From our previous knowledge we are now able to distinguish between a population and a sample, a parameter and statistic, and random and non-random sampling. We also have a little knowledge of some sampling distributions. The difficulty in dealing with populations is that we usually do not know the value of their parameters. Even if we could find these values, it is not practical in terms of time, money and reliability.
This area is devoted to the study of the most suitable values of these parameters based on the random samples from the given population. These values, which are functions of sample observations and derived on the basis of a certain criterion, are called the “estimates”. The formulae with which these estimates are obtained are called “estimators”. The methods by which we extract information about the population on the basis of samples is called “estimation”.
What makes estimation challenging is the problem of determining the most probable values of the parameters of probability distributions. For example, estimate the average height of individuals in a M.Sc class during the year 2000. A researcher then draws a sample of a few individuals, and on the basis of the information obtained from the sample they might express their view by saying that
- The average height of the individuals is 65 inches, or
- It is most probable that the average height is between 62 and 67 inches
We therefore have two kinds of estimates: An estimate of the type given in (1) above which is known as a “Point Estimate”, and an estimate of the type given in (2) above which is known as an “Interval Estimate”.