Question

A telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the Northeast and the Midwest. The representative's belief is based on the results of a survey. The survey included a random sample of 10001000 northeastern residents and 11401140 midwestern residents. 40%40% of the northeastern residents and 35%35% of the midwestern residents reported that they were completely satisfied with their local telephone service. Find the 95%95% confidence interval for the difference in two proportions.

Step 3 of 3 :  

Construct the 95%95% confidence interval. Round your answers to three decimal places.

Answer 1

Pooled poportion = (n1 * 1 + n2 * 2 ) / ( n1 + n2 )

= (0.40 * 1000 + 0.35 * 1140) / ( 1000 + 1140 )

= 0.3734

Margin of error = Z/2 * sqrt [ ( 1 -) * ( 1 / n1 + 1 / n2 ) ]

= 1.96 * sqrt [ 0.3734 ( 1 - 0.3734) * (1 / 1000 + 1/ 1140) ]

= 0.0411

95% CI is

(1 - 2) - E < p1 - p2 < (1 - 2) + E

(0.40 - 0.35) - 0.0411 < p1 - p2 < (0.40 - 0.35) + 0.0411

0.009 < p1 - p2 < 0.091

95% CI is ( 0.009 , 0.091 )