The probability distributions discussed in the preceding chapters will yield probabilities of the events of interest, provided that the family (or the type) of the distribution and the values of its parameters are known in advance. In practice, the family of the distribution and its associated parameters have to be estimated from data collected during the actual operation of the system under investigation.
In this chapter we investigate problems in which, from the knowledge of some characteristics of a suitably selected subset of a collection of elements, we draw inferences about the characteristics of the entire set. The collection of elements under investigation is known as the population, and its selected subset is called a sample. Methods of statistical inference help us in estimating the characteristics of the entire population based on the data collected from (or the evidence produced by) a sample. Statistical techniques are useful in both planning of the measurement activities and interpretation of the collected data.
Two aspects of the sampling process seem quite intuitive. First, as the sample size increases, the estimate generally gets closer to the “true” value, with complete correspondence being reached when the sample embraces the entire population. Second, whatever the sample size, the sample should be representative of the population. These two desirable aspects (not always satisfied) of the sampling process will ...