10.1: Introduction to Estimation

Skills to Develop

• 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.

Contributor

• Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University.