Question

Construct a confidence interval for p1−p2 at the given level of confidence.

x1=26​, n1=241​, x2=30​, n2=291​, 95​% confidence

The researchers are __% confident the difference between the two population​ proportions, p1−p2​, is between __ and __.

Answer 1

Values are given as,

x1=26​, n1=241​

x2=30​, n2=291​

z= 1.96 (critical value of 95​%)

Calcultaing = (x1/n1)= (26/241) = 0.108

Calcultaing = (x2/n2)= (30/291) = 0.103

Calculating 95% confidence interval for p1−p2 :

Putting the values

CI= -0.0475 <p1−p2< 0.0575

The researchers are 95% confident the difference between the two population​ proportions, p1−p2​, is between -0.0475 and 0.0575.