School

University of Northern Colorado **We aren't endorsed by this school

Course

MBA 605

Subject

Statistics

Date

Aug 28, 2023

Pages

10

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Chapter 6
In order to know about some characteristic of a population with
certainty, we must collect data from every element in the population of
interest; such an effort is referred to as a
census
.
However, there are
many potential difficulties associated with taking a census:
A census may be expensive; if resources are limited, it may not be
feasible to take a census.
A census may be time consuming; if the data need be collected
quickly, a census may not be suitable.
A census may be misleading; if the population is changing quickly,
by the time a census is completed the data may be obsolete.
A census may be unnecessary; if perfect information about the
characteristic(s) of the population of interest is not required, a
census may be excessive.
A census may be impractical; if observations are destructive,
taking a census would destroy the population of interest.
the objective of sampling is to gather data from a subset of the
population that is as similar as possible to the entire population, so that
what we learn from the sample data accurately reflects what we want to
understand about the entire population.
When we use the sample data
we have collected to make estimates of or draw conclusions about one or
more characteristics of a population (the value of one or more
parameters), we are using the process of
statistical inference
.
statistical inference
The process of making estimates and drawing conclusions
about one or more characteristics of a population (the value of one or more
parameters) through the analysis of sample data drawn from the population.
It is important to realize that sample results provide only
estimates
of the
values of the corresponding population characteristics
Some error, or deviation of the sample from the population, is to be
expected.
With proper sampling methods, the sample results will
provide "good" estimates of the population parameters
The
sampled population
is the population from which the sample is
drawn
, and a
frame
is a list of the elements from which the sample will
be selected
random sampling can be used to select a sample from a finite population
and we describe how a random sample can be taken from an infinite
population that is generated by an ongoing process
.

6.1
Selecting a Sample
A measurable factor that defines a characteristic of a population,
process, or system is called a
parameter
.
working with a sample would be preferable to working with the entire
population
Sampling from a Finite
Population
Statisticians recommend selecting a probability sample when sampling
from a finite population because a probability sample allows you to
make valid statistical inferences about the population.
The simplest type
of probability sample is one in which each sample of size
n
has the same
probability of being selected. It is called a simple random sample.
A
simple random sample
of size
n
from a finite population of size
N
is a
sample selected such that each possible sample of size
n
has the same
probability of being selected.
Procedures used to select a simple random sample from a finite
population are based on the use of random numbers
.
We can use Excel's
RAND function to generate a random number between 0 and 1 by
entering the formula =
RAND()
into any cell in a worksheet.
The number
generated is called a random number because the mathematical
procedure used by the RAND
function guarantees that every number
between 0 and 1 has the same probability of being selected
Sampling from an Infinite
Population
Sometimes we want to select a sample from a population, but the
population is infinitely large or the elements of the population are being
generated by an ongoing process for which there is no limit on the
number of elements that can be generated.
Thus, it is not possible to
develop a list of all the elements in the population.
This is considered the

infinite population case.
With an infinite population, we cannot select a
simple random sample because we cannot construct a frame consisting
of all the elements.
In the infinite population case, statisticians
recommend selecting what is called a random sample.
A
random sample
of size
n
from an infinite population is a sample selected such
that the following conditions are satisfied.
1.
Each element selected comes from the same population.
2.
Each element is selected independently.
Each case may require a different selection procedure. Let us consider
two examples to see what we mean by the conditions:
(1)Each element selected comes from the same population, and
(2)each element is selected independently.
A common quality-control application involves a production process for
which there is no limit on the number of elements that can be produced.
The conceptual population from which we are sampling is all the
elements that could be produced (not just the ones that are produced)
by the ongoing production process.
Because we cannot develop a list of
all the elements that could be produced, the population is considered
infinite.
Situations involving sampling from an infinite population are usually
associated with a process that operates over time
.
6.2
Point Estimation
To estimate the value of a population parameter, we compute a
corresponding characteristic of the sample, referred to as
a
sample statistic
.

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