Chapter 8 – Sampling Distributions
Defn
:
Sampling error
is the error resulting from using a sample to infer a population
characteristic.
Example
:
We want to estimate the mean amount of Pepsi-Cola in 12-oz. cans coming off an
assembly line by choosing a random sample of 16 cans, and using the sample mean as an
estimate of the mean for the population of cans.
Suppose that we choose 100 random samples of
size 16 and compute the sample mean for each of these samples.
These 100 values of
X
will
differ from each other somewhat due to sampling error, but the values should all be close to 12-
oz.
Defn
:
For a random variable X, and a given sample size n, the distribution of the variable
X
,
i.e., of all possible values of
X
, is called the sampling distribution of the mean
.
This
probability distribution is a set of pairs of numbers.
In each pair, the first number is a possible
value of the sample mean, and the second number is the probability of obtaining that value of the
mean occur when we select a random sample from the population.
Properties of the Sampling Distribution of the Mean:
1)
For samples of size n, the expectation (mean) of
X
, equals the expectation (mean) of X.
In
other words,
X
X
μ
μ
=
.
2)
The possible values of
X
cluster closer around the population mean for larger samples than
for smaller samples.
In other words, the larger the sample size, the smaller the sampling error.

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