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Statistical Inference and Sampling

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

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Title: Statistical Inference and Sampling


1
Statistical Inference and Sampling
Introduction to Business Statistics, 5e
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.

Introduction to Business Statistics, 5e
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.

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
4
Random Sampling and Estimation
Introduction to Business Statistics, 5e
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
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
6
Distribution of X
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 7.6
7
Distribution of X
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
8
Probabilities in the Sampling Distribution of X
Figure 7.8
Introduction to Business Statistics, 5e
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
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
s

x
n
10
Central Limit Theorem
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 7.10
11
Central Limit Theorem
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 7.11
12
Central Limit Theorem
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 7.12
13
Confidence for the Mean of a Normal Population (?
known)
Introduction to Business Statistics, 5e
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)
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
15
Confidence for the Mean of a Normal Population (?
known)
(1-?) 100 Confidence Interval
Introduction to Business Statistics, 5e
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

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
17
Students t Distribution
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
18
Confidence for the Mean of a Normal Population (?
unknown)
X

m
t
s
/
n
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
19
Introduction to Business Statistics, 5e
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
  • Specified in advance
  • Equation

Introduction to Business Statistics, 5e
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
Introduction to Business Statistics, 5e
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
Introduction to Business Statistics, 5e
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

Introduction to Business Statistics, 5e
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.

Introduction to Business Statistics, 5e
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.

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
26
Stratified Sampling
  • Stratified sampling obtains more information due
    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 ?.

Introduction to Business Statistics, 5e
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

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
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