# Statistical Inference and Sampling - PowerPoint PPT Presentation

PPT – Statistical Inference and Sampling PowerPoint presentation | free to download - id: 7911b0-ZDFhY

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

## Statistical Inference and Sampling

Description:

### Statistical Inference and Sampling Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing – PowerPoint PPT presentation

Number of Views:90
Avg rating:3.0/5.0
Slides: 28
Category:
Tags:
Transcript and Presenter's Notes

Title: Statistical Inference and Sampling

1
Statistical Inference and Sampling
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
2
Simple Random Sampling
• All items in the population have the same
probability of being selected.
• Finite Population To be sure that a simple
random sample is obtained from a finite
population the items should be numbered from 1 to
N.
• Nearly all statistical procedures require that a
random sample is obtained.

Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
3
Estimation
• The population consists of every item of
interest.
• The sample is randomly drawn from the population.
• Sample values should be selected randomly, one at
a time, from the population.

Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
4
Random Sampling and Estimation
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 7.1
5
Distribution of X
• The mean of the probability distribution for X
• Standard error of X standard deviation of the
probability distribution for X

m
x
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
6
Distribution of X
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 7.6
7
Distribution of X
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
8
Probabilities in the Sampling Distribution of X
Figure 7.8
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
9
Central Limit Theorem
• When obtaining large samples from any
population, the sample mean X will follow an
approximate normal distribution.
• What this means is that if you randomly sample
a large population the X distribution will be
approximately normal with a mean m and a standard
deviation (standard error) of

s
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
s

x
n
10
Central Limit Theorem
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 7.10
11
Central Limit Theorem
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 7.11
12
Central Limit Theorem
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 7.12
13
Confidence for the Mean of a Normal Population (?
known)
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 7.16
14
Confidence for the Mean of a Normal Population (?
known)
P(-1.96 ? Z ? 1.96)
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
15
Confidence for the Mean of a Normal Population (?
known)
(1-?) 100 Confidence Interval
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
16
Confidence for the Mean of a Normal Population (?
unknown)
• Students t Distribution
• Population variance unknown
• Degrees of freedom n - 1

Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
17
Students t Distribution
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
18
Confidence for the Mean of a Normal Population (?
unknown)
X

m
t
s
/
n
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
19
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
20
Selecting Necessary Sample Size Known ?
• Sample size based on the level of accuracy
required for the application.
• Maximum error E
• Used to determine the necessary sample size to
provide the specified level of accuracy
• Equation

Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
21
Selecting Necessary Sample Size Known ?
æ
ö
?
E

Z
ç

a
/
2
n
è
ø
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
22
Selecting Necessary Sample Size Unknown ?
2
Z

s
é
ù
a
/
2
n

ê
ú
E
ë
û
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
23
Other Sampling Procedures
• Population the collection of all items about
which we are interested.
• Sampling Unit a collection of elements selected
from the population.
• Cluster a sampling unit that is a group of
elements from the population, such as all adults
in a particular city block .
• Sampling frame a list of population elements

Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
24
Other Sampling Procedures
• Strata are nonoverlapping subpopulations.
• Sampling design specifies the manner in which
the sampling units are to be selected.

Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
25
Systematic Sampling
• The sampling frame consists of N records. The
sample of n is obtained by sampling every kth
record, where k is an integer approximately equal
N/n.
• The sampling frame should be ordered randomly.

Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
26
Stratified Sampling
to the homogenous nature of each strata.
• Stratified sampling obtains a cross section fo
the entire population.
• Obtain a mean within each strata as well as an
estimate of ?.

Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
27
Cluster Sampling
• Single-stage cluster sampling randomly select a
set of clusters for sampling. Include all
elements in the cluster in your sample.
• Two-stage cluster sampling randomly select a set
of clusters for sampling. Randomly select
elements from each sampled cluster