Estimation and confidence intervals

Abstract

In Chapter 2 we stated that often we wish to infer or to predict information about a population by considering a sample (or samples) of collected data consisting of a finite number of observations or measurements from that population. Also, even if the population is large but finite, because of restrictions in time and expense, usually it is not possible to collect all the data for the population, and we certainly cannot collect all the data for an infinite population. We wish to find estimates of population parameters (for example, population mean, or variance) from the corresponding sample statistics (for example, sample mean, or variance). If the mean of the sampling distribution of a particular statistic is equal to the corresponding population parameter, then we say that the statistic is an unbiased estimator of the corresponding population parameter. For example, in Chapter 2, we showed that the mean of the sampling distribution of means is equal to µ, the population mean. Hence, the sample mean, x, is an unbiased estimator of the population mean µ.