Question

Explain the roles of sample statistics, estimated standard errors and confidence intervals in the estimation of population parameters. Illustrate such in the context of estimating a population mean.

Answer 1

For estimating a population mean, the sample statistic like sample mean is taken as the point estimate of the population mean. The population can be estimated by sample mean.

The standard error gives us idea about the accuracy of sample mean as called as an estimator of population mean. As the standard error increases, the accuracy of sample mean being an estimator of population mean decreases.

Confidence interval gives an interval estimate of population mean. It gives the plausible range within which the population mean would lie.