Another important property is consistency which means that the variance and and the bias of the estimator both go to zero as the sample size gets large. We wouldn't want to use an estimator that is not consistent. Finally, we always want to use estimators that have low bias and low variance. Such estimators are called efficient estimators. Statistical Inference Random variables and their distributions, introduced in the previous two lessons, are used to describe and model populations.
Statistical inference deals with drawing conclusions about populations based on samples.
But more specifically these conclusions are based on estimators of the parameters of the population. That is, the sample mean and sample variance are very helpful in drawing conclusions about a population. Any inference about a population parameter will involve some uncertainty because it is based on a sample, rather than on the entire population. To be meaningful, statistical inference must include a specification of this uncertainty. In the next section we will explain confidence intervals.