Question

A poll reported that only 593 out of a total of 1594 adults in a particular region said they had a​ "great deal of​ confidence" or​ "quite a lot of​ confidence" in the public school system. This was down 5 percentage points from the previous year. Assume the conditions for using the CLT are met. Complete parts​ (a) through​ (d) below.

b. Find an 80​% confidence interval and interpret it.

The 80​% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is (__,__).

Round to three decimal places as needed.

Answer 1

We need to construct the 80% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases:

Favorable Cases X =	593
Sample Size N =	1594

The sample proportion is computed as follows, based on the sample size N = 1549 and the number of favorable cases X = 593

The critical value for α=0.2 is z_c = 1.282. The corresponding confidence interval is computed as shown below:

The 80​% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is (0.357,0.388).