Question

Given two independent random samples with the following results: n1=590, pˆ1=0.85, n2=414, pˆ2=0.59

Use this data to find the 99% confidence interval for the true difference between the population proportions.

Step 1 of 3:

Find the critical value that should be used in constructing the confidence interval.

Step 2 of 3:

Find the value of the standard error. Round your answer to three decimal places.

Step 3 of 3:

Construct the 99% confidence interval. Round your answers to three decimal places.

Answer 1

a)

z critical value at 0.01 significance level = 2.576 (From Z table )

b)

pooled proportion = [ 1 n1 + 2 n2 ] / ( n1 + n2 )

= ( 0.85 * 590 + 0.59 * 414 ) / ( 590 + 414 )

= 0.7428

Standard error = sqrt [ ( 1 - ) * ( 1 / n1 + 1 / n2) ]

= sqrt [ 0.7428 ( 1 - 0.7428) * ( 1 / 590 + 1 / 414 ) ]

= 0.028

c)

99% confidence interval is

(1 - 2)  - Z * SE < p1 - p2 < (1 - 2)  + Z * SE

(0.85 - 0.59) - 2.576 * 0.028 < p1 - p2 < (0.85 - 0.59) + 2.576 * 0.028

0.188 < p1 - p2 < 0.276

99% CI Is ( 0.188 , 0.276 )