For an election exit poll that uses random sampling, find the standard error of the sample proportion voting for a candidate for whom the population proportion is 0.50, when n = 100, when n = 1000, and when n = 10, 000.

In each case, predict an interval within which the sample proportion is almost certain to fall. Notice that the interval shrinks in width as the sample size increases. This is a consequence of the law of large numbers, which states that, with random sampling, the sample proportion tends to get closer and closer to the population proportion as n increases indefinitely.