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7.1: Introduction to Estimation

Last updated

Feb 2, 2022
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- 7: Estimation
- 7.2: Degrees of Freedom

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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.

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