Transcript Sampling

Math 145
January 29, 2008
Outline
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3.
Recap
Sampling Designs
Graphical methods
Statistics
is the science of collecting, analyzing,
interpreting, and presenting data.
Two kinds of Statistics:
1.
2.
Descriptive Statistics.
Inferential Statistics.
A statistical inference is an estimate, prediction,
or some other generalization about a population
based on information contained in the sample.
 representative sample
Methods of Acquiring Information
1.
2.
3.
Census
Sampling
Experimentation
Sampling Designs
Simple Random Sampling.
 Systematic Random Sampling.
 Cluster Sampling.
 Stratified Random Sampling with
Proportional Allocation.
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Simple Random Sampling
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A sampling procedure for which each
possible sample of a given size has the
same chance of being selected.
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Population of 5 objects: {A, B, C, D, E}
Take a sample of size 2.
Possible samples: {(A,B), (A,C), (A,D), (A,E),
(B,C), (B,D), (B,E), (C,D), (C,E), (D,E)}
Random number generators
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Systematic Random Sampling
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Step 1. Divide the population size by the sample
size and round the result down to the nearest
number, m.
Step 2. Use a random-number generator to
obtain a number k, between 1 and m.
Step 3. Select for the sample those numbers of
the population that are numbered k, k+m,
k+2m, …
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Expected number of customers = 1000
Sample size of 30  m = 1000/30 = 33.33  33
Suppose k = 5. Then select {5, 5+33, 5+66, …}
Cluster Sampling
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Step 1. Divide the population into groups
(clusters).
Step 2. Obtain a simple random sample of
clusters.
Step 3. Use all the members of the clusters in
step 2 as the sample.
Stratified Random Sampling
with Proportional Allocation
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Step 1. Divide the population into
subpopulations (strata).
Step 2. From each stratum, obtain a simple
random sample of size proportional to the size
of the stratum.
Step 3. Use all the members obtained in Step 2
as the sample.
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Population of 9,000 with 60% females and 40% males
Sample of size 80.
 48 females (from 5,400) and 32 males (from 3,600).
Homework
1. Submit the practice worksheet
2. (pp. 19-23) #1, 2, and 10.
Thank you!