0848 , 0.0196)

The researchers are 95% confident the difference between the two population​ proportions, p 1 minus p 2​, is between - 0.0848 and 0.0196.