Estimation
Prerequisites
See individual sections
 Introduction
 Degrees of Freedom
 Characteristics
of Estimators
 Bias and Variability Simulation
 Confidence Intervals
 Introduction
 Confidence Interval
for the Mean
 t distribution
 Confidence Interval
Simulation
 Confidence
Interval for the Difference Between Means
 Confidence
Interval for Pearson's Correlation
 Confidence
Interval for a Proportion
 Exercises
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.
The concept of degrees of freedom and its relationship to
estimation is discussed in Section B. "Characteristics
of Estimators" discusses two important concepts: bias and precision.
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%. The sections
on confidence interval show how to compute confidence intervals
for a variety of parameters.
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