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 South. The representative's belief is based on the results of a survey. The survey included a random sample of 1220 northeastern residents and 1340 southern residents. 59% of the northeastern residents and 46% of the southern residents reported that they were completely satisfied with their local telephone service. Find the 90% confidence interval for the difference in two 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 90%90% confidence interval. Round your answers to three decimal places.

Answer 1

1) At 90% confidence interval the critical value is z^* = 1.645

2) The pooled sample proportion(P) = ( * n1 + * n2)/(n1 + n2) = (0.59 * 1220 + 0.46 * 1340)/(1220 + 1340) = 0.522

SE = sqrt(P(1 - P)(1/n1 + 1/n2))

= sqrt(0.522 * (1 - 0.522) * (1/1220 + 1/1340))

= 0.020

3) The 90% confidence interval for population proportion is

() +/- z^* * SE

= (0.59 - 0.46) +/- 1.645 * 0.020

= 0.13 +/- 0.0329

= 0.0971, 0.1629

= 0.097, 0.163