Question

A telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the West and the Northeast. The representative's belief is based on the results of a survey. The survey included a random sample of 12401240 western residents and 13001300 northeastern residents. 46%46% of the western residents and 35%35% of the northeastern residents reported that they were completely satisfied with their local telephone service. Find the 98%98% confidence interval for the difference in two proportions.

Step 2 of 3:

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

Step 3 of 3:

Construct the 98%98% confidence interval. Round your answers to three decimal places.

Answer 1

Solution :

Given that,

n1 = 1240

1 = x1 / n1 = 0.46

n2 =1300

2 = x2 / n2 = 0.35

1) Point estimate of difference between two proportions

= 1 -  2

= 0.46 - 0.35

= 0.11

Step 2 of 3:

standard error

SE =

=

= 0.0193465

Our aim is to construct 98% confidence interval.

c = 0.98

= 1- c = 1- 0.98 = 0.02

  /2 = 0.02 2 = 0.01  

= 2.326 (use z table)

Margin of error =   * SE

= 2.326 *  0.0193465   

= 0.045

Step 3 of 3:

Required interval is

Point estimate   Margin of error

0.11   0.037734

(0.11 - 0.045, 0.11 +  0.045)

(0.065 , 0.155)