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Outline for ECON 2370 at UH


Outline for ECON 2370 at UH

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This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 20 views.

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Date Created: 02/06/15
Notes Econ 2370 Statistics and Probability 1 Moment Statistics Advantages Mathematically interrelated and related to other moments All have the same assumptions They provide the only i neasures of skewness and kurtosis They provide suf cient information to reconstruct a frequency distribution function Assumption Interval or ratio data univariate system General Moment Equation 1 N Wk i1 1 any variable having its origin at some point x x real or arbitrary origin operationally defined m the k moment about x Moments about the origin x O X raw score First Moment Ml Mean 2 X N 1 1 M1 w 2x g 2f7 caq gtlt X i1 i1 Second Moment Mg Mg 172 i7 ZUWM i1 i1 Third Moment fl13 Mg A Z X i7 2qu X3 i1 i1 Fourth Moment flI4 2m IT 2 X3 IT 2mm gtlt X4 i1 i1 Spring 2000 1 Notes Econ 2370 Statistics and Probability Moments about the mean r X x1 Xi X raw score First Moment m1 1 m1 0 Second Moment mz Variance N 1 1 m2 1T M2 ME Standard Deviation s 1hug Third Moment m3 1 y m3 IT 7 x3 M3 311111112 2MB For a symmetrical distribution M3 0 This functionm is related to skewness but it is in uenced by the size of the unit of measure Fourth Moment m4 1 7m X Z x M4 411111113 631151112 3M i1 m4 is directly related to kurtosis but it in uenced by the size of the metric unit Spring 2000 2 Notes Econ 2370 Statistics and Probability Standardized Moments r X 21 standardized score First Moment m 1 r111jzil Second Moment 12 1 121jzf1 Third Moment 13 Skewness N 4 1 M 3M M 23b3 a3 Z 73 7 3 1 2 1 m3 7 Z 1quot MA12 M f 9 Fourth Moment a4 Kurtosis a4 30 1 4 7 AMA 411111113 6Ali217l12 317W 7 77M 4 i Zi Mg M 122 Variach N i1 Interpretation of Moment Statistics Mean M 1 15 moment about the origin central tendency measure Variance m2 2nd moment about the mean dispersion measure Skewness r13 3rd standardize moment skewness measure 13 0 gt symmetrical 13 gt 0 gt positively skewed r13 lt 0 gt negatively skewed for 13 between 2 02 the distribution can be assumed to be normal with respect to skewness Kurtosis 14 30 45 standardized moment kurtosis measure 14 3 0 gt same peakedness normal curve 14 3 gt 0 gt more peakedness than normal curve Spring 2000 3 Notes Econ 2370 Statistics and Probability a4 3 lt 0 gt flattter than normal curve for 14 3 between 2 05 the curve can be considered normal with respect to kurtosis Example of years attending University of Houston Years Studmts X F FgtltX FgtltX2 FgtltX3 FgtltX4 2 4 8 16 32 64 3 3 9 27 81 243 4 7 28 112 448 1792 5 1 5 25 125 6 1 6 36 216 1296 N21 2X 61 Ml 290476 ml 000000 01 000000 2X2 221 M2 1052381 m2 208617 02 100000 2X3 907 M3 4319048 W 050167 03 016649 2X4 4025 M4 1916666 7m 902988 14 207483 Mean M 1 290476 Variance m2 208617 Standard Deviation 14443572 Skewness r13 016649 gt assumed normal Kurtosis a4 4192517 gt flatter than a normal distribution curve Spring 2000 4 Notes Econ 2370 Statistics and Probability 2 Single Sample Tests 21 Single sample test of the mean Where a is known Make Assumption Level of measurement interval Model random sampling population nornally distributed a some known value HO p some number Obtain a Sampling Distribution Z distribution M some number 0 a Choose a Signi cance Level and Critical Region X 005 001 or 0001 One or two tail test H1 p 7 some number Compute a Test Statistics Make a decision Formula for computing the con dence interval Zgax 3 p 3 X Z0X 1 x Spring 2000 O1


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