Question: The Social Security system in the United States may encounter serious financial difficulties as baby boomers begin to retire in the future. Several polls have asked Americans their opinion about the financial condition of Social Security. In one poll, taken in August 2000 by the Gallup Organization (Gallup Poll Topics: A–Z, Social Security), 42 percent of a sample of 798 non-retired persons said they did not think "the Social Security system will be able to pay you a benefit when you retire."

(a) Calculate the 95 percent confidence interval to estimate the percentage of Americans who don't think that Social Security will be able to provide for them.

(b) Calculate the 99 percent confidence interval.

(c) Are both of these results compatible with the conclusion that fewer than 50 percent of Americans believe that the Social Security system will not be able to pay their benefits after retirement?