Tests for One Poisson Mean


 Aubrie O’Neal’
 2 years ago
 Views:
Transcription
1 Chpter 412 Tests for One Poisson Men Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson distribution is often used to fit count dt, such s the number of defects on n item, the number of ccidents t n intersection during yer, the number of clls to cll center during n hour, or the number of meteors seen in the evening sky during n hour. The Poisson distribution is chrcterized by single prmeter, λ, which is the men number of occurrences during the intervl. This procedure clcultes the power or smple size for testing whether λ is less thn or greter thn specified vlue. This test is usully clled the test of the Poisson men. The test is described in Ostle (1988) nd the power clcultion is given in Guenther (1977). Test Procedure Assume tht the men is λ 0. To test H : λ λ vs. 0 0 H : λ > λ0, you would tke the following steps. 1. Find the criticl vlue. Choose the criticl vlue X so tht the probbility of rejecting H 0 when it is true is equl to α. This is done by solving the following inequlity for X. x= X ( nλ ) nλ0 0 e α. x! Note tht becuse X is n integer, equlity will seldom occur. Therefore, the minimum vlue of for which the inequlity holds. 2. Select smple of n items compute the totl number of events X = of H. x n x i i= 1 The test in the other direction ( H : λ λ vs. 0 0 H : λ < λ0 ) is computed similrly.. If X is found X > X reject H0 in fvor 4121
2 Assumptions The ssumptions of the onesmple Poisson test re: 1. The dt re counts (discrete) tht follow the Poisson distribution. 2. The smple is simple rndom smple from its popultion. Ech individul in the popultion hs n equl probbility of being selected in the smple. Limittions There re few limittions when using these tests. As long s the ssumption tht the men occurrence rte is constnt is met, the test is vlid. Technicl Detils Computing Power The power is computing for specific lterntive vlue λ1 using the following formul. Power = 1 β = x= X e nλ 1 ( nλ ) 1 x! x Computing Smple Size Following Guenther (1977), the smple size, n, is found by incresing the vlue of d in the following expression until the lefthnd endpoint is less thn the righthnd endpoint nd the intervl contins t lest one integer. Χ 2 2 2d ;1 Χ β 2 ; n d α, d = 1,2,3, λ 2λ Here Χ 2 v;p is percentge point of the chisqure distribution with v degrees of freedom. Procedure Options This section describes the options tht re specific to this procedure. These re locted on the Design tb. For more informtion bout the options of other tbs, go to the Procedure Window chpter. The Design tb contins most of the prmeters nd options tht you will be concerned with. Solve For Solve For This option specifies the prmeter to be clculted from the vlues of the other prmeters. Under most conditions, you would select either Power or Smple Size
3 Select Smple Size when you wnt to determine the smple size needed to chieve given power nd lph error level. Select Power when you wnt to clculte the power of n experiment tht hs lredy been run. Test H (Alterntive Hypothesis) This option specifies the lterntive hypothesis. This implicitly specifies the direction of the hypothesis test. The null hypothesis is lwys H : λ = λ Possible selections for the lterntive hypothesis re: 1. H : λ1 λ0. This option yields onetiled t test. 2. H : λ1 λ0. This option yields onetiled t test. Power nd Alph Power This option specifies one or more vlues for power. Power is the probbility of rejecting flse null hypothesis, nd is equl to one minus bet. Bet is the probbility of typeii error, which occurs when flse null hypothesis is not rejected. Vlues must be between zero nd one. Historiclly, the vlue of 0.80 (bet = 0.20) ws used for power. Now, 0.90 (bet = 0.10) is lso commonly used. A single vlue my be entered here or rnge of vlues such s 0.8 to 0.95 by 0.05 my be entered. Alph This option specifies one or more vlues for the probbility of typei error. A typei error occurs when true null hypothesis is rejected. Vlues must be between zero nd one. For onesided tests such s this, the vlue of is recommended for lph. You my enter rnge of vlues such s or to 0.05 by Smple Size n (Smple Size) This option specifies one or more vlues of the smple size, the number of individuls in the study. This vlue must be n integer greter thn one. Note tht you my enter list of vlues using the syntx 50,100,150,200,250 or 50 to 250 by 50. Effect Size Mens λ0 (Null or Bseline Men) This option specifies one or more vlues of the men occurrence rte corresponding to the null hypothesis. This vlue must be greter thn zero. λ1 (Alterntive Men) This option specifies one or more vlues of the men occurrence rte corresponding to the lterntive hypothesis. This vlue must be greter thn zero
4 Exmple 1 Power fter Study This exmple demonstrtes how to clculte the power for specific vlues of the other prmeters. Suppose tht ccidents hve occurred t n intersection t n verge rte of 1 per month for the lst severl yers. Recently, distrction hs been constructed ner the intersection tht ppers to hve incresed the ccident rte. Suppose the smple sizes re 12 nd 24 months nd lph is Wht is the power to detect lterntives of 1.1, 1.5, 2.0, nd 2.5? Setup This section presents the vlues of ech of the prmeters needed to run this exmple. First, from the PASS Home window, lod the procedure window by expnding Mens, then One Men, then clicking on Test (Inequlity), nd then clicking on. You my then mke the pproprite entries s listed below, or open Exmple 1 by going to the File menu nd choosing Open Exmple Templte. Option Vlue Solve For... Power H (Alterntive Hypothesis)... H: λ0 < λ1 Alph n (Smple Size) λ0 (Null or Bseline) λ1 (Alterntive) Annotted Output Click the Clculte button to perform the clcultions nd generte the following output. Numeric Results Numeric Results for OneSmple Poisson Test Null Hypothesis: λ0 = λ1 Alterntive Hypothesis: λ0 < λ1 Trget Actul Diff Effect Power n Alph Alph λ0 λ1 (λ0λ1) Size Bet References Guenther, Willim C Smpling Inspection in Sttisticl Qulity Control. Griffin's Sttisticl Monogrphs. Mcmilln, NY. Pges Ostle, B. nd Mlone, L Sttistics in Reserch, 4th Edition. Iow Stte University Press. Iow. Pges
5 Report Definitions Power is the probbility of rejecting flse null hypothesis. It should be close to one. n is the size of the smple drwn from the popultion. To conserve resources, it should be smll. Alph is the probbility of rejecting true null hypothesis. It should be smll. Diff is the vlue of λ0  λ1, the difference being tested. λ0 is the vlue of the popultion men under the null hypothesis. λ1 is the vlue of the popultion men under the lterntive hypothesis. Effect Size is the vlue of (λ0  λ1) / (λ1). Bet is the probbility of ccepting flse null hypothesis. It should be smll. Summry Sttements A smple size of 12 chieves 5% power to detect difference of between the null hypothesis men of 1.00 nd the lterntive hypothesis men of 1.10 nd with significnce level (lph) of using onesided onesmple Poisson test. This report shows the vlues of ech of the prmeters, one scenrio per row. The vlues of power nd bet were clculted from the other prmeters. Note tht the ctul power chieved is greter thn the trget power. Similrly, the ctul lph is less thn the trget lph. These differences occur becuse only integer vlues of the count vrible occur. Plots Section 4125
6 These plots show the reltionship between smple size nd power for vrious vlues of the lterntive men nd the smple size
7 Exmple 2 Finding the Smple Size This exmple will extend Exmple 1 to the cse in which we wnt to find the necessry smple size to chieve t lest 90% power. This is done s follows. Setup This section presents the vlues of ech of the prmeters needed to run this exmple. First, from the PASS Home window, lod the procedure window by expnding Mens, then One Men, then clicking on Test (Inequlity), nd then clicking on. You my then mke the pproprite entries s listed below, or open Exmple 2 by going to the File menu nd choosing Open Exmple Templte. Option Vlue Solve For... Smple Size H (Alterntive Hypothesis)... H: λ0 < λ1 Power Alph λ0 (Null or Bseline) λ1 (Alterntive) Annotted Output Click the Clculte button to perform the clcultions nd generte the following output. Numeric Results Numeric Results for OneSmple Poisson Test Null Hypothesis: λ0 = λ1 Alterntive Hypothesis: λ0 < λ1 Trget Actul Diff Effect Power n Alph Alph λ0 λ1 (λ0λ1) Size Bet This report shows the smple sizes tht re necessry to chieve the required power
8 Exmple 3 Finding the Minimum Detectble Difference Continuing with the previous exmple, suppose only 10 months of dt re vilble. Wht is the minimum detectble difference tht cn be detected by this design? Setup This section presents the vlues of ech of the prmeters needed to run this exmple. First, from the PASS Home window, lod the procedure window by expnding Mens, then One Men, then clicking on Test (Inequlity), nd then clicking on. You my then mke the pproprite entries s listed below, or open Exmple 3 by going to the File menu nd choosing Open Exmple Templte. Option Vlue Solve For... λ1 H (Alterntive Hypothesis)... H: λ0 < λ1 Power Alph n (Smple Size) λ0 (Null or Bseline) Output Click the Clculte button to perform the clcultions nd generte the following output. Numeric Results Numeric Results for OneSmple Poisson Test Null Hypothesis: λ0 = λ1 Alterntive Hypothesis: λ0 < λ1 Trget Actul Diff Effect Power n Alph Alph λ0 λ1 (λ0λ1) Size Bet This report shows tht the minimum detectble difference is =
9 Exmple 4 Vlidtion using Guenther Guenter (1977) pge 27 gives n exmple in which λ0 = 0.05, λ1 =.2, α = 0.05, β = 0.10, nd n = 47. We will now run this exmple. Setup This section presents the vlues of ech of the prmeters needed to run this exmple. First, from the PASS Home window, lod the procedure window by expnding Mens, then One Men, then clicking on Test (Inequlity), nd then clicking on. You my then mke the pproprite entries s listed below, or open Exmple 4 by going to the File menu nd choosing Open Exmple Templte. Option Vlue Solve For... Smple Size H (Alterntive Hypothesis)... H: λ0 < λ1 Power Alph λ0 (Null or Bseline) λ1 (Alterntive) Output Click the Clculte button to perform the clcultions nd generte the following output. Numeric Results Numeric Results for OneSmple Poisson Test Null Hypothesis: λ0 = λ1 Alterntive Hypothesis: λ0 < λ1 Trget Actul Diff Effect Power n Alph Alph λ0 λ1 (λ0λ1) Size Bet Note tht the vlue of n is indeed
Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the ttest is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the ttest cn be used to compre the mens of only
More informationHelicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
More informationLecture 3 Gaussian Probability Distribution
Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike
More informationChapter 8  Practice Problems 1
Chpter 8  Prctice Problems 1 MULTIPLE CHOICE. Choose the one lterntive tht best completes the sttement or nswers the question. A hypothesis test is to be performed. Determine the null nd lterntive hypotheses.
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More informationUnit 29: Inference for TwoWay Tables
Unit 29: Inference for TwoWy Tbles Prerequisites Unit 13, TwoWy Tbles is prerequisite for this unit. In ddition, students need some bckground in significnce tests, which ws introduced in Unit 25. Additionl
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationDlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report
DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of
More informationExample 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.
2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More information9 CONTINUOUS DISTRIBUTIONS
9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More informationAP Statistics Testbank 7
AP Sttistics Testbnk 7 MultipleChoice Questions 1) In formulting hypotheses for sttisticl test of significnce, the null hypothesis is often ) sttement of "no effect" or "no difference." b) the probbility
More information1 Numerical Solution to Quadratic Equations
cs42: introduction to numericl nlysis 09/4/0 Lecture 2: Introduction Prt II nd Solving Equtions Instructor: Professor Amos Ron Scribes: Yunpeng Li, Mrk Cowlishw Numericl Solution to Qudrtic Equtions Recll
More informationBasic Analysis of Autarky and Free Trade Models
Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently
More informationDistributions. (corresponding to the cumulative distribution function for the discrete case).
Distributions Recll tht n integrble function f : R [,] such tht R f()d = is clled probbility density function (pdf). The distribution function for the pdf is given by F() = (corresponding to the cumultive
More informationMATH 150 HOMEWORK 4 SOLUTIONS
MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive
More information4: RIEMANN SUMS, RIEMANN INTEGRALS, FUNDAMENTAL THEOREM OF CALCULUS
4: RIEMA SUMS, RIEMA ITEGRALS, FUDAMETAL THEOREM OF CALCULUS STEVE HEILMA Contents 1. Review 1 2. Riemnn Sums 2 3. Riemnn Integrl 3 4. Fundmentl Theorem of Clculus 7 5. Appendix: ottion 10 1. Review Theorem
More informationFactoring Polynomials
Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles
More informationBinary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse rel number to its binry representtion,. convert binry number to n equivlent bse number. In everydy
More information15.6. The mean value and the rootmeansquare value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style
The men vlue nd the rootmensqure vlue of function 5.6 Introduction Currents nd voltges often vry with time nd engineers my wish to know the verge vlue of such current or voltge over some prticulr time
More informationMath 135 Circles and Completing the Square Examples
Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for
More informationPhysics 43 Homework Set 9 Chapter 40 Key
Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nmwide region t x
More informationMath Review 1. , where α (alpha) is a constant between 0 and 1, is one specific functional form for the general production function.
Mth Review Vribles, Constnts nd Functions A vrible is mthemticl bbrevition for concept For emple in economics, the vrible Y usully represents the level of output of firm or the GDP of n economy, while
More informationLecture 15  Curve Fitting Techniques
Lecture 15  Curve Fitting Techniques Topics curve fitting motivtion liner regression Curve fitting  motivtion For root finding, we used given function to identify where it crossed zero where does fx
More informationHomework #4: Answers. 1. Draw the array of world outputs that free trade allows by making use of each country s transformation schedule.
Text questions, Chpter 5, problems 15: Homework #4: Answers 1. Drw the rry of world outputs tht free trde llows by mking use of ech country s trnsformtion schedule.. Drw it. This digrm is constructed
More informationRIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS
RIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS Known for over 500 yers is the fct tht the sum of the squres of the legs of right tringle equls the squre of the hypotenuse. Tht is +b c. A simple proof is
More informationMorgan Stanley Ad Hoc Reporting Guide
spphire user guide Ferury 2015 Morgn Stnley Ad Hoc Reporting Guide An Overview For Spphire Users 1 Introduction The Ad Hoc Reporting tool is ville for your reporting needs outside of the Spphire stndrd
More informationBiostatistics 102: Quantitative Data Parametric & Nonparametric Tests
Singpore Med J 2003 Vol 44(8) : 391396 B s i c S t t i s t i c s F o r D o c t o r s Biosttistics 102: Quntittive Dt Prmetric & Nonprmetric Tests Y H Chn In this rticle, we re going to discuss on the
More informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationMATLAB Workshop 13  Linear Systems of Equations
MATLAB: Workshop  Liner Systems of Equtions pge MATLAB Workshop  Liner Systems of Equtions Objectives: Crete script to solve commonly occurring problem in engineering: liner systems of equtions. MATLAB
More informationCurve Sketching. 96 Chapter 5 Curve Sketching
96 Chpter 5 Curve Sketching 5 Curve Sketching A B A B A Figure 51 Some locl mximum points (A) nd minimum points (B) If (x, f(x)) is point where f(x) reches locl mximum or minimum, nd if the derivtive of
More informationExample A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding
1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde
More informationPlotting and Graphing
Plotting nd Grphing Much of the dt nd informtion used by engineers is presented in the form of grphs. The vlues to be plotted cn come from theoreticl or empiricl (observed) reltionships, or from mesured
More information5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.
5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous relvlued
More informationPASS Sample Size Software
Chapter 250 Introduction The Chisquare test is often used to test whether sets of frequencies or proportions follow certain patterns. The two most common instances are tests of goodness of fit using multinomial
More informationAssuming all values are initially zero, what are the values of A and B after executing this Verilog code inside an always block? C=1; A <= C; B = C;
B26 Appendix B The Bsics of Logic Design Check Yourself ALU n [Arthritic Logic Unit or (rre) Arithmetic Logic Unit] A rndomnumer genertor supplied s stndrd with ll computer systems Stn KellyBootle,
More informationOr more simply put, when adding or subtracting quantities, their uncertainties add.
Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re
More informationEconomics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999
Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,
More informationUnit 6: Exponents and Radicals
Eponents nd Rdicls : The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N):  counting numers. {,,,,, } Whole Numers (W):  counting numers with 0. {0,,,,,, } Integers (I): 
More informationFormal Languages and Automata Exam
Forml Lnguges nd Automt Exm Fculty of Computers & Informtion Deprtment: Computer Science Grde: Third Course code: CSC 34 Totl Mrk: 8 Dte: 23//2 Time: 3 hours Answer the following questions: ) Consider
More informationMathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100
hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by
More informationReview guide for the final exam in Math 233
Review guide for the finl exm in Mth 33 1 Bsic mteril. This review includes the reminder of the mteril for mth 33. The finl exm will be cumultive exm with mny of the problems coming from the mteril covered
More informationThe Chain Rule. rf dx. t t lim " (x) dt " (0) dx. df dt = df. dt dt. f (r) = rf v (1) df dx
The Chin Rule The Chin Rule In this section, we generlize the chin rule to functions of more thn one vrible. In prticulr, we will show tht the product in the singlevrible chin rule extends to n inner
More informationEQUATIONS OF LINES AND PLANES
EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in pointdirection nd twopoint
More informationProject 6 Aircraft static stability and control
Project 6 Aircrft sttic stbility nd control The min objective of the project No. 6 is to compute the chrcteristics of the ircrft sttic stbility nd control chrcteristics in the pitch nd roll chnnel. The
More informationBayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the
More informationAntiSpyware Enterprise Module 8.5
AntiSpywre Enterprise Module 8.5 Product Guide Aout the AntiSpywre Enterprise Module The McAfee AntiSpywre Enterprise Module 8.5 is n ddon to the VirusScn Enterprise 8.5i product tht extends its ility
More informationMathematics Higher Level
Mthemtics Higher Level Higher Mthemtics Exmintion Section : The Exmintion Mthemtics Higher Level. Structure of the exmintion pper The Higher Mthemtics Exmintion is divided into two ppers s detiled below:
More informationBusiness Examples. What is a hypothesis? Recap : Hypothesis Testing. Recap : Confidence Intervals. Hypothesis Testing (intro)
ypthesis Testing (intr) We hve discussed tw methds f mking inference n prmeters in ppultin bsed n rndm smple (in English, hw d we figure ut the true men r prprtin) Pint estimtes give us single guess Stt
More informationSquare Roots Teacher Notes
Henri Picciotto Squre Roots Techer Notes This unit is intended to help students develop n understnding of squre roots from visul / geometric point of view, nd lso to develop their numer sense round this
More informationAREA OF A SURFACE OF REVOLUTION
AREA OF A SURFACE OF REVOLUTION h cut r πr h A surfce of revolution is formed when curve is rotted bout line. Such surfce is the lterl boundr of solid of revolution of the tpe discussed in Sections 7.
More informationPROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
More informationSmall Businesses Decisions to Offer Health Insurance to Employees
Smll Businesses Decisions to Offer Helth Insurnce to Employees Ctherine McLughlin nd Adm Swinurn, June 2014 Employersponsored helth insurnce (ESI) is the dominnt source of coverge for nonelderly dults
More informationPearson's Correlation Tests
Chapter 800 Pearson's Correlation Tests Introduction The correlation coefficient, ρ (rho), is a popular statistic for describing the strength of the relationship between two variables. The correlation
More informationThe Velocity Factor of an Insulated TwoWire Transmission Line
The Velocity Fctor of n Insulted TwoWire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the
More informationHealth insurance marketplace What to expect in 2014
Helth insurnce mrketplce Wht to expect in 2014 33096VAEENBVA 06/13 The bsics of the mrketplce As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum
More informationContextualizing NSSE Effect Sizes: Empirical Analysis and Interpretation of Benchmark Comparisons
Contextulizing NSSE Effect Sizes: Empiricl Anlysis nd Interprettion of Benchmrk Comprisons NSSE stff re frequently sked to help interpret effect sizes. Is.3 smll effect size? Is.5 relly lrge effect size?
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More information1.00/1.001 Introduction to Computers and Engineering Problem Solving Fall 2011  Final Exam
1./1.1 Introduction to Computers nd Engineering Problem Solving Fll 211  Finl Exm Nme: MIT Emil: TA: Section: You hve 3 hours to complete this exm. In ll questions, you should ssume tht ll necessry pckges
More informationHealth insurance exchanges What to expect in 2014
Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 02/13 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount
More information4.11 Inner Product Spaces
314 CHAPTER 4 Vector Spces 9. A mtrix of the form 0 0 b c 0 d 0 0 e 0 f g 0 h 0 cnnot be invertible. 10. A mtrix of the form bc d e f ghi such tht e bd = 0 cnnot be invertible. 4.11 Inner Product Spces
More informationSection 54 Trigonometric Functions
5 Trigonometric Functions Section 5 Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form
More informationRegular Sets and Expressions
Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite
More informationand thus, they are similar. If k = 3 then the Jordan form of both matrices is
Homework ssignment 11 Section 7. pp. 24925 Exercise 1. Let N 1 nd N 2 be nilpotent mtrices over the field F. Prove tht N 1 nd N 2 re similr if nd only if they hve the sme miniml polynomil. Solution: If
More informationIntegration. 148 Chapter 7 Integration
48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but
More informationHomework 3 Solutions
CS 341: Foundtions of Computer Science II Prof. Mrvin Nkym Homework 3 Solutions 1. Give NFAs with the specified numer of sttes recognizing ech of the following lnguges. In ll cses, the lphet is Σ = {,1}.
More informationWeek 7  Perfect Competition and Monopoly
Week 7  Perfect Competition nd Monopoly Our im here is to compre the industrywide response to chnges in demnd nd costs by monopolized industry nd by perfectly competitive one. We distinguish between
More informationRotating DC Motors Part II
Rotting Motors rt II II.1 Motor Equivlent Circuit The next step in our consiertion of motors is to evelop n equivlent circuit which cn be use to better unerstn motor opertion. The rmtures in rel motors
More informationAnswer, Key Homework 10 David McIntyre 1
Answer, Key Homework 10 Dvid McIntyre 1 This printout should hve 22 questions, check tht it is complete. Multiplechoice questions my continue on the next column or pge: find ll choices efore mking your
More information6.2 Volumes of Revolution: The Disk Method
mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine soclled volumes of
More informationSpace Vector Pulse Width Modulation Based Induction Motor with V/F Control
Interntionl Journl of Science nd Reserch (IJSR) Spce Vector Pulse Width Modultion Bsed Induction Motor with V/F Control Vikrmrjn Jmbulingm Electricl nd Electronics Engineering, VIT University, Indi Abstrct:
More informationModule Summary Sheets. C3, Methods for Advanced Mathematics (Version B reference to new book) Topic 2: Natural Logarithms and Exponentials
MEI Mthemtics in Ection nd Instry Topic : Proof MEI Structured Mthemtics Mole Summry Sheets C, Methods for Anced Mthemtics (Version B reference to new book) Topic : Nturl Logrithms nd Eponentils Topic
More informationPoint Biserial Correlation Tests
Chapter 807 Point Biserial Correlation Tests Introduction The point biserial correlation coefficient (ρ in this chapter) is the productmoment correlation calculated between a continuous random variable
More information274 Chapter 13. Chapter 13
74 hpter 3 hpter 3 3. () ounts will be obtined from the smples so th problem bout compring proportions. (b) h n observtionl study compring rndom smples selected from two independent popultions. 3. () cores
More information2015 EDITION. AVMA Report on Veterinary Compensation
2015 EDITION AVMA Report on Veterinry Compenstion AVMA Report on Veterinry Compenstion 2015 EDITION Copyright 2015 by the All rights reserved. ISBN13: 9781882691319 AVMA Report on Veterinry Compenstion
More informationSPECIAL PRODUCTS AND FACTORIZATION
MODULE  Specil Products nd Fctoriztion 4 SPECIAL PRODUCTS AND FACTORIZATION In n erlier lesson you hve lernt multipliction of lgebric epressions, prticulrly polynomils. In the study of lgebr, we come
More informationHealth insurance exchanges What to expect in 2014
Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 11/12 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount
More informationAppendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:
Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you
More informationSection 74 Translation of Axes
62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 74 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the
More informationFinite Automata. Informatics 2A: Lecture 3. John Longley. 25 September School of Informatics University of Edinburgh
Lnguges nd Automt Finite Automt Informtics 2A: Lecture 3 John Longley School of Informtics University of Edinburgh jrl@inf.ed.c.uk 25 September 2015 1 / 30 Lnguges nd Automt 1 Lnguges nd Automt Wht is
More informationCalculus of variations with fractional derivatives and fractional integrals
Anis do CNMAC v.2 ISSN 1984820X Clculus of vritions with frctionl derivtives nd frctionl integrls Ricrdo Almeid, Delfim F. M. Torres Deprtment of Mthemtics, University of Aveiro 3810193 Aveiro, Portugl
More informationSmall Business Cloud Services
Smll Business Cloud Services Summry. We re thick in the midst of historic sechnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly
More informationWeek 11  Inductance
Week  Inductnce November 6, 202 Exercise.: Discussion Questions ) A trnsformer consists bsiclly of two coils in close proximity but not in electricl contct. A current in one coil mgneticlly induces n
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationQUANTITATIVE METHODS IN PSYCHOLOGY A Power Primer
QUANTITATIE METHODS IN PSYCHOLOGY A Power Primer Jcob Cohen New \brk University One possible reson for the continued neglect of sttisticl power nlysis in reserch in the behviorl sciences is the inccessibility
More informationSTATUS OF LANDBASED WIND ENERGY DEVELOPMENT IN GERMANY
Yer STATUS OF LANDBASED WIND ENERGY Deutsche WindGurd GmbH  Oldenburger Strße 6526316 Vrel  Germny +49 (4451)/9515  info@windgurd.de  www.windgurd.com Annul Added Cpcity [MW] Cumultive Cpcity [MW]
More informationCOMPONENTS: COMBINED LOADING
LECTURE COMPONENTS: COMBINED LOADING Third Edition A. J. Clrk School of Engineering Deprtment of Civil nd Environmentl Engineering 24 Chpter 8.4 by Dr. Ibrhim A. Asskkf SPRING 2003 ENES 220 Mechnics of
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationWarmup for Differential Calculus
Summer Assignment Wrmup for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:
More information** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand
Modelling nd Simultion of hemicl Processes in Multi Pulse TP Experiment P. Phnwdee* S.O. Shekhtmn +. Jrungmnorom** J.T. Gleves ++ * Dpt. hemicl Engineering, Ksetsrt University, Bngkok 10900, Thilnd + Dpt.hemicl
More informationExponential and Logarithmic Functions
Nme Chpter Eponentil nd Logrithmic Functions Section. Eponentil Functions nd Their Grphs Objective: In this lesson ou lerned how to recognize, evlute, nd grph eponentil functions. Importnt Vocbulr Define
More informationI calculate the unemployment rate as (In Labor Force Employed)/In Labor Force
Introduction to the Prctice of Sttistics Fifth Edition Moore, McCbe Section 4.5 Homework Answers to 98, 99, 100,102, 103,105, 107, 109,110, 111, 112, 113 Working. In the lnguge of government sttistics,
More information2 DIODE CLIPPING and CLAMPING CIRCUITS
2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of
More informationNOTES. Cohasset Associates, Inc. 2015 Managing Electronic Records Conference 8.1
Cohsset Assocites, Inc. Expnding Your Skill Set: How to Apply the Right Serch Methods to Your Big Dt Problems Juli L. Brickell H5 Generl Counsel MER Conference My 18, 2015 H5 POWERING YOUR DISCOVERY GLOBALLY
More informationTHE RATIONAL NUMBERS CHAPTER
CHAPTER THE RATIONAL NUMBERS When divided by b is not n integer, the quotient is frction.the Bbylonins, who used number system bsed on 60, epressed the quotients: 0 8 s 0 60 insted of 8 s 7 60,600 0 insted
More informationLowWage Workers and Health Insurance Coverage: Can Policymakers Target Them through Their Employers?
Stephen H. Long M. Susn Mrquis LowWge Workers nd Helth Insurnce Coverge: Cn Policymkers Trget Them through Their Employers? Mny policy inititives to increse helth insurnce coverge would subsidize employers
More information