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 920 northeastern residents and 840 midwestern residents. 54% of the northeastern residents and 44% of the midwestern residents reported that they were completely satisfied with their local telephone service. Find the 90% confidence interval for the difference in two proportions.

Find the point estimate that should be used in constructing the confidence interval.

Find the margin of error. Round your answer to six decimal places.

Construct the 90% confidence interval. Round your answers to three decimal places.

Answer 1

Sample 1, Northeast:  
n1 =   920, p̂1 = 0.54
Sample 2, Mideast:  
n2 =   840, p̂2 = 0.44

Point estimate = p̂1 - p̂2 = 0.54-0.44 = 0.10

At α = 0.10, two tailed critical value, z_c = NORM.S.INV( 0.10/ 2) = 1.644854

Margin of error, E =

90% confidence interval: