normal quantile plotsapstatsmonkey.com/statsmonkey/readbestpractice_files/... · 2012. 4. 14. ·...

Pick a Pack of Pennies: A Fathom Sampling Distribution Project

Dr. Laura SchultzRowan University

Penny_Population

Age

10.5743

9.41958

686

S1 = ( )mean

S2 = ( )popStdDev

S3 = ( )count

Penny_Population

Measures from Sample of Penny_Population




Column Summary

MeanAge

5

50

SampleSize

10.4922

1000

4.12582

10.542

1000

1.28914

10.5171

2000

3.0566

S1 = ( )mean

S2 = ( )count

S3 = ( )popStdDev

Measures from Sample of Penny_Population (Proportions)

RowSummary

Proportion_oneYr

S1 = ( )mean

S2 = ( )popStdDev

S3 = ( )count

20

40

60

80

100

120

0 10 20 30 40 50 60

Age

Penny_Population Histogram

-4

-3

-2

-1

0

1

2

3

4

0 10 20 30 40 50 60

Age

Normal Quantile = -1.1 + 0.106Age

Penny_Population Normal Quantile Plot

Sample of Penny_Population Measures from Sample of Penny_PopulationPenny_Population

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0 10 20 30 40 50 60

Age


Penny_Population





Column Summary

MeanAge

5

50

SampleSize

10.4922

1000

4.12582

10.542

1000

1.28914

10.5171

2000

3.0566

S1 = ( )mean

S2 = ( )count

S3 = ( )popStdDev


RowSummary

Proportion_oneYr

S1 = ( )mean

S2 = ( )popStdDev

S3 = ( )count

20

40

60

80

100

120

0 10 20 30 40 50 60

Age


-4

-3

-2

-1

0

1

2

3

4

0 10 20 30 40 50 60

Age




Penny_Population





Column Summary

MeanAge

5

50

SampleSize

10.4922

1000

4.12582

10.542

1000

1.28914

10.5171

2000

3.0566

S1 = ( )mean

S2 = ( )count

S3 = ( )popStdDev


RowSummary

Proportion_oneYr

S1 = ( )mean

S2 = ( )popStdDev

S3 = ( )count

20

40

60

80

100

120

0 10 20 30 40 50 60

Age


-4

-3

-2

-1

0

1

2

3

4

0 10 20 30 40 50 60

Age




Penny_Population





Column Summary

MeanAge

5

50

SampleSize

10.4922

1000

4.12582

10.542

1000

1.28914

10.5171

2000

3.0566

S1 = ( )mean

S2 = ( )count

S3 = ( )popStdDev


RowSummary

Proportion_oneYr

S1 = ( )mean

S2 = ( )popStdDev

S3 = ( )count

20

40

60

80

100

120

0 10 20 30 40 50 60

Age


-4

-3

-2

-1

0

1

2

3

4

0 10 20 30 40 50 60

Age




0.04

0.08

0.12

0.16

0.20

MeanAge

0 5 10 15 20 25 30 35

Measures from Sample of Penny_Population Histogram





RowSummary

Proportion_oneYr

S1 = ( )mean

S2 = ( )popStdDev

S3 = ( )count

20

40

60

80

100

120

0 10 20 30 40 50 60

Age


Sample of Penny_PopulationPenny_Population


Penny_Population

Repeat for n = 50Sampling Distributions of the Sample Mean

for n = 5 and n = 50

0.00

0.05

0.10

0.15

0.20

0.25

0.30

5

0.05

0.10

0.15

0.20

0.25

0.30

50

0 5 10 15 20 25 30 35

MeanAge

Density of MeanAge = x ( )mean ( )popStdDev, ,( )normalDensity

Measures from Sample of Penny_Population Histogram

Normal Quantile Plots

-4

-2

0

2

4

5

-4

-2

0

2

4

50

0 5 10 15 20 25 30 35

MeanAge

Normal Quantile (5) = -2.54 + 0.242MeanAge

Normal Quantile (50) = -8.2 + 0.775MeanAge

Measures from Sample of Penny_Population Normal Quantile Plot

Confirming the Central Limit TheoremPenny_Population

Age

10.5743

9.41958

S1 = ( )mean

S2 = ( )popStdDev


Column Summary

MeanAge

5

50

SampleSize

10.4922

1000

4.12582

10.542

1000

1.28914

10.5171

2000

3.0566

S1 = ( )mean

S2 = ( )count

S3 = ( )popStdDev

!x̄ =9.41958!

5= 4.2 years

!x̄ =9.41958!

50= 1.3 years

µx̄ = µ

!x̄ =!!n

Sampling Distributions of the Sample Proportion

0

10

20

30

40

10

0

10

20

30

40

100

10

20

30

40

200

0.0 0.1 0.2 0.3 0.4

Proportion_oneYr

Measures from Sample of Penny_Population (Proporti…Histogram

µp̂ = p

!p̂ =!

pq

n

Penny_Population

Age

0.122449

S1 = Age 1=( )proportion


RowSummary

SampleSizeSampleSize

100 200

SampleSize

10

Proportion_oneYr

0.1216

0.103216

1000

0.12132

0.031104

1000

0.12365

0.0230126

1000

0.12219

0.0636493

3000

S1 = ( )mean

S2 = ( )popStdDev

S3 = ( )count

Files Available to Download

Penny_Project08.ftm (Fathom data file)

Penny_Project.pdf (Student handout)

Penny_Slides.pdf (Slide handout for this presentation)

Copyright © 2008 by Laura Schultz

http://users.rowan.edu/~schultzl/AP2008.html

normal quantile plotsapstatsmonkey.com/statsmonkey/readbestpractice_files/... · 2012. 4. 14. ·...

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