A recent Gallup poll found that 35% of the adult population of the United States believes that the theory of evolution is “well-supported by the evidence.” Gallup polled 1928 Americans selected uniformly and independently at random. Of these, 675 asserted belief in evolution, leading to Gallup’s estimate that the fraction of Americans who believe in evolution is 675=1928 _ 0:350. Gallup claims a margin of error of 3 percentage points, that is, he claims to be confident that his estimate is within 0.03 of the actual percentage.
(a) What is the largest variance an indicator variable can have?
(b) Use the Pair wise Independent Sampling Theorem to determine a confidence level with which Gallup can make his claim.
(c) Gallup actually claims greater than 99% confidence in his estimate. How might he have arrived at this conclusion? (Just explain what quantity he could calculate; you do not need to carry out a calculation.)
(d) Accepting the accuracy of all of Gallup’s polling data and calculations, can you conclude that there is a high probability that the number of adult Americans who believe in evolution is 35 +- 3 percent?