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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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Statistical Terms in SamplingStatistical Terms in Sampling

VariableVariable

Self-esteemSelf-esteem

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Statistical Terms in SamplingStatistical Terms in Sampling

VariableVariable

StatisticStatistic

Self-esteemSelf-esteem

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Statistical Terms in SamplingStatistical Terms in Sampling

VariableVariable

StatisticStatistic

Self-esteemSelf-esteem

Average = 3.72Average = 3.72SampleSample

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Statistical Terms in SamplingStatistical Terms in Sampling

VariableVariable

StatisticStatistic

ParameterParameter

Self-esteemSelf-esteem

Average = 3.72Average = 3.72SampleSample

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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).

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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