Question

A telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the South and the Midwest. The representative's belief is based on the results of a survey. The survey included a random sample of 840 southern residents and 940 midwestern residents. 386 of the southern residents and 555 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. (Round to two decimal places.)

Lower and Upper bound?

Answer 1

z critical for 90% is 1.645 [From z table]

sample proportion = x1/n1 = 386/840 = 0.456

sample proportion = x2/n2 = 555/940 = 0.590

sample size n1 and n2 are 840 and 940 respectively

Confidence interval calculation

Lower bound is -0.17

Upper bound is -0.09