Hi, everyone: I am teaching an intro. stats course, and I want to find a convincing explanation of how we can "reasonably" estimate a population parameter by taking random samples. Given that the course is introductory, I cannot do a proof of the CLT. Specifically, what has seemed difficult in previous years for many students to accept, is that one can estimate a parameter (with any degree of confidence)from a population of around 310 million (current U.S pop.) by taking a random sample of size, say n=10,000 or less. AFAIK, the Central Limit Theorem is used to explain the representability of the larger population in a sample, from the fact that, informally (please correct me if I am wrong) biases, or deviations from the average cancel each other out, so that the aggregate deviates less from the mean, i.e., the standard deviation decreases as the sample size increases.. Would someone please comment on the accuracy of this statement and/or offer refs. about it.? Thanks in Advance.