# Research Question Is the average body temperature of healthy adults 98.6 F? Introduction to Hypothesis Testing. Statistical Hypothesis

Size: px
Start display at page:

Download "Research Question Is the average body temperature of healthy adults 98.6 F? Introduction to Hypothesis Testing. Statistical Hypothesis"

## Transcription

1 Inroducion o Hypohesis Tesing Research Quesion Is he average body emperaure of healhy aduls 98.6 F? HT - 1 HT - 2 Scienific Mehod 1. Sae research hypoheses or quesions. µ = 98.6? 2. Gaher daa or evidence (observaional or experimenal) o answer he quesion. x = Summarize daa and es he hypohesis. 4. Draw a conclusion. HT - 3 Saisical Hypohesis Null hypohesis (H ): Hypohesis of no difference or no relaion, ofen has =,, or noaion when esing value of parameers. Example: H : µ = 98.6 F or H : Average body emperaure is 98.6 HT - 4 Saisical Hypohesis Alernaive hypohesis (H A ): [or H 1 or H a ] Usually corresponds o research hypohesis and opposie o null hypohesis, ofen has >, < or noaion in esing mean. Example: H A : µ 98.6 F or H A : Average body emperaure is no 98.6 F HT - 5 Hypoheses Saemens Example A researcher is ineresed in finding ou wheher average hourly salary for baby siing is differen from \$6.. H : µ = 6 H A : µ 6 [Two-ailed es] HT - 6 Hypohesis Tesing - 1

2 Hypoheses Saemens Example A researcher is ineresed in finding ou wheher average life ime of male is higher han 77 years. H : µ = 77 ( or µ 77 ) H A : µ > 77 [Righ-ailed es] Hypoheses Saemens Example A researcher is ineresed in finding ou wheher he average regular gasoline price is less han \$1.45 in Mid-Wes region. H : µ = 1.45 ( or µ 1.45 ) H A : µ < 1.45 [Lef-ailed es] HT - 7 HT - 8 Evidence Tes Saisic (Evidence): A sample saisic used o decide wheher o rejec he null hypohesis. HT - 9 Logic Behind Hypohesis Tesing In esing saisical hypohesis, he null hypohesis is firs assumed o be rue. We collec evidence o see if he evidence is srong enough o rejec he null hypohesis and suppor he alernaive hypohesis. HT - 1 I. Hypohesis One Sample -Tes for Mean (Large sample es) Two-Sided Tes One wishes o es wheher he average body emperaure for healhy aduls is differen from 98.6 F. H o : µ = 98.6 F v.s. H A : µ 98.6 F HT - 11 HT - 12 Hypohesis Tesing - 2

3 Evidence Wha will be he key saisic (evidence) o use for esing he hypohesis abou populaion mean? Sample mean: A random sample of 36 subjecs is chosen and he sample mean is F and sample sandard deviaion is.3 F. x HT - 13 Sampling Disribuion If H : µ = 98.6 F is rue, sampling disribuion of mean will be approximaely normally disribued wih mean 98.6 and sandard.3 deviaion (or sandard error) = σ x =.5 X HT - 14 II. Tes Saisic x µ x µ z = = σ x σ n = = = This implies ha he saisic is 2.8 sandard deviaions away from he mean 98.6 under H, and is o he lef of 98.6 (or less han 98.6) X HT - 15 Level of Significance Level of significance for he es (α) A probabiliy level seleced by he researcher a he beginning of he analysis ha defines unlikely values of sample saisic if null hypohesis is rue. c.v. = criical value Toal ail area = α c.v. c.v. HT - 16 Criical value approach: Compare he es saisic wih he criical values defined by significance level α, usually α =.5. We rejec he null hypohesis, if he es saisic z < z α/2 = z.25 = 1.96, or z > z α/2 = z.25 = ( i.e., z > z α/2 ) p-value approach: Compare he probabiliy of he evidence or more exreme evidence o occur when null hypohesis is rue. If his probabiliy is less han he level of significance of he es, α, hen we rejec he null hypohesis. p-value = P( 2.8 or 2.8) =2 x P( 2.8) = 2 x.3 =.6 Rejecion Rejecion region region Lef ail area.3 α/2=.25 α/2=.25 Two-sided Tes Two-sided Tes Criical values HT - 17 HT - 18 Hypohesis Tesing - 3

4 p-value p-value The probabiliy of obaining a es saisic ha is as exreme or more exreme han acual sample saisic value given null hypohesis is rue. I is a probabiliy ha indicaes he exremeness of evidence agains H. The smaller he p-value, he sronger he evidence for supporing Ha and rejecing H. HT - 19 IV. Draw conclusion Since from eiher criical value approach z = 2.8 < z α/2 = 1.96 or p-value approach p-value =.6 < α =.5, we rejec null hypohesis. Therefore we conclude ha here is sufficien evidence o suppor he alernaive hypohesis ha he average body emperaure is differen from 98.6ºF. HT - 2 Seps in Hypohesis Tesing 1. Sae hypoheses: H and H A. 2. Choose a proper es saisic, collec daa, checking he assumpion and compue he value of he saisic. 3. Make decision rule based on level of significance(α). 4. Draw conclusion. (Rejec null hypohesis or no) When do we use his z-es for esing he mean of a populaion? Large random sample. A random sample from normally disribued populaion wih known variance. HT - 21 HT - 22 I. Hypohesis One-Sided Tes One wishes o es wheher he average body emperaure for healhy aduls is less han 98.6 F. Example wih he same daa: A random sample of 36 subjecs is chosen and he sample mean is F and sample sandard deviaion is.3 F. H o : µ = 98.6 F v.s. H A : µ < 98.6 F This is a one-sided es, lef-side es. HT - 23 HT - 24 Hypohesis Tesing - 4

5 II. Tes Saisic x µ x µ z = = σ x σ n = = = This implies ha he saisic is 2.8 sandard deviaions away from he mean 98.6 in H, and is o he lef of 98.6 (or less han 98.6) HT - 25 Criical value approach: Compare he es saisic wih he criical values defined by significance level α, usually α =.5. We rejec he null hypohesis, if he es saisic z < z α = z.5 = Lef-sided Tes Rejecion region α= Criical values HT - 26 p-value approach: Compare he probabiliy of he evidence or more exreme evidence o occur when null hypohesis is rue. If his probabiliy is less han he level of significance of he es, α, hen we rejec he null hypohesis. p-value = P(z 2.8) =.3 Lef ail area.3 Lef-sided Tes α = HT - 27 IV. Draw conclusion Since from eiher criical value approach z = 2.8 < z α = 1.64 or p-value approach p-value =.3 < α =.5, we rejec null hypohesis. Therefore we conclude ha here is sufficien evidence o suppor he alernaive hypohesis ha he average body emperaure is less han 98.6 F. HT - 28 Decision Rule Criical value approach: Deermine criical value(s) using α, rejec H agains i) H A : µ µ, if z > z α/2 ii) H A : µ > µ, if z > z α iii) H A : µ < µ, if z < z α HT - 29 Decision Rule p-value approach: Compue p-value, : µ µ, p-value = 2 P( z ) : µ > µ, p-value = P( z ) : µ < µ, p-value = P( z ) rejec H if p-value < α HT - 3 Hypohesis Tesing - 5

6 Errors in Hypohesis Tesing Possible saisical errors: Type I error: The null hypohesis is rue, bu we rejec i. Type II error: The null hypohesis is false, bu we don rejec i. α is he probabiliy of commiing Type I Error. α Can we see daa and hen make hypohesis? 1. Choose a es saisic, collec daa, checking he assumpion and compue he value of he saisic. 2. Sae hypoheses: H and H A. 3. Make decision rule based on level of significance(α). 4. Draw conclusion. (Rejec null hypohesis or no) HT - 31 HT - 32 One Sample -Tes for Mean x µ = s n HT - 33 One-sample Tes wih Unknown Variance σ 2 In pracice, populaion variance is unknown mos of he ime. The sample sandard deviaion s 2 is used insead for σ 2. If he random sample of size n is from a normal disribued populaion and if he null hypohesis is rue, he es saisic (sandardized sample mean) will have a -disribuion wih degrees of freedom n 1. x µ Tes Saisic : = s n HT - 34 I. Sae Hypohesis One-side es example: If one wish o es wheher he body emperaure is less han 98.6 or no. H : µ = 98.6 v.s. H A : µ < 98.6 (Lef-sided Tes) HT - 35 II. Tes Saisic If we have a random sample of size 16 from a normal populaion ha has a mean of F, and a sample sandard deviaion.2. The es saisic will be a -es saisic and he value will be: (sandardized score of sample mean) x µ Tes Saisic : = = = = 2.8 s.2.5 n 16 Under null hypohesis, his -saisic has a - disribuion wih degrees of freedom n 1, ha is, 15 = HT - 36 Hypohesis Tesing - 6

7 Criical Value Approach: To es he hypohesis a α level.5, he criical value is α =.5 = Rejecion Region Descion Rule: Rejec null hypohesis if < HT - 37 HT - 38 Decision Rule: Rejec null hypohesis if p-value < α. HT - 39 p-value Calculaion p-value corresponding he es saisic: For es, unless compuer program is used, p- value can only be approximaed wih a range because of he limiaion of -able. p-value = P(T< 2.8) P(T<-2.8) = <? P(T< 2.62) =.1 Since he area o he lef of 2.62 is.1, he area o he lef of 2.8 is definiely less han.1. Area o he lef of 2.62 is HT - 4 IV. Conclusion Decision Rule: If < 1.753, we rejec he null hypohesis, or if p-value <.5, we rejec he null hypohesis. Conclusion: Since = 2.8 < 1.753, or say p-value <.1 <.5, we rejec he null hypohesis. There is sufficien evidence o suppor he research hypohesis ha he average body emperaure is less han 98.6 F. Wha if we wish o es wheher he average body emperaure is differen from 98.6 F using -es wih he same daa? The p-value is equal o wice he p-value of he lef-sided es which will be less han.2. HT HT - 42 Hypohesis Tesing - 7

8 Decision Rule Criical value approach: Deermine criical value(s) using α, rejec H agains i) H A : µ µ, if > α/2 ii) H A : µ > µ, if > α Decision Rule p-value approach: Compue p-value, : µ µ, p-value = 2 P( T ) : µ > µ, p-value = P( T ) : µ < µ, p-value = P( T ) iii) H A : µ < µ, if < α rejec H if p-value < α HT - 43 HT - 44 When do we use his -es for esing he mean of a populaion? A random sample from normally disribued populaion wih unknown variance. When sample size is relaively large he -score is approximaely equal o z-score herefore -es will be almos he same as z-es. HT - 45 Remarks If he sample size is relaively large (>3) boh z and ess can be used for esing hypohesis. -es is robus agains normaliy. In fac, if he sample size is small and he sample is from a very skewed or any nonnormal disribuion, we can use nonparameric alernaives such Sign Tes or Signed-Rank Tes. Many commercial packages only provide -es since sandard deviaion of he populaion is ofen unknown. HT - 46 "Our findings confliced wih Wunderlich's in ha 36.8 degrees C (98.2 degrees F) raher han 37. degrees C (98.6 degrees F) was he mean oral emperaure of our subjecs.... Thiry-seven degrees cenigrade (98.6 degrees F) should be abandoned as a concep relevan o clinical hermomery..." Mackowiak, P. A., Wasserman, S. S., and Levine, M. M. "A Criical Appraisal of 98.6 Degrees F, he Upper Limi of he Normal Body Temperaure, and Oher Legacies of Carl Reinhold Augus Wunderlich." Journal of he American Medical Associaion. 268, 12 (23-3 Sepember 1992): Research Quesion (Revisi) Is he average choleserol level of a cerain populaion 211 mg/1ml? HT - 47 HT - 48 Hypohesis Tesing - 8

9 P( X > 225) =? X ~ N (µ = 211, s = ) x x n = 1 H : µ = 211 H A : µ > 211 Conclusion! 4.6 Criical Value: Claim: Choleserol Level has a mean 211. Evidence: x = 225 s = 46.1 x = z P-value for righ sided es! HT - 49 Saisical Significance A saisical repor shows ha he average blood pressure for women in cerain populaion is significanly differen from a recommended level, wih a p-value of.2 and he -saisic of 6.2. I generally means ha he difference beween he acual average and he recommended level is saisically significan. And, i is a wo-sided es. Is he average blood pressure significanly less han he recommended level? HT - 5 = 6.2 H A : µ µ H A : µ < µ Saisical Repor p-value for wo-sided es = p-value for lef-sided es = p-value for righ-sided es =.999 Average Weigh for Female Ten Year Children In US Info. from a random sample: n = 1, x = 8 lb, s = 18.5 lb. Is average weigh greaer han 78 lb a α =.5 level? (H A : µ > 78) Tes Saisic: 8 78 = = α =.5, d.f. = 1 1 = 9,.5, 9 = H A : µ > µ Rejec H, if =.35 < Failed o rejec H! 6.2 HT - 51 HT - 52 Average Weigh for Female Ten Year Children In US Info. from a random sample: n = 4, x = 8 lb, s = 18.5 lb. Is average weigh greaer han 78 lb a α =.5 level? (H A : µ > 78) 8 78 Tes Saisic: = = α =.5, d.f. = 4 1 = 399,.5, 399 = 1.65 Rejec H, if = 2.22 > Rejec H! HT - 53 Sampling Disribuion 18.5 S.E. = = n = 1 X S.E. = =.9 4 n = 4 X Pracical Significance? 78 8 HT - 54 Hypohesis Tesing - 9

### Measuring macroeconomic volatility Applications to export revenue data, 1970-2005

FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970-005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a

### SURVEYING THE RELATIONSHIP BETWEEN STOCK MARKET MAKER AND LIQUIDITY IN TEHRAN STOCK EXCHANGE COMPANIES

Inernaional Journal of Accouning Research Vol., No. 7, 4 SURVEYING THE RELATIONSHIP BETWEEN STOCK MARKET MAKER AND LIQUIDITY IN TEHRAN STOCK EXCHANGE COMPANIES Mohammad Ebrahimi Erdi, Dr. Azim Aslani,

### Cointegration: The Engle and Granger approach

Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be non-saionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require

### Stability. Coefficients may change over time. Evolution of the economy Policy changes

Sabiliy Coefficiens may change over ime Evoluion of he economy Policy changes Time Varying Parameers y = α + x β + Coefficiens depend on he ime period If he coefficiens vary randomly and are unpredicable,

### Journal Of Business & Economics Research September 2005 Volume 3, Number 9

Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy Yi-Kang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo

### Entropy: From the Boltzmann equation to the Maxwell Boltzmann distribution

Enropy: From he Bolzmann equaion o he Maxwell Bolzmann disribuion A formula o relae enropy o probabiliy Ofen i is a lo more useful o hink abou enropy in erms of he probabiliy wih which differen saes are

### Chapter 8: Regression with Lagged Explanatory Variables

Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

### Two-Group Designs Independent samples t-test & paired samples t-test. Chapter 10

Two-Group Deign Independen ample -e & paired ample -e Chaper 0 Previou e (Ch 7 and 8) Z-e z M N -e (one-ample) M N M = andard error of he mean p. 98-9 Remember: = variance M = eimaed andard error p. -

### 3.1. The F distribution [ST&D p. 99]

Topic 3: Fundamenals of analysis of variance "The analysis of variance is more han a echnique for saisical analysis. Once i is undersood, ANOVA is a ool ha can provide an insigh ino he naure of variaion

### ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,

### A Further Examination of Insurance Pricing and Underwriting Cycles

A Furher Examinaion of Insurance ricing and Underwriing Cycles AFIR Conference, Sepember 2005, Zurich, Swizerland Chris K. Madsen, GE Insurance Soluions, Copenhagen, Denmark Svend Haasrup, GE Insurance

### Morningstar Investor Return

Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion

### Multiple Structural Breaks in the Nominal Interest Rate and Inflation in Canada and the United States

Deparmen of Economics Discussion Paper 00-07 Muliple Srucural Breaks in he Nominal Ineres Rae and Inflaion in Canada and he Unied Saes Frank J. Akins, Universiy of Calgary Preliminary Draf February, 00

### Usefulness of the Forward Curve in Forecasting Oil Prices

Usefulness of he Forward Curve in Forecasing Oil Prices Akira Yanagisawa Leader Energy Demand, Supply and Forecas Analysis Group The Energy Daa and Modelling Cener Summary When people analyse oil prices,

### A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation

A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion

### Acceleration Lab Teacher s Guide

Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion

### A Re-examination of the Joint Mortality Functions

Norh merican cuarial Journal Volume 6, Number 1, p.166-170 (2002) Re-eaminaion of he Join Morali Funcions bsrac. Heekung Youn, rkad Shemakin, Edwin Herman Universi of S. Thomas, Sain Paul, MN, US Morali

### Part 1: White Noise and Moving Average Models

Chaper 3: Forecasing From Time Series Models Par 1: Whie Noise and Moving Average Models Saionariy In his chaper, we sudy models for saionary ime series. A ime series is saionary if is underlying saisical

### 11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge

### AP Calculus AB 2007 Scoring Guidelines

AP Calculus AB 7 Scoring Guidelines The College Board: Connecing Sudens o College Success The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and

### cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer

### AP Calculus BC 2010 Scoring Guidelines

AP Calculus BC Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board

### A Probability Density Function for Google s stocks

A Probabiliy Densiy Funcion for Google s socks V.Dorobanu Physics Deparmen, Poliehnica Universiy of Timisoara, Romania Absrac. I is an approach o inroduce he Fokker Planck equaion as an ineresing naural

### How to calculate effect sizes from published research: A simplified methodology

WORK-LEARNING RESEARCH How o alulae effe sizes from published researh: A simplified mehodology Will Thalheimer Samanha Cook A Publiaion Copyrigh 2002 by Will Thalheimer All righs are reserved wih one exepion.

### USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES Mehme Nuri GÖMLEKSİZ Absrac Using educaion echnology in classes helps eachers realize a beer and more effecive learning. In his sudy 150 English eachers were

### TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.

### Purchasing Power Parity (PPP), Sweden before and after EURO times

School of Economics and Managemen Purchasing Power Pariy (PPP), Sweden before and afer EURO imes - Uni Roo Tes - Coinegraion Tes Masers hesis in Saisics - Spring 2008 Auhors: Mansoor, Rashid Smora, Ami

### CHARGE AND DISCHARGE OF A CAPACITOR

REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:

### PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees

### Novelty and Collective Attention

ovely and Collecive Aenion Fang Wu and Bernardo A. Huberman Informaion Dynamics Laboraory HP Labs Palo Alo, CA 9434 Absrac The subjec of collecive aenion is cenral o an informaion age where millions of

### Hedging with Forwards and Futures

Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buy-side of a forward/fuures

### Time Series Analysis Using SAS R Part I The Augmented Dickey-Fuller (ADF) Test

ABSTRACT Time Series Analysis Using SAS R Par I The Augmened Dickey-Fuller (ADF) Tes By Ismail E. Mohamed The purpose of his series of aricles is o discuss SAS programming echniques specifically designed

### Issues Using OLS with Time Series Data. Time series data NOT randomly sampled in same way as cross sectional each obs not i.i.d

These noes largely concern auocorrelaion Issues Using OLS wih Time Series Daa Recall main poins from Chaper 10: Time series daa NOT randomly sampled in same way as cross secional each obs no i.i.d Why?

### Long Run Purchasing Power Parity: Cassel or Balassa-Samuelson?

Long Run Purchasing Power Pariy: Cassel or Balassa-Samuelson? David H. Papell and Ruxandra Prodan Universiy of Houson November 003 We use long-horizon real exchange rae daa for 6 indusrialized counries

### YEN FUTURES: EXAMINING HEDGING EFFECTIVENESS BIAS AND CROSS-CURRENCY HEDGING RESULTS ROBERT T. DAIGLER FLORIDA INTERNATIONAL UNIVERSITY SUBMITTED FOR

YEN FUTURES: EXAMINING HEDGING EFFECTIVENESS BIAS AND CROSS-CURRENCY HEDGING RESULTS ROBERT T. DAIGLER FLORIDA INTERNATIONAL UNIVERSITY SUBMITTED FOR THE FIRST ANNUAL PACIFIC-BASIN FINANCE CONFERENCE The

### Fakultet for informasjonsteknologi, Institutt for matematiske fag

Page 1 of 5 NTNU Noregs eknisk-naurviskaplege universie Fakule for informasjonseknologi, maemaikk og elekroeknikk Insiu for maemaiske fag - English Conac during exam: John Tyssedal 73593534/41645376 Exam

### Establishing Prefabricated Wood I-Joist Composite EI

July 008 Esablishing Prefabricaed Wood I- Composie EI INTRODUCTION Composie (glued/nailed) floors are common in boh residenial and commercial consrucion, and have been successfully designed by Prefabricaed

### Signal Rectification

9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, half-wae and fullwae. Le s firs consider he ideal

### 9. Capacitor and Resistor Circuits

ElecronicsLab9.nb 1 9. Capacior and Resisor Circuis Inroducion hus far we have consider resisors in various combinaions wih a power supply or baery which provide a consan volage source or direc curren

### Idealistic characteristics of Islamic Azad University masters - Islamshahr Branch from Students Perspective

Available online a www.pelagiaresearchlibrary.com European Journal Experimenal Biology, 202, 2 (5):88789 ISSN: 2248 925 CODEN (USA): EJEBAU Idealisic characerisics Islamic Azad Universiy masers Islamshahr

### 4. International Parity Conditions

4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency

### Vector Autoregressions (VARs): Operational Perspectives

Vecor Auoregressions (VARs): Operaional Perspecives Primary Source: Sock, James H., and Mark W. Wason, Vecor Auoregressions, Journal of Economic Perspecives, Vol. 15 No. 4 (Fall 2001), 101-115. Macroeconomericians

### MTH6121 Introduction to Mathematical Finance Lesson 5

26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random

### COMPUTATION OF CENTILES AND Z-SCORES FOR HEIGHT-FOR-AGE, WEIGHT-FOR-AGE AND BMI-FOR-AGE

COMPUTATION OF CENTILES AND Z-SCORES FOR HEIGHT-FOR-AGE, WEIGHT-FOR-AGE AND BMI-FOR-AGE The mehod used o consruc he 2007 WHO references relied on GAMLSS wih he Box-Cox power exponenial disribuion (Rigby

### A Mathematical Description of MOSFET Behavior

10/19/004 A Mahemaical Descripion of MOSFET Behavior.doc 1/8 A Mahemaical Descripion of MOSFET Behavior Q: We ve learned an awful lo abou enhancemen MOSFETs, bu we sill have ye o esablished a mahemaical

### Unstructured Experiments

Chaper 2 Unsrucured Experimens 2. Compleely randomized designs If here is no reason o group he plos ino blocks hen we say ha Ω is unsrucured. Suppose ha reamen i is applied o plos, in oher words ha i is

### House Price Index (HPI)

House Price Index (HPI) The price index of second hand houses in Colombia (HPI), regisers annually and quarerly he evoluion of prices of his ype of dwelling. The calculaion is based on he repeaed sales

### Time-Expanded Sampling (TES) For Ensemble-based Data Assimilation Applied To Conventional And Satellite Observations

27 h WAF/23 rd NWP, 29 June 3 July 2015, Chicago IL. 1 Time-Expanded Sampling (TES) For Ensemble-based Daa Assimilaion Applied To Convenional And Saellie Observaions Allen Zhao 1, Qin Xu 2, Yi Jin 1, Jusin

### Estimating the immediate impact of monetary policy shocks on the exchange rate and other asset prices in Hungary

Esimaing he immediae impac of moneary policy shocks on he exchange rae and oher asse prices in Hungary András Rezessy Magyar Nemzei Bank 2005 Absrac The paper applies he mehod of idenificaion hrough heeroskedasiciy

### Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary

Random Walk in -D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes

### Volatility in Returns of Islamic and Commercial Banks in Pakistan

Volailiy in Reurns of Islamic and Commercial Banks in Pakisan Muhammad Iqbal Non-Linear Time Series Analysis Prof. Rober Kuns Deparmen of Economic, Universiy of Vienna, Vienna, Ausria Inroducion Islamic

### Determinants of Capital Structure: Comparison of Empirical Evidence from the Use of Different Estimators

Serrasqueiro and Nunes, Inernaional Journal of Applied Economics, 5(1), 14-29 14 Deerminans of Capial Srucure: Comparison of Empirical Evidence from he Use of Differen Esimaors Zélia Serrasqueiro * and

### When Do TIPS Prices Adjust to Inflation Information?

When Do TIPS Prices Adjus o Inflaion Informaion? Quenin C. Chu a, *, Deborah N. Piman b, Linda Q. Yu c Augus 15, 2009 a Deparmen of Finance, Insurance, and Real Esae. The Fogelman College of Business and

### ARCH 2013.1 Proceedings

Aricle from: ARCH 213.1 Proceedings Augus 1-4, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference

### Chapter 7. Response of First-Order RL and RC Circuits

Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural

### Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.

Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one

### A Simple Way to Estimate Bid-Ask Spreads from Daily High and Low Prices

A Simple Way o Esimae Bid-Ask Spreads from Daily High and Low Prices Shane A. Corwin and Paul Schulz * January 010 * Boh auhors are from he Mendoza College of Business a he Universiy of Nore Dame. We are

### The Application of Multi Shifts and Break Windows in Employees Scheduling

The Applicaion of Muli Shifs and Brea Windows in Employees Scheduling Evy Herowai Indusrial Engineering Deparmen, Universiy of Surabaya, Indonesia Absrac. One mehod for increasing company s performance

### Module 3 Design for Strength. Version 2 ME, IIT Kharagpur

Module 3 Design for Srengh Lesson 2 Sress Concenraion Insrucional Objecives A he end of his lesson, he sudens should be able o undersand Sress concenraion and he facors responsible. Deerminaion of sress

### Working Paper A fractionally integrated exponential model for UK unemployment

econsor www.econsor.eu Der Open-Access-Publikaionsserver der ZBW Leibniz-Informaionszenrum Wirschaf The Open Access Publicaion Server of he ZBW Leibniz Informaion Cenre for Economics Gil-Alaña, Luis A.

### A Note on the Impact of Options on Stock Return Volatility. Nicolas P.B. Bollen

A Noe on he Impac of Opions on Sock Reurn Volailiy Nicolas P.B. Bollen ABSTRACT This paper measures he impac of opion inroducions on he reurn variance of underlying socks. Pas research generally finds

### Risk Modelling of Collateralised Lending

Risk Modelling of Collaeralised Lending Dae: 4-11-2008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies

### Individual Health Insurance April 30, 2008 Pages 167-170

Individual Healh Insurance April 30, 2008 Pages 167-170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve

### Testing the linearity of a time series. Some Monte Carlo and Empirical Tests

Tesing he lineariy of a ime series. Some Mone Carlo and Empirical Tess By Efsraios Tserkezos (Corresponding auhor). Mahemaical Modelling in new Technologies and Economy Posgraduae Programme. Applied Mahemaics

### DYNAMIC ECONOMETRIC MODELS Vol. 7 Nicolaus Copernicus University Toruń 2006. Ryszard Doman Adam Mickiewicz University in Poznań

DYNAMIC ECONOMETRIC MODELS Vol. 7 Nicolaus Copernicus Universiy Toruń 26 1. Inroducion Adam Mickiewicz Universiy in Poznań Measuring Condiional Dependence of Polish Financial Reurns Idenificaion of condiional

### Do Property-Casualty Insurance Underwriting Margins Have Unit Roots?

Do Propery-Casualy Insurance Underwriing Margins Have Uni Roos? Sco E. Harringon* Moore School of Business Universiy of Souh Carolina Columbia, SC 98 harringon@moore.sc.edu (83) 777-495 Tong Yu College

### Full-wave rectification, bulk capacitor calculations Chris Basso January 2009

ull-wave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal

### Statistical Analysis with Little s Law. Supplementary Material: More on the Call Center Data. by Song-Hee Kim and Ward Whitt

Saisical Analysis wih Lile s Law Supplemenary Maerial: More on he Call Cener Daa by Song-Hee Kim and Ward Whi Deparmen of Indusrial Engineering and Operaions Research Columbia Universiy, New York, NY 17-99

LEASNG VERSUSBUYNG Conribued by James D. Blum and LeRoy D. Brooks Assisan Professors of Business Adminisraion Deparmen of Business Adminisraion Universiy of Delaware Newark, Delaware The auhors discuss

### The Sensitivity of Corporate Bond Volatility to Macroeconomic Announcements. by Nikolay Kosturov* and Duane Stock**

The Sensiiviy of Corporae Bond Volailiy o Macroeconomic nnouncemens by Nikolay Kosurov* and Duane Sock** * Michael F.Price College of Business, Universiy of Oklahoma, 307 Wes Brooks, H 205, Norman, OK

### Consumer sentiment is arguably the

Does Consumer Senimen Predic Regional Consumpion? Thomas A. Garre, Rubén Hernández-Murillo, and Michael T. Owyang This paper ess he abiliy of consumer senimen o predic reail spending a he sae level. The

### Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand

36 Invesmen Managemen and Financial Innovaions, 4/4 Marke Liquidiy and he Impacs of he Compuerized Trading Sysem: Evidence from he Sock Exchange of Thailand Sorasar Sukcharoensin 1, Pariyada Srisopisawa,

### BALANCE OF PAYMENTS. First quarter 2008. Balance of payments

BALANCE OF PAYMENTS DATE: 2008-05-30 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se

### AP Calculus AB 2013 Scoring Guidelines

AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a mission-driven no-for-profi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was

### Modelling the dependence of the UK stock market on the US stock market: A need for multiple regimes

Modelling he dependence of he UK sock marke on he US sock marke: A need for muliple regimes A J Khadaroo Deparmen of Economics and Saisics Universiy of Mauriius Redui Mauriius Email: j.khadaroo@uom.ac.mu

### µ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ

Page 9 Design of Inducors and High Frequency Transformers Inducors sore energy, ransformers ransfer energy. This is he prime difference. The magneic cores are significanly differen for inducors and high

### Aggregate Output. Aggregate Output. Topics. Aggregate Output. Aggregate Output. Aggregate Output

Topics (Sandard Measure) GDP vs GPI discussion Macroeconomic Variables (Unemploymen and Inflaion Rae) (naional income and produc accouns, or NIPA) Gross Domesic Produc (GDP) The value of he final goods

### Time Series Modeling for Risk of Stock. Price with Value at Risk Computation

Applied Mahemaical Sciences, Vol 9, 015, no 56, 779-787 HIKARI Ld, wwwm-hikaricom hp://dxdoiorg/101988/ams0155144 Time Series Modeling for Risk of Sock Price wih Value a Risk Compuaion Dodi Deviano, Maiyasri

### Chapter 4: Exponential and Logarithmic Functions

Chaper 4: Eponenial and Logarihmic Funcions Secion 4.1 Eponenial Funcions... 15 Secion 4. Graphs of Eponenial Funcions... 3 Secion 4.3 Logarihmic Funcions... 4 Secion 4.4 Logarihmic Properies... 53 Secion

### Segmentation, Probability of Default and Basel II Capital Measures. for Credit Card Portfolios

Segmenaion, Probabiliy of Defaul and Basel II Capial Measures for Credi Card Porfolios Draf: Aug 3, 2007 *Work compleed while a Federal Reserve Bank of Philadelphia Dennis Ash Federal Reserve Bank of Philadelphia

### Markit Excess Return Credit Indices Guide for price based indices

Marki Excess Reurn Credi Indices Guide for price based indices Sepember 2011 Marki Excess Reurn Credi Indices Guide for price based indices Conens Inroducion...3 Index Calculaion Mehodology...4 Semi-annual

### Theoretical Analysis of Inverse Weibull Distribution

Theoreical Analysis of Inverse Weibull Disribuion M. SUAIB KAN Deparmen of saisics The Islamia universiy of Bahawalpur. e-mail: skn_8@yahoo.com G.R PASA Deparmen of saisics Bahauddin Zakariya Universiy

### Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m

Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m

### 1 HALF-LIFE EQUATIONS

R.L. Hanna Page HALF-LIFE EQUATIONS The basic equaion ; he saring poin ; : wrien for ime: x / where fracion of original maerial and / number of half-lives, and / log / o calculae he age (# ears): age (half-life)

### Permutations and Combinations

Permuaions and Combinaions Combinaorics Copyrigh Sandards 006, Tes - ANSWERS Barry Mabillard. 0 www.mah0s.com 1. Deermine he middle erm in he expansion of ( a b) To ge he k-value for he middle erm, divide

### Revisions to Nonfarm Payroll Employment: 1964 to 2011

Revisions o Nonfarm Payroll Employmen: 1964 o 2011 Tom Sark December 2011 Summary Over recen monhs, he Bureau of Labor Saisics (BLS) has revised upward is iniial esimaes of he monhly change in nonfarm

### TESTING OF SEASONAL FRACTIONAL INTEGRATION IN UK AND JAPANESE CONSUMPTION AND INCOME *

TESTING OF SEASONAL FRACTIONAL INTEGRATION IN UK AND JAPANESE CONSUMPTION AND INCOME * by L A Gil-Alaña Humbold Universiy, Berlin, and Universiy of Navarre, Spain and P M Robinson London School of Economics

### Trends in TCP/IP Retransmissions and Resets

Trends in TCP/IP Reransmissions and Reses Absrac Concordia Chen, Mrunal Mangrulkar, Naomi Ramos, and Mahaswea Sarkar {cychen, mkulkarn, msarkar,naramos}@cs.ucsd.edu As he Inerne grows larger, measuring

### The Identification of the Response of Interest Rates to Monetary Policy Actions Using Market-Based Measures of Monetary Policy Shocks

The Idenificaion of he Response of Ineres Raes o Moneary Policy Acions Using Marke-Based Measures of Moneary Policy Shocks Daniel L. Thornon Federal Reserve Bank of S. Louis Phone (314) 444-8582 FAX (314)

### THE NEW MARKET EFFECT ON RETURN AND VOLATILITY OF SPANISH STOCK SECTOR INDEXES

THE NEW MARKET EFFECT ON RETURN AND VOLATILITY OF SPANISH STOCK SECTOR INDEXES Juan Ángel Lafuene Universidad Jaume I Unidad Predeparamenal de Finanzas y Conabilidad Campus del Riu Sec. 1080, Casellón

### MSCI Index Calculation Methodology

Index Mehodology MSCI Index Calculaion Mehodology Index Calculaion Mehodology for he MSCI Equiy Indices Index Mehodology MSCI Index Calculaion Mehodology Conens Conens... 2 Inroducion... 5 MSCI Equiy Indices...

### Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is \$613.

Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised

### 17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides

7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion

### THE MATHEMATICAL MODEL FOR THE SECRETION OF LUTEINIZING HORMONE BY USING PROPORTIONAL HAZARD MODEL

IJMS, Vol. 11, No. 3-4, (July-December 212), pp. 463-469 Serials Publicaions ISSN: 972-754X THE MATHEMATICAL MODEL FOR THE SECRETION OF LUTEINIZING HORMONE BY USING PROPORTIONAL HAZARD MODEL S. Lakshmi

### Diane K. Michelson, SAS Institute Inc, Cary, NC Annie Dudley Zangi, SAS Institute Inc, Cary, NC

ABSTRACT Paper DK-02 SPC Daa Visualizaion of Seasonal and Financial Daa Using JMP Diane K. Michelson, SAS Insiue Inc, Cary, NC Annie Dudley Zangi, SAS Insiue Inc, Cary, NC JMP Sofware offers many ypes

### NASDAQ-100 Futures Index SM Methodology

NASDAQ-100 Fuures Index SM Mehodology Index Descripion The NASDAQ-100 Fuures Index (The Fuures Index ) is designed o rack he performance of a hypoheical porfolio holding he CME NASDAQ-100 E-mini Index

### II.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal

Quarerly Repor on he Euro Area 3/202 II.. Deb reducion and fiscal mulipliers The deerioraion of public finances in he firs years of he crisis has led mos Member Saes o adop sizeable consolidaion packages.

### Recovering Market Expectations of FOMC Rate Changes with Options on Federal Funds Futures

w o r k i n g p a p e r 5 7 Recovering Marke Expecaions of FOMC Rae Changes wih Opions on Federal Funds Fuures by John B. Carlson, Ben R. Craig, and William R. Melick FEDERAL RESERVE BANK OF CLEVELAND