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Chapter 10: Sampling Distributions and the Central Limit Theorem
Since the population of interest is too large for us to observe all Americans,
we can estimate the true proportion by observing a random sample from the
population. If we let the sample proportion be denoted by
̂
(read as
“
hat”), then the point estimate
̂
can be defined by
This single numerical value
̂
is called a point estimate for the population
proportion
.
The symbol
̂
is called a point estimator for the population
proportion
.
Definition: Point Estimate
A point estimate is a single numerical value that is used to estimate a
population parameter.
Generally, we can select a random sample of size
from any population
with some attribute of interest and if we let
represent the number of
successes in the sample and we let
represent the true proportion for the
attribute then we can pictorially represent this experimental design as shown
in
Figure 10-1
.