10.1: Introduction to Estimation
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Learning Objectives
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Define statistic
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Define parameter
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Define point estimate
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Define interval estimate
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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.