UCR SOC 005 STAT SPR 2010 Session 17 V2

UCR SOC 005 STAT SPR 2010 Session 17 V2 - SOCIOLOGY005...

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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Session 17 Wednesday, 5 May 2010 David Swanson Watkins 1223 [email protected] SOCIOLOGY 005  STATISTICAL ANALYSIS
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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Today’s Schedule   Drawing inferences from samples, Part  2
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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Normal Curve Formula P(X) =     {1/((2 Πσ 2 ) (.5) )} {e (-(X-μ) 2 /(2 σ 2 )) } (1) You only need to know the mean ( μ)  and the standard  deviation ( ) σ  of a set of numbers  to create the curve (2)  in inferential statistics, one substitutes the sample mean     ( )  for the population mean ( μ)  and the sample’s        standard error (se) for the population       standard deviation ( ) σ
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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science A Normal Curve
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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Another Normal Curve                                       
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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Both of the preceding Normal  Curves were generated from P(X) =     {1/((2 Πσ 2 ) (.5) )} {e (-(X-μ) 2 /(2 σ 2 )) } Using the mean ( μ)  and the standard deviation ( ) σ and in inferential statistics, recall that one substitutes the  sample mean ( )  for the population mean ( μ)  and the  sample’s standard error (se) for the population standard  deviation ( σ to generate a  “SAMPLING DISTRIBUTION”
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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Working with the Normal Distribution               CENTRAL LIMIT THEOREM* If x 1 , x 2 , …., x n  constitute a random sample from an infinite  population having mean μ , variance  σ 2  and the moment  generating function M x (t) then the limiting distribution of             Z = ( f8e5 X   – μ)/( σ /√n).  As n      ∞  is the standard normal distribution *Freund, J. and R. Walpole. 1987. Mathematical Statistics 4 th   Edition. Englewood Cliffs, NJ: Prentice Hall (pp. 274-277)
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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Working with the Normal Distribution Suppose that all possible samples of size n are drawn (with 
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UCR SOC 005 STAT SPR 2010 Session 17 V2 - SOCIOLOGY005...

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