4.50. For an election exit poll for a Senatorial election, find the standard error of the sample proportion voting for a candidate for whom the population proportion is 0.50, when n = 100,1000, and 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 ofthe law oflarge numbers, which states that the sample proportion tends to get closer and closer to the population proportion as n increases indefinitely.