MSOR221
1 / 4
Topic One
Sampling Concepts and Distributions
Sampling Concepts
–
Sample statistics
are used to make inferences (estimates or decisions) about
unknown
population parameters
θ
.
Because a statistic
T
is a function of the
random variables,
X
1
,
X
2
, …,
X
n
, observed in a sample (
T
=
f
(
X
1
,
X
2
, …,
X
n
)), the
statistic itself is a random variable.
Typical of what we mean by “statistic” are the
sample mean, the sample variance, and the sample proportion.
Since statistics are
random variables, their values will vary from sample to sample, and it is customary
to refer to their distribution as
sampling distribution
.
–
Consider all possible samples of size
n
that can be drawn from a given population.
For each sample, we can compute a statistic
T
(such as the mean, the variance, and
the proportion) that will vary from sample to sample.
In this manner we obtain a
distribution of the possible values of the statistic that is called its sampling
distribution.
From a practical point of view, the sampling distribution for a statistic
provides a theoretical probability distribution of the possible values of the statistic.
Population Parameter
Sample Statistic
Mean
N
X
∑
=
μ
n
x
x
∑
=
Variance
N
N
X
N
X
2
2
2
2
)
(
μ
μ
σ

∑
=

∑
=
1
1
)
(
2
2
2
2


∑
=


∑
=
n
x
n
x
n
x
x
s
Proportion
N
X
p
=
n
x
p
=
ˆ
Sampling Distribution of the Mean
–
The sampling distribution of the mean is the distribution of all possible sample
means if all possible samples of a certain size are selected from the population.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 patrickchu
 Normal Distribution, Standard Deviation, Variance, Probability theory

Click to edit the document details