1
Introduction to Probability
and Statistics
Thirteenth Edition
Chapter 7
Sampling Distributions
Introduction
• Parameters are numerical descriptive measures
for populations.
– For the normal distribution, the location and
shape are described by
m
and
s
.
– For a binomial distribution consisting of
n
trials, the location and shape are determined
by
p
.
• Often the values of parameters that specify the
exact form of a distribution are unknown.
• You must rely on the
sample
to learn about these
parameters.
Sampling
Examples:
• A pollster is sure that the responses to his
“agree/disagree” question will follow a binomial
distribution, but
p
, the proportion of those who
“agree” in the population, is unknown.
• An agronomist believes that the yield per acre of
a variety of wheat is approximately normally
distributed, but the mean
m
and the standard
deviation
s
of the yields are unknown.
If you want the sample to provide reliable
information about the population, you must
select your sample in a certain way!
Simple Random Sampling
• The
sampling plan
or
experimental
design
determines the amount of
information you can extract, and
often allows you to measure the
reliability of your inference
.
•
Simple random sampling
is a
method of sampling that allows each
possible sample of size
n
an equal
probability of being selected.
Example
•There are 89 students in a
statistics class. The instructor
wants to choose 5 students to form
a project group. How should he
proceed?
1.
Give each student a number from
01 to 89.
2.
Choose 5 pairs of random digits
from the random number table.
3.
If a number between 90 and 00 is
chosen, choose another number.
4.
The five students with those
numbers form the group.
Types of Samples
• Sampling can occur in two types of
practical situations:
1. Observational studies:
The data existed before
you decided to study it. Watch out for
Nonresponse:
Are the responses biased
because only opinionated people
responded?
Undercoverage:
Are certain segments of the
population systematically excluded?
Wording bias:
The question may be too
complicated or poorly worded.
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Types of Samples
• Sampling can occur in two types of
practical situations:
2. Experimentation:
The data are generated by
imposing an experimental condition or treatment
on the experimental units.
Hypothetical populations
can make
random sampling difficult if not impossible.
Samples must sometimes be chosen so that
the experimenter believes they are
representative
of the whole population.
Samples must
behave like random
samples!
Other Sampling Plans
• There are several other sampling plans
that still involve
randomization
:
1. Stratified random sample:
Divide the
population into subpopulations or
strata
and
select a simple random sample from each strata.
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 Fall '08
 Any
 Statistics, Normal Distribution, Probability, Standard Deviation, Probability theory, Cumulative distribution function

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