Statistical Inference: A Short Course

1.3 Selecting a Sample from a Population

While there are many different ways of constructing a sampling plan, our attention will be focused on the notion of simple random sampling. Specifically, a sample of size n drawn from a population of size N is obtained via simple random sampling if every possible sample of size n has an equal chance of being selected. A sample obtained in this fashion is then termed a simple random sample; each element in the population has the same chance of being included in a simple random sample.

Before any sampling is actually undertaken, a list of items (called the sampling frame) in the population is formed and thus serves as the formal source of the sample, with the individual items listed on the frame termed elementary sampling units. So, given the sampling frame, the actual process of random sample selection will be accomplished without replacement, that is, once an item from the population has been selected for inclusion in the sample, it is not eligible for selection again—it is not returned to the population pool (it is, so to speak, “crossed off” the frame) and consequently cannot be chosen, say, a second time as the simple random sampling process commences. (Under sampling with replacement, the item chosen is returned to the population before the next selection is made.)

Will the process of random sampling guarantee that a representative sample will be acquired? The answer is, “probably.” That is, while randomization does not absolutely guarantee ...