Question

A poll reported that only 1211 out of a total of 1560 adults in a particular region said they had a "great deal of confidence" or "quite a lot of confidence" in the military. Assume the conditions for using the CLT are met. Complete parts (a) through (d) below. a. Find a 95 % confidence interval for the proportion that expresses a great deal of confidence or quite a lot of confidence in the military, and interpret this interval. B. use 80 percent interval

Answer 1

Sample size = n = 1560

x = 1211

Sample proportion is

We have to construct a 95% confidence interval for the population proportion.

Formula is

Here E is a margin of error.

Zc = 1.96

So confidence interval is ( 0.7763 - 0.0207 , 0.7763 + 0.0207) => ( 0.7556 , 0.7970)

Interpretation: We are 95% confidence that the population proportion lies in the above interval.

b)

Sample size = n = 1560

x = 1211

Sample proportion is

We have to construct a 80% confidence interval for the population proportion.

Formula is

Here E is a margin of error.

Zc = 1.28

So confidence interval is ( 0.7763 - 0.0235 , 0.7763 + 0.0235) => ( 0.7628 , 0.7898)