1-1
Chapter Seven
Sampling Methods and
Sampling Distributions
GOALS
When you have completed this chapter, you will be able to:
ONE
Explain why a sample is the only feasible way to learn about a population.
TWO
Explain methods for selecting a sample.
THREE
Define and construct a sampling distribution of the sample means.
FOUR
Explain the central limit theorem.
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2000
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1-1
Chapter Seven
Sampling Methods and
Sampling Distributions
GOALS
When you have completed this chapter, you will be able to:
FIVE
Calculate confidence intervals for means and proportions.
SIX
Determine the sample size for attribute and variable sampling.
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2000
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7-3
Why Sample the Population?
• The physical impossibility of checking all
items in the population.
• The cost of studying all the items in a
population.
• The sample results are usually adequate.
• Contacting the whole population would
often be time-consuming.
• The destructive nature of certain tests.
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Probability Sampling
• A probability sample is a sample selected
in such a way that each item or person in
the population being studied has a known
likelihood of being included in the sample.
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Methods of Probability Sampling
• Simple Random Sample: A sample
formulated so that each item or person in
the population has the same chance of
being included.
• Systematic Random Sampling: The items
or individuals of the population are
arranged in some order. A random
starting point is selected and then every
kth member of the population is selected
for the sample.
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Methods of Probability Sampling
• Stratified Random Sampling: A
population is first divided into subgroups,
called strata, and a sample is selected
from each stratum.
• Cluster Sampling: A population is first
divided into subgroups (strata), and a
sample of the strata is selected. The
sample is then taken from these selected
strata.
• A sampling error is the difference
between a sample statistic and its
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Sampling Distribution of the Sample Means
• The sampling distribution of the sample
means is a probability distribution
consisting of all possible sample means
of a given sample size selected from a
population, and the probability of
occurrence associated with each sample
mean.
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EXAMPLE 1
• The law firm of Hoya and Associates has five
partners. At their weekly partners meeting each
reported the number of hours they charged
clients for their services last week.
Partner
Hours
Dunn
22
Hardy
26
Kiers
30
Malinowski
26
Tillman
22
• If two partners are selected randomly, how many
different samples are possible?
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EXAMPLE 1
continued
• This is the combination of 5 objects taken
2 at a time. That
5 Cis,
2  (5!) /[( 2!)(3!)]  10
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Partners
Total
Mean
1,2
48
24
1,3
52
26
1,4
48
24
1,5
44
22
2,3
56
28
2,4
52
26
2,5
48
24
3,4
56
28
3,5
52
26
4,5
48
24
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EXAMPLE 1
continued
• Organize the sample means into a
sampling distribution.
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Sample
Mean
Frequency
22
1
Relative
Frequency
probability
1/10
24
4
4/10
26
3
3/10
28
2
2/10
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EXAMPLE 1
continued
• Compute the mean of the sample means
and compare it with the population mean:
· The mean of the sample means =
[(22)(1) + (24)(4) + (26)(3) +
(28)(2)]/10=25.2
· The population mean =
(22+26+30+26+22)/5 = 25.2
· Observe that the mean of the sample
means is equal to the population mean.
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Central Limit Theorem
• If samples of a particular size are selected
from any population, the sampling
distribution of the sample means is
approximately a normal distribution.
• This approximation improves with larger
samples.
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