Question

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

x1=378 ,n1=523, x2=402 , n2=583, 90​% confidence.

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

Answer 1

1 = 378 / 523 = 0.723

2 = 402 / 583 = 0.690

Pooled proportion = (378 + 523) / ( 402 + 583)

= 0.705

90% confidence interval for p is

1 - 2 - Z * sqrt{ 1 ( 1 - 1) / n1 + 2 ( 1 - 2 ) / n2 ] < p1 - p2 <

1 - 2 + Z * sqrt{ 1 ( 1 - 1) / n1 + 2 ( 1 - 2 ) / n2 ]

0.723 - 0.690 - 1.645 * sqrt( 0.723 * 0.277 / 523 + 0.690 * 0.310 / 583 ) < p 1 - p2 <

0.723 + 0.690 - 1.645 * sqrt( 0.723 * 0.277 / 523 + 0.690 * 0.310 / 583 )

-0.012 < p1 - p2 < 0.078

The 90% CI is between -0.012 and 0.078