In a Time/Money Magazine poll of Americans of age 18 years and older, 65% agreed with the statement, “We are less sure our children will achieve the American Dream” (Time, October 10, 2011). Assume that this poll was based on a random sample of 1600 Americans.
a. Construct a 95% confidence interval for the proportion of all Americans of age 18 years and older who will agree with the aforementioned statement.
b. Explain why we need to construct a confidence interval. Why can we not simply say that 65% of all Americans of age 18 years and older agree with the aforementioned statement?