Point Estimation

Estimation represents ways or a process of learning and determining the population parameter based on the model fitted to the data.

Point estimation and interval estimation, and hypothesis testing are three main ways of learning about the population parameter from the sample statistic.

An estimator is particular example of a statistic, which becomes an estimate when the formula is replaced with actual observed sample values.

Point estimation = a single value that estimates the parameter. Point estimates are single values calculated from the sample

Height Example

We are interested in estimating the true average height of the student population at Penn State. We collect a simple random sample of 54 students. Here is a graphical summary of that sample.

Height example plot

  • Parameter of interest is the population mean height, μ.
  • Sample statistic, or a point estimator is \(\bar{X}\), and an estimate, which in this example, is 66.432.
  • The sample mean is the best point estimate and so it also becomes the center of the confidence interval.