Skip to main content
Statistics LibreTexts

10.1: Introduction to Estimation

  • Page ID
    2138
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    Learning Objectives

    • Define statistic

    • Define parameter

    • Define point estimate

    • Define interval estimate

    • Define margin of error

    One of the major applications of statistics is estimating population parameters from sample statistics. For example, a poll may seek to estimate the proportion of adult residents of a city that support a proposition to build a new sports stadium. Out of a random sample of \(200\) people, \(106\) say they support the proposition. Thus in the sample, \(0.53\) of the people supported the proposition. This value of \(0.53\) is called a point estimate of the population proportion. It is called a point estimate because the estimate consists of a single value or point.

    Point estimates are usually supplemented by interval estimates called confidence intervals. Confidence intervals are intervals constructed using a method that contains the population parameter a specified proportion of the time. For example, if the pollster used a method that contains the parameter \(95\%\) of the time it is used, he or she would arrive at the following \(95\%\) confidence interval: \(0.46 < \pi < 0.60\). The pollster would then conclude that somewhere between \(0.46\) and \(0.60\) of the population supports the proposal. The media usually reports this type of result by saying that \(53\%\) favor the proposition with a margin of error of \(7\%\).

    In an experiment on memory for chess positions, the mean recall for tournament players was \(63.8\) and the mean for non-players was \(33.1\). Therefore a point estimate of the difference between population means is \(30.7\). The \(95\%\) confidence interval on the difference between means extends from \(19.05\) to \(42.35\). You will see how to compute this kind of interval in another section.


    This page titled 10.1: Introduction to Estimation is shared under a Public Domain license and was authored, remixed, and/or curated by David Lane via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

    • Was this article helpful?