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Chapter 1 Introduction
1.1 A model for problem solving
Definition:
Statistics
is the science of (or a collection of techniques for)
Collecting
(sampling, census)
Classifying
(descriptive statistics)
Analyzing
(e.g., regression analysis)
Generalizing
(statistical inference)
A set of data for a special purpose
Each of these activities is based on
probability
.
These activities are carried out to solve some problems observed by the decisionmakers. The
following are important steps in the decision making process:
1.
Specify your goal(s) by clearly stating the problem or question.
2.
Collect and analyze data.
3.
Interpret the findings of your analyses and make a decision.
4.
Implement the decision and verify that it is the right approach to solving the problem
stated in step 1.
5.
Plan the next action.
When we have census data relevant to the problem at hand, the decisionmaking process is
relatively easy. However, in many real life problems we do not have (recent) census data. In
such a case we will collect data from a random sample of population units. Then we make our
decision about one or more characteristic of the population, based on the information in the
sample data. This process is called
statistical inference
and that is the main subject of this
course (Chapters 8 to 12). The necessary tools for statistical inference are developed in the first
seven chapters of your text.
We will emphasize
making inferences about one or more population parameters
based on
data from
random samples
.
This process is a systematic approach to decision making.
Some new terms need to be defined:
•
Population:
a set of welldefined units (objects or outcomes) about which information is
sought.
•
Sample:
A subset of the population, containing objects or outcomes that are actually
observed.
•
Random sample:
A sample selected according to some rules of probability
o
Simple Random Sample (SRS):
A sample of size n, selected in such a way that
every sample of size n (from the population of size N) has an equal chance of being
the selected sample.
As a result of this property
every element in the population
has an equal chance (n/N) of being in the random sample.
STA3032 Chapter 1, Page 1 of 10
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o
SRS Selected with replacement:
Some population units may appear more than
once. This is used in theoretical studies.
o
SRS selected without replacement:
Any population unit may appear in the sample
at most once. This method is used in real life problems.
o
Although the two selection methods are different, the difference becomes negligible
when the population size (N) is extremely large, relative to the sample size (n).
o
In this course whenever we talk about a sample we mean a
SRS selected with
replacement.
o
A SRS selected with replacement gives independent observations,
i.e., knowing
the value of any one element in the sample does not help in predicting the value of
the of he elements.
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 Summer '08
 Kyung
 Statistics, Standard Deviation

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