Sampling Error and Estimation

Abstract

How far can an estimate of a parameter be from the true value of the parameter? In particular, how far can a sample mean be from a population mean? For example, all car manufacturers are required to post the average gas mileage of their cars. Typically, an estimate is obtained by taking a sample of cars, driving them under different driving conditions, and calculating the average gas mileage for this sample. It is also assumed that if everything stays the same, this sample mean can be used as an estimate of the mean of the gas mileage of all cars of that model. But how accurate is that estimate? How far is it from the true value? Can we get some understanding of the difference between the estimate and the true value, called the sampling error? How often will we observe large sampling errors? If we made certain assumptions, there are theoretical results that will give us a margin of sam?pling error. For example, based on our sample standard deviation and sample size, we may be able to state that the sampling error should be between −5 and +5 in, say, 90 out of 100 cases. So we can assume that there is a 90% chance that our sample mean is within 5 units of the unknown population mean. Another way of saying it is that the margin of sampling error is +5 with a probability of 90%.