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 West. The representative's belief is based on the results of a survey. The survey included a random sample of 960960 southern residents and 860860 western residents. 38%38% of the southern residents and 51%51% of the western residents reported that they were completely satisfied with their local telephone service. Find the 80%80% 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.

Answer 1

The pooled proportion first is computed here as

Therefore the standard error now is computed here as:

Therefore 0.023 is the required standard error value here.

From standard normal tables, we have:
P(Z < 1.282) = 0.9

Therefore, due to symmetry,
P( -1.282 < Z < 1.282) = 0.8

The confidence interval here is computed as:

This is the required 80% confidence interval here.