One of the major applications of statistics is
estimating populationparameters
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
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.