Statistical Inference Procedures
|
|
- Christiana Ferguson
- 6 years ago
- Views:
Transcription
1 Statitical Iferece Procedure Cofidece Iterval Hypothei Tet Statitical iferece produce awer to pecific quetio about the populatio of iteret baed o the iformatio i a ample. Iferece procedure mut iclude a tatemet of how cofidet we ca be that the awer i correct. Thi preetatio coider oly cofidece iterval for µ. The bai for thi importat topic i the amplig ditributio of. X Cofidece Iterval A cofidece iterval i a formula that tell u how to ue ample data to etimate a populatio parameter. The cofidece level idicate the percetage of iterval cotructed i thi maer which cotai the value of the parameter. Cofidece Iterval for µ Sice X i a ubiaed etimator of the populatio mea, µ, we ue X to etimate µ. The amplig ditributio of X, provide the tool we eed to build a cofidece iterval for µ. A 100(1 α)% Cofidece Iterval for µ (1 α) i the cofidece coefficiet. It i the probability that the iterval etimator ecloe the populatio parameter. If the cofidece coefficiet i (1 α), the 100(1 α)% i the cofidece level. The cofidece level i the percetage of the iterval cotructed by the formula will cotai the true value of µ. 1
2 A 100(1 α)% Cofidece Iterval for µ Aume the populatio tadard deviatio i kow. Aume that X i ormally ditributed with mea, µ, ad tadard deviatio,. For ample of ize, i ormally ditributed with mea, µ, ad tadard deviatio,. X Let Ue What We Kow P µ z < x < µ + z = P < z ( z < z ) α/ What i z α/? z α/ i the value of z that awer the quetio what i the value of z uch that 100(1 α)% of the value of z lie betwee z α/ ad z α/. If 100(1-α) = 95, the P(- z α/ < z < z α/ ) =.95. Therefore, z α/ = What i the formula for a 100(1-α)% cofidece iterval for µ? Uig algebra which you are ot repoible for doig, I ca take the expreio below ad chage it from a probability tatemet about X to oe about µ. P µ z P X z < X < µ + z < µ < X + z = I thi expreio we are talkig about the variable X, ot a oberved value of the variable. x z The formula for a C% cofidece iterval for µ i < µ < x + z α Whe we ubtitute the value of the ample mea for a particular ample, we ca o loger talk about the probability. Itead we ay that we are 100(1 α)% ure that the true mea µ lie betwee the two value we obtaied by uig the ample mea. A Example We wat to etimate the mea time required to perform a tak with 95% cofidece. We elect a radom ample of ubject ad fid that x = 43 ecod. Aume that = ecod. We mut alo aume that the time required to perform thi tak i ormally ditributed. Give a 95% Cofidece Iterval for µ x zα/ < µ < x + zα < µ < < µ < We are 95% cofidet that the mea time required to perform thi tak i betwee 4.0 ad ecod.
3 Thi Formula i uually writte x ± z Thi formula i i the form we ue for may cofidece iterval, etimate margi of error. Give a 95% CI for µ x ± zα 43± ± < µ < Thi i the way I wat you to how your work. Iterpret the Cofidece Iterval We are 95% cofidet that the mea time to perform thi tak i betwee 4.0 ad ecod Propertie of the Margi of Error All other thig beig equal, the margi of error of a cofidece iterval decreae a the cofidece level 100(1-α) decreae. the ample ize icreae. the populatio tadard deviatio decreae. What happe whe we do ot kow the populatio tadard deviatio? We ue the ample tadard deviatio a a ubtitute for. I thi cae the formula to be ued deped o the ample ize,. If < 30, we eed to kow the propertie of a ew ample tatitic called t. x µ t = Compare the z-core for X the t-core for X. x µ z = t = x µ to 3
4 The t Ditributio The t ditributio are a family of ditributio oe for each umber of degree of freedom. We ue df to deote the umber of degree of freedom. Each t ditributio i ymmetric about 0. A table givig value of t α for variou probabilitie ad umber of degree of freedom i give i the frot cover of your book. The table etrie are t α uch that P(t > t α ) = α. Example: If α =.0 ad df = 14, t α =.145. The formula for a 100(1 α)% cofidece iterval for µ whe i ot kow ad < 30 i x t < µ df < x + t = 1 α / Thi Formula i uually writte x ± tα, df = 1 Thi formula i i the form we ue for may cofidece iterval, etimate margi of error. A Example uig t We wat to etimate the mea time required to perform a tak with 95% cofidece. We elect a SRS of ubject ad fid that X = 43 ecod ad = ecod. We mut aume that the time required to perform thi tak i ormally ditributed. Give a 95% CI for µ t x tα / < µ < x + tα < µ < < µ < We are 95% cofidet that the mea time required to perform thi tak i betwee ad ecod. Give a 95% CI for µ x ± tα, df = 1= 4 43 ± ± < µ < Thi i the way I wat you to how your work. 4
5 What happe whe X i ot ormally ditributed? The Cetral Limit Theorem provide a guide. If i large eough the amplig ditributio of X i approximately ormally ditributed. Remember, we claim that i large eough if i at leat 30. If we kew the we could ue the x ± z formula. What if we do ot kow ad i at leat 30? We imply ue the formula x ± zα/ ad ubtitute for. Summary There are formula ued to create a cofidece iterval for µ. How do we chooe which formula to ue? We ak the followig quetio: I X ormally ditributed? I kow? What i? If X i ormally ditributed ad i kow, the for every ue x ± z If X i ormally ditributed ad i ot kow, the for < 30 x ± t, df = 1 a 5
6 If X i ormally ditributed ad i ot kow, the for greater tha or equal to 30 ue x ± z If X i ot ormally ditributed ad i ot kow, the for greater tha or equal to 30 ue x ± z If X i ot ormally ditributed ad i ot kow, the for le tha 30 either of thee formula ca be ued. 6
Chapter 9. Key Ideas Hypothesis Test (Two Populations)
Chapter 9 Key Idea Hypothei Tet (Two Populatio) Sectio 9-: Overview I Chapter 8, dicuio cetered aroud hypothei tet for the proportio, mea, ad tadard deviatio/variace of a igle populatio. However, ofte
More informationComments on Discussion Sheet 18 and Worksheet 18 ( ) An Introduction to Hypothesis Testing
Commet o Dicuio Sheet 18 ad Workheet 18 ( 9.5-9.7) A Itroductio to Hypothei Tetig Dicuio Sheet 18 A Itroductio to Hypothei Tetig We have tudied cofidece iterval for a while ow. Thee are method that allow
More informationSOLUTION: The 95% confidence interval for the population mean µ is x ± t 0.025; 49
C22.0103 Sprig 2011 Homework 7 olutio 1. Baed o a ample of 50 x-value havig mea 35.36 ad tadard deviatio 4.26, fid a 95% cofidece iterval for the populatio mea. SOLUTION: The 95% cofidece iterval for the
More informationx z Increasing the size of the sample increases the power (reduces the probability of a Type II error) when the significance level remains fixed.
] z-tet for the mea, μ If the P-value i a mall or maller tha a pecified value, the data are tatitically igificat at igificace level. Sigificace tet for the hypothei H 0: = 0 cocerig the ukow mea of a populatio
More informationM227 Chapter 9 Section 1 Testing Two Parameters: Means, Variances, Proportions
M7 Chapter 9 Sectio 1 OBJECTIVES Tet two mea with idepedet ample whe populatio variace are kow. Tet two variace with idepedet ample. Tet two mea with idepedet ample whe populatio variace are equal Tet
More informationVIII. Interval Estimation A. A Few Important Definitions (Including Some Reminders)
VIII. Iterval Etimatio A. A Few Importat Defiitio (Icludig Some Remider) 1. Poit Etimate - a igle umerical value ued a a etimate of a parameter.. Poit Etimator - the ample tatitic that provide the poit
More information20. CONFIDENCE INTERVALS FOR THE MEAN, UNKNOWN VARIANCE
20. CONFIDENCE INTERVALS FOR THE MEAN, UNKNOWN VARIANCE If the populatio tadard deviatio σ i ukow, a it uually will be i practice, we will have to etimate it by the ample tadard deviatio. Sice σ i ukow,
More informationSTUDENT S t-distribution AND CONFIDENCE INTERVALS OF THE MEAN ( )
STUDENT S t-distribution AND CONFIDENCE INTERVALS OF THE MEAN Suppoe that we have a ample of meaured value x1, x, x3,, x of a igle uow quatity. Aumig that the meauremet are draw from a ormal ditributio
More informationTESTS OF SIGNIFICANCE
TESTS OF SIGNIFICANCE Seema Jaggi I.A.S.R.I., Library Aveue, New Delhi eema@iari.re.i I applied ivetigatio, oe i ofte itereted i comparig ome characteritic (uch a the mea, the variace or a meaure of aociatio
More informationREVIEW OF SIMPLE LINEAR REGRESSION SIMPLE LINEAR REGRESSION
REVIEW OF SIMPLE LINEAR REGRESSION SIMPLE LINEAR REGRESSION I liear regreio, we coider the frequecy ditributio of oe variable (Y) at each of everal level of a ecod variable (X). Y i kow a the depedet variable.
More informationS T A T R a c h e l L. W e b b, P o r t l a n d S t a t e U n i v e r s i t y P a g e 1. = Population Variance
S T A T 4 - R a c h e l L. W e b b, P o r t l a d S t a t e U i v e r i t y P a g e Commo Symbol = Sample Size x = Sample Mea = Sample Stadard Deviatio = Sample Variace pˆ = Sample Proportio r = Sample
More informationStatistics and Chemical Measurements: Quantifying Uncertainty. Normal or Gaussian Distribution The Bell Curve
Statitic ad Chemical Meauremet: Quatifyig Ucertaity The bottom lie: Do we trut our reult? Should we (or ayoe ele)? Why? What i Quality Aurace? What i Quality Cotrol? Normal or Gauia Ditributio The Bell
More informationTools Hypothesis Tests
Tool Hypothei Tet The Tool meu provide acce to a Hypothei Tet procedure that calculate cofidece iterval ad perform hypothei tet for mea, variace, rate ad proportio. It i cotrolled by the dialog box how
More informationIntroEcono. Discrete RV. Continuous RV s
ItroEcoo Aoc. Prof. Poga Porchaiwiekul, Ph.D... ก ก e-mail: Poga.P@chula.ac.th Homepage: http://pioeer.chula.ac.th/~ppoga (c) Poga Porchaiwiekul, Chulalogkor Uiverity Quatitative, e.g., icome, raifall
More informationSTA 4032 Final Exam Formula Sheet
Chapter 2. Probability STA 4032 Fial Eam Formula Sheet Some Baic Probability Formula: (1) P (A B) = P (A) + P (B) P (A B). (2) P (A ) = 1 P (A) ( A i the complemet of A). (3) If S i a fiite ample pace
More information100(1 α)% confidence interval: ( x z ( sample size needed to construct a 100(1 α)% confidence interval with a margin of error of w:
Stat 400, ectio 7. Large Sample Cofidece Iterval ote by Tim Pilachowki a Large-Sample Two-ided Cofidece Iterval for a Populatio Mea ectio 7.1 redux The poit etimate for a populatio mea µ will be a ample
More informationCHAPTER 6. Confidence Intervals. 6.1 (a) y = 1269; s = 145; n = 8. The standard error of the mean is = s n = = 51.3 ng/gm.
} CHAPTER 6 Cofidece Iterval 6.1 (a) y = 1269; = 145; = 8. The tadard error of the mea i SE ȳ = = 145 8 = 51.3 g/gm. (b) y = 1269; = 145; = 30. The tadard error of the mea i ȳ = 145 = 26.5 g/gm. 30 6.2
More information18.05 Problem Set 9, Spring 2014 Solutions
18.05 Problem Set 9, Sprig 2014 Solutio Problem 1. (10 pt.) (a) We have x biomial(, θ), o E(X) =θ ad Var(X) = θ(1 θ). The rule-of-thumb variace i jut 4. So the ditributio beig plotted are biomial(250,
More informationCOMPARISONS INVOLVING TWO SAMPLE MEANS. Two-tail tests have these types of hypotheses: H A : 1 2
Tetig Hypothee COMPARISONS INVOLVING TWO SAMPLE MEANS Two type of hypothee:. H o : Null Hypothei - hypothei of o differece. or 0. H A : Alterate Hypothei hypothei of differece. or 0 Two-tail v. Oe-tail
More informationConfidence Intervals: Three Views Class 23, Jeremy Orloff and Jonathan Bloom
Cofidece Iterval: Three View Cla 23, 18.05 Jeremy Orloff ad Joatha Bloom 1 Learig Goal 1. Be able to produce z, t ad χ 2 cofidece iterval baed o the correpodig tadardized tatitic. 2. Be able to ue a hypothei
More informationUNIVERSITY OF CALICUT
Samplig Ditributio 1 UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION BSc. MATHEMATICS COMPLEMENTARY COURSE CUCBCSS 2014 Admiio oward III Semeter STATISTICAL INFERENCE Quetio Bak 1. The umber of poible
More informationStatistics 511 Additional Materials
Cofidece Itervals o mu Statistics 511 Additioal Materials This topic officially moves us from probability to statistics. We begi to discuss makig ifereces about the populatio. Oe way to differetiate probability
More informationON THE SCALE PARAMETER OF EXPONENTIAL DISTRIBUTION
Review of the Air Force Academy No. (34)/7 ON THE SCALE PARAMETER OF EXPONENTIAL DISTRIBUTION Aca Ileaa LUPAŞ Military Techical Academy, Bucharet, Romaia (lua_a@yahoo.com) DOI:.96/84-938.7.5..6 Abtract:
More information11/19/ Chapter 10 Overview. Chapter 10: Two-Sample Inference. + The Big Picture : Inference for Mean Difference Dependent Samples
/9/0 + + Chapter 0 Overview Dicoverig Statitic Eitio Daiel T. Laroe Chapter 0: Two-Sample Iferece 0. Iferece for Mea Differece Depeet Sample 0. Iferece for Two Iepeet Mea 0.3 Iferece for Two Iepeet Proportio
More informationConfidence Intervals. Confidence Intervals
A overview Mot probability ditributio are idexed by oe me parameter. F example, N(µ,σ 2 ) B(, p). I igificace tet, we have ued poit etimat f parameter. F example, f iid Y 1,Y 2,...,Y N(µ,σ 2 ), Ȳ i a poit
More informationInterval Estimation (Confidence Interval = C.I.): An interval estimate of some population parameter is an interval of the form (, ),
Cofidece Iterval Estimatio Problems Suppose we have a populatio with some ukow parameter(s). Example: Normal(,) ad are parameters. We eed to draw coclusios (make ifereces) about the ukow parameters. We
More informationChapter 8.2. Interval Estimation
Chapter 8.2. Iterval Etimatio Baic of Cofidece Iterval ad Large Sample Cofidece Iterval 1 Baic Propertie of Cofidece Iterval Aumptio: X 1, X 2,, X are from Normal ditributio with a mea of µ ad tadard deviatio.
More informationBIOS 4110: Introduction to Biostatistics. Breheny. Lab #9
BIOS 4110: Itroductio to Biostatistics Brehey Lab #9 The Cetral Limit Theorem is very importat i the realm of statistics, ad today's lab will explore the applicatio of it i both categorical ad cotiuous
More informationEstimation Theory. goavendaño. Estimation Theory
Etimatio Theory Statitical Iferece method by which geeralizatio are made about a populatio Two Major Area of Statitical Iferece. Etimatio a parameter i etablihed baed o the amplig ditributio of a proportio,
More informationStatistics Parameters
Saplig Ditributio & Cofidece Iterval Etiator Statitical Iferece Etiatio Tetig Hypothei Statitic Ued to Etiate Populatio Paraeter Statitic Saple Mea, Saple Variace, Saple Proportio, Paraeter populatio ea
More informationTables and Formulas for Sullivan, Fundamentals of Statistics, 2e Pearson Education, Inc.
Table ad Formula for Sulliva, Fudametal of Statitic, e. 008 Pearo Educatio, Ic. CHAPTER Orgaizig ad Summarizig Data Relative frequecy frequecy um of all frequecie Cla midpoit: The um of coecutive lower
More informationMTH 212 Formulas page 1 out of 7. Sample variance: s = Sample standard deviation: s = s
MTH Formula age out of 7 DESCRIPTIVE TOOLS Poulatio ize = N Samle ize = x x+ x +... + x x Poulatio mea: µ = Samle mea: x = = N ( µ ) ( x x) Poulatio variace: = Samle variace: = N Poulatio tadard deviatio:
More informationMathacle PSet Stats, Confidence Intervals and Estimation Level Number Name: Date: Unbiased Estimators So we don t have favorite.
PSet ----- Stat, Cofidece Iterval ad Etimatio Ubiaed Etimator So we do t have favorite. IV. CONFIDENCE INTERVAL AND ESTIMATION 4.1. Sigificat Level ad Critical Value z ad The igificat level, ofte deoted
More informationFormula Sheet. December 8, 2011
Formula Sheet December 8, 2011 Abtract I type thi for your coveice. There may be error. Ue at your ow rik. It i your repoible to check it i correct or ot before uig it. 1 Decriptive Statitic 1.1 Cetral
More informationTI-83/84 Calculator Instructions for Math Elementary Statistics
TI-83/84 Calculator Itructio for Math 34- Elemetary Statitic. Eterig Data: Data oit are tored i Lit o the TI-83/84. If you have't ued the calculator before, you may wat to erae everythig that wa there.
More informationm = Statistical Inference Estimators Sampling Distribution of Mean (Parameters) Sampling Distribution s = Sampling Distribution & Confidence Interval
Saplig Ditributio & Cofidece Iterval Uivariate Aalyi for a Nueric Variable (or a Nueric Populatio) Statitical Iferece Etiatio Tetig Hypothei Weight N ( =?, =?) 1 Uivariate Aalyi for a Categorical Variable
More informationChapter 8: Estimating with Confidence
Chapter 8: Estimatig with Cofidece Sectio 8.2 The Practice of Statistics, 4 th editio For AP* STARNES, YATES, MOORE Chapter 8 Estimatig with Cofidece 8.1 Cofidece Itervals: The Basics 8.2 8.3 Estimatig
More informationTopic 9: Sampling Distributions of Estimators
Topic 9: Samplig Distributios of Estimators Course 003, 2016 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be
More informationFig. 1: Streamline coordinates
1 Equatio of Motio i Streamlie Coordiate Ai A. Soi, MIT 2.25 Advaced Fluid Mechaic Euler equatio expree the relatiohip betwee the velocity ad the preure field i ivicid flow. Writte i term of treamlie coordiate,
More informationChapter 9: Hypothesis Testing
Chapter 9: Hypothei Tetig Chapter 5 dicued the cocept of amplig ditributio ad Chapter 8 dicued how populatio parameter ca be etimated from a ample. 9. Baic cocept Hypothei Tetig We begi by makig a tatemet,
More informationDifference tests (1): parametric
NST B Eperimetal Pychology Statitic practical Differece tet (): parametric Rudolf Cardial & Mike Aitke / 3 December 003; Departmet of Eperimetal Pychology Uiverity of Cambridge Hadout: Awer to Eample (from
More informationIsolated Word Recogniser
Lecture 5 Iolated Word Recogitio Hidde Markov Model of peech State traitio ad aligmet probabilitie Searchig all poible aligmet Dyamic Programmig Viterbi Aligmet Iolated Word Recogitio 8. Iolated Word Recogier
More informationStat 3411 Spring 2011 Assignment 6 Answers
Stat 3411 Sprig 2011 Aigmet 6 Awer (A) Awer are give i 10 3 cycle (a) 149.1 to 187.5 Sice 150 i i the 90% 2-ided cofidece iterval, we do ot reject H 0 : µ 150 v i favor of the 2-ided alterative H a : µ
More informationOverview. p 2. Chapter 9. Pooled Estimate of. q = 1 p. Notation for Two Proportions. Inferences about Two Proportions. Assumptions
Chapter 9 Slide Ifereces from Two Samples 9- Overview 9- Ifereces about Two Proportios 9- Ifereces about Two Meas: Idepedet Samples 9-4 Ifereces about Matched Pairs 9-5 Comparig Variatio i Two Samples
More informationStatistical Equations
Statitical Equatio You are permitted to ue the iformatio o thee page durig your eam. Thee page are ot guarateed to cotai all the iformatio you will eed. If you fid iformatio which you believe hould be
More informationHomework 5 Solutions
Homework 5 Solutios p329 # 12 No. To estimate the chace you eed the expected value ad stadard error. To do get the expected value you eed the average of the box ad to get the stadard error you eed the
More informationTopic 9: Sampling Distributions of Estimators
Topic 9: Samplig Distributios of Estimators Course 003, 2018 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be
More informationStatistical Intervals Based on a Single Sample (Devore Chapter Seven)
Statitical Iterval Baed o a Sigle Sample Devore Chapter Seve MATH-252-01: robability ad Statitic II Sprig 2018 Cotet 0 Itroductio 1 0.1 Motivatio...................... 1 0.2 Remider of Notatio................
More informationCONFIDENCE INTERVALS STUDY GUIDE
CONFIDENCE INTERVALS STUDY UIDE Last uit, we discussed how sample statistics vary. Uder the right coditios, sample statistics like meas ad proportios follow a Normal distributio, which allows us to calculate
More informationElementary Statistics
Two Samle Mea Cha08 Dr. Ghamary Page Elemetary Statitic M. Ghamary, Ph.D. Chater 8 Tet of Hyothei a Cofiece Iterval for Two Samle Two Samle Mea Cha08 Dr. Ghamary Page Tet of Hyothei for Two amle: A Statitical
More informationChapter 8 Part 2. Unpaired t-test With Equal Variances With Unequal Variances
Chapter 8 Part Upaired t-tet With Equal Variace With Uequal Variace December, 008 Goal: To eplai that the choice of the two ample t-tet deped o whether the ample are depedet or idepedet ad for the idepedet
More informationExam II Covers. STA 291 Lecture 19. Exam II Next Tuesday 5-7pm Memorial Hall (Same place as exam I) Makeup Exam 7:15pm 9:15pm Location CB 234
STA 291 Lecture 19 Exam II Next Tuesday 5-7pm Memorial Hall (Same place as exam I) Makeup Exam 7:15pm 9:15pm Locatio CB 234 STA 291 - Lecture 19 1 Exam II Covers Chapter 9 10.1; 10.2; 10.3; 10.4; 10.6
More informationTopic 9: Sampling Distributions of Estimators
Topic 9: Samplig Distributios of Estimators Course 003, 2018 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be
More informationChapter 22. Comparing Two Proportions. Copyright 2010, 2007, 2004 Pearson Education, Inc.
Chapter 22 Comparig Two Proportios Copyright 2010, 2007, 2004 Pearso Educatio, Ic. Comparig Two Proportios Read the first two paragraphs of pg 504. Comparisos betwee two percetages are much more commo
More informationChapter 22. Comparing Two Proportions. Copyright 2010 Pearson Education, Inc.
Chapter 22 Comparig Two Proportios Copyright 2010 Pearso Educatio, Ic. Comparig Two Proportios Comparisos betwee two percetages are much more commo tha questios about isolated percetages. Ad they are more
More informationLECTURE 13 SIMULTANEOUS EQUATIONS
NOVEMBER 5, 26 Demad-upply ytem LETURE 3 SIMULTNEOUS EQUTIONS I thi lecture, we dicu edogeeity problem that arie due to imultaeity, i.e. the left-had ide variable ad ome of the right-had ide variable are
More informationSTA Learning Objectives. Population Proportions. Module 10 Comparing Two Proportions. Upon completing this module, you should be able to:
STA 2023 Module 10 Comparig Two Proportios Learig Objectives Upo completig this module, you should be able to: 1. Perform large-sample ifereces (hypothesis test ad cofidece itervals) to compare two populatio
More informationMBACATÓLICA. Quantitative Methods. Faculdade de Ciências Económicas e Empresariais UNIVERSIDADE CATÓLICA PORTUGUESA 9. SAMPLING DISTRIBUTIONS
MBACATÓLICA Quatitative Methods Miguel Gouveia Mauel Leite Moteiro Faculdade de Ciêcias Ecoómicas e Empresariais UNIVERSIDADE CATÓLICA PORTUGUESA 9. SAMPLING DISTRIBUTIONS MBACatólica 006/07 Métodos Quatitativos
More information7-1. Chapter 4. Part I. Sampling Distributions and Confidence Intervals
7-1 Chapter 4 Part I. Samplig Distributios ad Cofidece Itervals 1 7- Sectio 1. Samplig Distributio 7-3 Usig Statistics Statistical Iferece: Predict ad forecast values of populatio parameters... Test hypotheses
More informationStatistical treatment of test results
SCAN-G :07 Revied 007 Pulp, paper ad board Statitical treatmet of tet reult 0 Itroductio The value of tatitical method lie i the fact that they make it poible to iterpret tet reult accordig to trictly
More informationHYPOTHESIS TESTS FOR ONE POPULATION MEAN WORKSHEET MTH 1210, FALL 2018
HYPOTHESIS TESTS FOR ONE POPULATION MEAN WORKSHEET MTH 1210, FALL 2018 We are resposible for 2 types of hypothesis tests that produce ifereces about the ukow populatio mea, µ, each of which has 3 possible
More informationMATH/STAT 352: Lecture 15
MATH/STAT 352: Lecture 15 Sectios 5.2 ad 5.3. Large sample CI for a proportio ad small sample CI for a mea. 1 5.2: Cofidece Iterval for a Proportio Estimatig proportio of successes i a biomial experimet
More information1 Inferential Methods for Correlation and Regression Analysis
1 Iferetial Methods for Correlatio ad Regressio Aalysis I the chapter o Correlatio ad Regressio Aalysis tools for describig bivariate cotiuous data were itroduced. The sample Pearso Correlatio Coefficiet
More informationInferential Statistics. Inference Process. Inferential Statistics and Probability a Holistic Approach. Inference Process.
Iferetial Statistics ad Probability a Holistic Approach Iferece Process Chapter 8 Poit Estimatio ad Cofidece Itervals This Course Material by Maurice Geraghty is licesed uder a Creative Commos Attributio-ShareAlike
More informationStatistical Inference for Two Samples. Applied Statistics and Probability for Engineers. Chapter 10 Statistical Inference for Two Samples
4/3/6 Applied Statitic ad Probability for Egieer Sixth Editio Dougla C. Motgomery George C. Ruger Chapter Statitical Iferece for Two Sample Copyright 4 Joh Wiley & So, Ic. All right reerved. CHAPTER OUTLINE
More informationStatistical Inference (Chapter 10) Statistical inference = learn about a population based on the information provided by a sample.
Statistical Iferece (Chapter 10) Statistical iferece = lear about a populatio based o the iformatio provided by a sample. Populatio: The set of all values of a radom variable X of iterest. Characterized
More informationMATHEMATICS LW Quantitative Methods II Martin Huard Friday April 26, 2013 TEST # 4 SOLUTIONS
ATHATICS 360-55-L Quatitative ethod II arti Huard Friday April 6, 013 TST # 4 SOLUTIONS Name: Awer all quetio ad how all your work. Quetio 1 (10 poit) To oberve the effect drikig a Red Bull ha o cocetratio,
More informationRead through these prior to coming to the test and follow them when you take your test.
Math 143 Sprig 2012 Test 2 Iformatio 1 Test 2 will be give i class o Thursday April 5. Material Covered The test is cummulative, but will emphasize the recet material (Chapters 6 8, 10 11, ad Sectios 12.1
More informationA quick activity - Central Limit Theorem and Proportions. Lecture 21: Testing Proportions. Results from the GSS. Statistics and the General Population
A quick activity - Cetral Limit Theorem ad Proportios Lecture 21: Testig Proportios Statistics 10 Coli Rudel Flip a coi 30 times this is goig to get loud! Record the umber of heads you obtaied ad calculate
More information- E < p. ˆ p q ˆ E = q ˆ = 1 - p ˆ = sample proportion of x failures in a sample size of n. where. x n sample proportion. population proportion
1 Chapter 7 ad 8 Review for Exam Chapter 7 Estimates ad Sample Sizes 2 Defiitio Cofidece Iterval (or Iterval Estimate) a rage (or a iterval) of values used to estimate the true value of the populatio parameter
More information10-716: Advanced Machine Learning Spring Lecture 13: March 5
10-716: Advaced Machie Learig Sprig 019 Lecture 13: March 5 Lecturer: Pradeep Ravikumar Scribe: Charvi Ratogi, Hele Zhou, Nicholay opi Note: Lae template courtey of UC Berkeley EECS dept. Diclaimer: hee
More informationChem Exam 1-9/14/16. Frequency. Grade Average = 72, Median = 72, s = 20
0 4 8 6 0 4 8 3 36 40 44 48 5 56 60 64 68 7 76 80 84 88 9 96 00 Chem 53 - Exam - 9/4/6 8 7 6 5 4 3 Frequecy 0 Grade Average = 7, Media = 7, = 0 Exam Chem 53 September 4, 065 Quetio, 7 poit each for quetio
More informationStatistical Intervals for a Single Sample
3/5/06 Applied Statistics ad Probability for Egieers Sixth Editio Douglas C. Motgomery George C. Ruger Chapter 8 Statistical Itervals for a Sigle Sample 8 CHAPTER OUTLINE 8- Cofidece Iterval o the Mea
More information2 1. The r.s., of size n2, from population 2 will be. 2 and 2. 2) The two populations are independent. This implies that all of the n1 n2
Chapter 8 Comparig Two Treatmets Iferece about Two Populatio Meas We wat to compare the meas of two populatios to see whether they differ. There are two situatios to cosider, as show i the followig examples:
More informationStat 421-SP2012 Interval Estimation Section
Stat 41-SP01 Iterval Estimatio Sectio 11.1-11. We ow uderstad (Chapter 10) how to fid poit estimators of a ukow parameter. o However, a poit estimate does ot provide ay iformatio about the ucertaity (possible
More informationChapter 6 Sampling Distributions
Chapter 6 Samplig Distributios 1 I most experimets, we have more tha oe measuremet for ay give variable, each measuremet beig associated with oe radomly selected a member of a populatio. Hece we eed to
More informationData Analysis and Statistical Methods Statistics 651
Data Aalysis ad Statistical Methods Statistics 651 http://www.stat.tamu.edu/~suhasii/teachig.html Suhasii Subba Rao Review of testig: Example The admistrator of a ursig home wats to do a time ad motio
More informationSection 9.2. Tests About a Population Proportion 12/17/2014. Carrying Out a Significance Test H A N T. Parameters & Hypothesis
Sectio 9.2 Tests About a Populatio Proportio P H A N T O M S Parameters Hypothesis Assess Coditios Name the Test Test Statistic (Calculate) Obtai P value Make a decisio State coclusio Sectio 9.2 Tests
More informationConfidence Interval for one population mean or one population proportion, continued. 1. Sample size estimation based on the large sample C.I.
Cofidece Iterval for oe populatio mea or oe populatio proportio, cotiued 1. ample size estimatio based o the large sample C.I. for p ˆ(1 ˆ) ˆ(1 ˆ) From the iterval ˆ p p Z p ˆ, p Z p p L legh of your 100(1
More informationThis is an introductory course in Analysis of Variance and Design of Experiments.
1 Notes for M 384E, Wedesday, Jauary 21, 2009 (Please ote: I will ot pass out hard-copy class otes i future classes. If there are writte class otes, they will be posted o the web by the ight before class
More informationStatistics Problem Set - modified July 25, _. d Q w. i n
Statitic Problem Set - modified July 5, 04 x i x i i x i _ x x _ t d Q w F x x t pooled calculated pooled. f d x x t calculated / /.. f d Kow cocept of Gauia Curve Sytematic Error Idetermiate Error t-tet
More information(7 One- and Two-Sample Estimation Problem )
34 Stat Lecture Notes (7 Oe- ad Two-Sample Estimatio Problem ) ( Book*: Chapter 8,pg65) Probability& Statistics for Egieers & Scietists By Walpole, Myers, Myers, Ye Estimatio 1 ) ( ˆ S P i i Poit estimate:
More informationWorking with Two Populations. Comparing Two Means
Workig with Two Populatios Comparig Two Meas Coditios for Two-Sample Iferece The data are from two radom samples from two distict idepedet populatios. Normality. Two sample t procedures are more robust
More informationBig Picture. 5. Data, Estimates, and Models: quantifying the accuracy of estimates.
5. Data, Estimates, ad Models: quatifyig the accuracy of estimates. 5. Estimatig a Normal Mea 5.2 The Distributio of the Normal Sample Mea 5.3 Normal data, cofidece iterval for, kow 5.4 Normal data, cofidece
More informationQuestions about the Assignment. Describing Data: Distributions and Relationships. Measures of Spread Standard Deviation. One Quantitative Variable
Quetio about the Aigmet Read the quetio ad awer the quetio that are aked Experimet elimiate cofoudig variable Decribig Data: Ditributio ad Relatiohip GSS people attitude veru their characteritic ad poue
More informationCommon Large/Small Sample Tests 1/55
Commo Large/Small Sample Tests 1/55 Test of Hypothesis for the Mea (σ Kow) Covert sample result ( x) to a z value Hypothesis Tests for µ Cosider the test H :μ = μ H 1 :μ > μ σ Kow (Assume the populatio
More informationChapter 6 Part 5. Confidence Intervals t distribution chi square distribution. October 23, 2008
Chapter 6 Part 5 Cofidece Itervals t distributio chi square distributio October 23, 2008 The will be o help sessio o Moday, October 27. Goal: To clearly uderstad the lik betwee probability ad cofidece
More informationCH19 Confidence Intervals for Proportions. Confidence intervals Construct confidence intervals for population proportions
CH19 Cofidece Itervals for Proportios Cofidece itervals Costruct cofidece itervals for populatio proportios Motivatio Motivatio We are iterested i the populatio proportio who support Mr. Obama. This sample
More informationChapter 1 Econometrics
Chapter Ecoometric There are o exercie or applicatio i Chapter. 0 Pearo Educatio, Ic. Publihig a Pretice Hall Chapter The Liear Regreio Model There are o exercie or applicatio i Chapter. 0 Pearo Educatio,
More informationLecture 5. Materials Covered: Chapter 6 Suggested Exercises: 6.7, 6.9, 6.17, 6.20, 6.21, 6.41, 6.49, 6.52, 6.53, 6.62, 6.63.
STT 315, Summer 006 Lecture 5 Materials Covered: Chapter 6 Suggested Exercises: 67, 69, 617, 60, 61, 641, 649, 65, 653, 66, 663 1 Defiitios Cofidece Iterval: A cofidece iterval is a iterval believed to
More informationWidely used? average out effect Discrete Prior. Examplep. More than one observation. using MVUE (sample mean) yy 1 = 3.2, y 2 =2.2, y 3 =3.6, y 4 =4.
Dicrete Prior for (μ Widely ued? average out effect Dicrete Prior populatio td i kow equally likely or ubjective weight π ( μ y ~ π ( μ l( y μ π ( μ e Examplep ( μ y Set a ubjective prior ad a gueig value
More informationSociété de Calcul Mathématique, S. A. Algorithmes et Optimisation
Société de Calcul Mathématique S A Algorithme et Optimiatio Radom amplig of proportio Berard Beauzamy Jue 2008 From time to time we fid a problem i which we do ot deal with value but with proportio For
More informationRule of probability. Let A and B be two events (sets of elementary events). 11. If P (AB) = P (A)P (B), then A and B are independent.
Percetile: the αth percetile of a populatio is the value x 0, such that P (X x 0 ) α% For example the 5th is the x 0, such that P (X x 0 ) 5% 05 Rule of probability Let A ad B be two evets (sets of elemetary
More informationReaction Time VS. Drug Percentage Subject Amount of Drug Times % Reaction Time in Seconds 1 Mary John Carl Sara William 5 4
CHAPTER Smple Lear Regreo EXAMPLE A expermet volvg fve ubject coducted to determe the relatohp betwee the percetage of a certa drug the bloodtream ad the legth of tme t take the ubject to react to a tmulu.
More informationEstimation of a population proportion March 23,
1 Social Studies 201 Notes for March 23, 2005 Estimatio of a populatio proportio Sectio 8.5, p. 521. For the most part, we have dealt with meas ad stadard deviatios this semester. This sectio of the otes
More informationLESSON 20: HYPOTHESIS TESTING
LESSN 20: YPTESIS TESTING utlie ypothesis testig Tests for the mea Tests for the proportio 1 YPTESIS TESTING TE CNTEXT Example 1: supervisor of a productio lie wats to determie if the productio time of
More informationConfidence Intervals for the Population Proportion p
Cofidece Itervals for the Populatio Proportio p The cocept of cofidece itervals for the populatio proportio p is the same as the oe for, the samplig distributio of the mea, x. The structure is idetical:
More informationBelow are the following formulas for the z-scores section.
Statitic 010: Statitic for the Social ad Behavioral Sciece Formula Hadout Below are the followig formula for the z-core ectio. eaure of cetral tedecy ad variability ea Rage Rage = highet lowet Variace
More informationEstimating the Population Mean - when a sample average is calculated we can create an interval centered on this average
6. Cofidece Iterval for the Populatio Mea p58 Estimatig the Populatio Mea - whe a sample average is calculated we ca create a iterval cetered o this average x-bar - at a predetermied level of cofidece
More informationt distribution [34] : used to test a mean against an hypothesized value (H 0 : µ = µ 0 ) or the difference
EXST30 Backgroud material Page From the textbook The Statistical Sleuth Mea [0]: I your text the word mea deotes a populatio mea (µ) while the work average deotes a sample average ( ). Variace [0]: The
More information