Question

Construct a confidence interval for p1−p2 at the given level of confidence. x1=365365​, n1=516516​, x2=405405​, n2=577577​, 9999​% confidence

Answer 1

Solution:

Given:

x₁ = 365

n₁ = 516

x₂ = 405

n₂ = 577

c = confidence level = 99%

We have to construct the confidence interval for p₁ - p₂.

where

and

and

Z_c is z critical value for c = 0.99 confidence level.

Find Area = ( 1+c)/2 = ( 1 + 0.99 ) / 2 = 1.99 /2 = 0.9950

Thus look in z table for Area = 0.9950 or its closest area and find corresponding z critical value.

From above table we can see area 0.9950 is in between 0.9949 and 0.9951 and both are at same distance from 0.9950, Hence corresponding z values are 2.57 and 2.58

Thus average of both z values is 2.575

Thus Z_c = 2.575

Thus

Thus 99% confidence interval for p₁ - p₂ is: