L19.7 Polling Revisited
We now revisit the polling problem that we have started earlier. When we first looked at that problem, we used the Chebyshev inequality to obtain certain bounds and numerical results. What we want to do now is instead to use a central limit theorem-type approximation, which we hope that it will be more accurate and more informative. Let us remind ourselves of the setting. We want to estimate a certain number, p, which is the fraction of the population that will vote yes in a certain referendum. And we estimate p by picking a sample out of the population. We pick n people. We pick them randomly, uniformly over the population and independently. For each one of the people in the sample, we ask them if they will vote to yes or no, and then we record their answers in Bernoulli random variables, Xi. So by the assumptions that we have made, these Xi's are independent Bernoulli random variables, and their mean is equal to p. We count how many X's were equal to 1. That...