Question

A newsgroup is interested in constructing a 95% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 573 randomly selected Americans surveyed, 404 were in favor of the initiative. Round answers to 4 decimal places where possible.

a. With 95% confidence the proportion of all Americans who favor the new Green initiative is between ____ and _____.

b. If many groups of 573 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About ____ percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about ___ 99.9 percent will not contain the true population proportion.

Answer 1

= 404/ 573 = 0.705, 1 - = 0.295, n = 573, = 0.05

The Zcritical (2 tail) for = 0.05, is 1.96

The Confidence Interval is given by ME, where

The Lower Limit = 0.705 - 0.0373 = 0.6677

The Upper Limit = 0.705 + 0.0373 = 0.7423

(a) With 95% Confidence the proportion of all Americans who favor the new green initiative is between 0.6677 and 0.7423.

(b) About 95 percent of these confidence intervals will contain the true population proportion of Americans who favor the new green initiative and about 5 percent will not contain the true population proportion.