Introduction to Estimation
Prerequisites
Measures
of Central Tendency, Variability
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
< π < 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
nonplayers 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.
