Post on 30-May-2018
8/14/2019 Probability in Sampling
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Probability in SamplingProbability in Sampling
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Key ConceptsKey Concepts
Statistical terms in samplingStatistical terms in sampling
Sampling errorSampling error
The sampling distributionThe sampling distribution
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Statistical Terms in SamplingStatistical Terms in Sampling
VariableVariable
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11 22 33 44 55
Statistical Terms in SamplingStatistical Terms in Sampling
VariableVariable
Self-esteemSelf-esteem
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11 22 33 44 55
Statistical Terms in SamplingStatistical Terms in Sampling
VariableVariable
StatisticStatistic
Self-esteemSelf-esteem
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11 22 33 44 55
Statistical Terms in SamplingStatistical Terms in Sampling
VariableVariable
StatisticStatistic
Self-esteemSelf-esteem
Average = 3.72Average = 3.72SampleSample
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11 22 33 44 55
Statistical Terms in SamplingStatistical Terms in Sampling
VariableVariable
StatisticStatistic
ParameterParameter
Self-esteemSelf-esteem
Average = 3.72Average = 3.72SampleSample
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11 22 33 44 55
Statistical Terms in SamplingStatistical Terms in Sampling
VariableVariable
StatisticStatistic
ParameterParameter
Self-esteemSelf-esteem
Average = 3.72Average = 3.72
Average = 3.75Average = 3.75
SampleSample
PopulationPopulation
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Sampling ErrorSampling Error
4.54.03.53.0
150
100
50
0
Self-esteemSelf-esteem
Frequency
Frequenc
y
The population hasThe population hasa mean of 3.75.a mean of 3.75.
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Sampling ErrorSampling Error
4.54.03.53.0
150
100
50
0
Self-esteemSelf-esteem
Frequency
Frequenc
y
The population hasThe population hasa mean of 3.75...a mean of 3.75...
...and a...and a
standardstandarderror of .25.error of .25.
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Sampling ErrorSampling Error
4.54.03.53.0
150
100
50
0
Self-esteemSelf-esteem
FF
Frequenc
y
Frequenc
y
The population hasThe population hasa mean of 3.75...a mean of 3.75...
...and a...and a
standardstandarderror of .25.error of .25.
ThisThis means that...means that...
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Sampling ErrorSampling Error
4.54.03.53.0
150
100
50
0
Self-esteemSelf-esteem
Frequenc
y
Frequenc
y
The population hasThe population hasa mean of 3.75...a mean of 3.75...
...and a...and a
standardstandarderror of .25.error of .25.
This means that...This means that...
about 64% of cases fall between 3.5 - 4.0.about 64% of cases fall between 3.5 - 4.0.
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Sampling ErrorSampling Error
4.54.03.53.0
150
100
50
0
Self-esteemSelf-esteem
Frequenc
y
Frequenc
y
The population hasThe population hasa mean of 3.75...a mean of 3.75...
...and a...and a
standardstandarderror of .25.error of .25.
This means...This means...
About 64% of cases fall between 3.5 - 4.0.About 64% of cases fall between 3.5 - 4.0.
About 95% of cases fall between 3.25 - 4.25.About 95% of cases fall between 3.25 - 4.25.
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Sampling ErrorSampling Error
4.54.03.53.0
150
100
50
0
Self esteemSelf esteem
Frequenc
y
Frequenc
y
The population hasThe population hasa mean of 3.75...a mean of 3.75...
...and a...and a
standardstandarderror of .25.error of .25.
This meansThis means
About 64% of cases fall between 3.5 - 4.0.About 64% of cases fall between 3.5 - 4.0.
About 95% of cases fall between 3.25 - 4.25.About 95% of cases fall between 3.25 - 4.25.
about 99% of cases fall between 3.0 - 4.5about 99% of cases fall between 3.0 - 4.5
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Sampling ErrorSampling Error
The standard error is called theThe standard error is called the sampling error.sampling error.
4.54.03.53.0
150
100
50
0
The sample of 1000The sample of 1000has a mean of 3.74has a mean of 3.74
and a standard errorand a standard error
of .0074.of .0074.
Self-esteemSelf-esteem
Frequen
cy
Frequen
cy
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Sampling ErrorSampling Error
The sampling error shows that the odds are .95 thatThe sampling error shows that the odds are .95 that
the population mean is 3.74the population mean is 3.74++
2(.0074).2(.0074).
4.54.03.53.0
150
100
50
0
Self-esteemSelf-esteem
Frequenc
y
Frequenc
y
The sample of 1000The sample of 1000has a mean of 3.74has a mean of 3.74
and a standard errorand a standard error
of .0074.of .0074.
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Sampling ErrorSampling Error
4.54.03.53.0
150
100
50
0
Self-esteemSelf-esteem
Frequenc
y
Frequenc
y
The sampling error shows that the odds are .95 thatThe sampling error shows that the odds are .95 that
the population mean is 3.74the population mean is 3.74++
2(.0074).2(.0074).
The sample of 1000The sample of 1000has a mean of 3.74has a mean of 3.74
and a standard errorand a standard error
of .0074.of .0074.
Confidence levelConfidence level
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Sampling ErrorSampling Error
4.54.03.53.0
150
100
50
0
Self-esteemSelf-esteem
Frequenc
y
Frequenc
y
The sampling error shows that the odds are .95 thatThe sampling error shows that the odds are .95 that
the population mean is 3.74the population mean is 3.74++
2(.0074).2(.0074).
The sample of 1000The sample of 1000has a mean of 3.74has a mean of 3.74
and a standard errorand a standard error
of .0074.of .0074.
Confidence intervalConfidence interval
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The Sampling DistributionThe Sampling Distribution
SampleSample SampleSample SampleSample
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The Sampling DistributionThe Sampling Distribution
SampleSample
4.44.24.03.83.63.43.23.0
5
0
5
0
SampleSample
4.44.24.03.83.63.43.23.0
5
0
5
0
SampleSample
4.44.24.03.83.63.43.23.0
5
0
5
0
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The Sampling DistributionThe Sampling Distribution
SampleSample
4.44.24.03.83.63.43.23.0
5
0
5
0
SampleSample
4.44.24.03.83.63.43.23.0
5
0
5
0
SampleSample
4.44.24.03.83.63.43.23.0
5
0
5
0
AverageAverage AverageAverage AverageAverage
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The Sampling DistributionThe Sampling Distribution
AverageAverage AverageAverage AverageAverage
4 44 24 03 83 63 43 23 0
15
10
5
0
The sampling
distribution...
...is the distribution
of a statistic across
an infinite number
of samples.
SampleSample
4.44.24.03.83.63.43.23.0
5
0
5
0
SampleSample
4.44.24.03.83.63.43.23.0
5
0
5
0
SampleSample
4.44.24.03.83.63.43.23.0
5
0
5
0