Chapter 20. Comparing Two Proportions. BPS - 5th Ed. Chapter 20 1
|
|
- Charla Bailey
- 5 years ago
- Views:
Transcription
1 Chapter 0 Comparig Two Proportios BPS - 5th Ed. Chapter 0
2 Case Study Machie Reliability A study is performed to test of the reliability of products produced by two machies. Machie A produced 8 defective parts i a ru of 40, while machie B produced 0 defective parts i a ru of 00. Defects Machie A 40 8 Machie B 00 BPS - 5th Ed. Chapter 0
3 Two-Sample Problems The goal of iferece is to compare the resposes to two treatmets or to compare the characteristics of two populatios. We have a separate sample from each treatmet or each populatio. The uits are ot matched, ad the samples ca be of differig sizes. BPS - 5th Ed. Chapter 0 3
4 Case Study Machie Reliability A study is performed to test of the reliability of products produced by two machies. Machie A produced 8 defective parts i a ru of 40, while machie B produced 0 defective parts i a ru of 00. This is a example of whe to use the two-proportio z procedures. Defects Machie A 40 8 Machie B 00 BPS - 5th Ed. Chapter 0 4
5 Iferece about the Differece p p Simple Coditios The differece i the populatio proportios is estimated by the differece i the sample proportios: ˆ p Whe both of the samples are large, the samplig distributio of this differece is approximately Normal with mea p p ad stadard deviatio p ( ) ( ) p p p + BPS - 5th Ed. Chapter 0 5
6 Iferece about the Differece p p Samplig Distributio BPS - 5th Ed. Chapter 0 6
7 Stadard Error Sice the populatio proportios p ad p are ukow, the stadard deviatio of the differece i sample proportios will eed to be estimated by substitutig ad for p ad p : SE = ( ) ( ) + BPS - 5th Ed. Chapter 0 7
8 BPS - 5th Ed. Chapter 0 8
9 ( ) ± z Case Study: Reliability Compute a 90% cofidece iterval for the differece i reliabilities (as measured by proportio of defectives) for the two machies. Cofidece Iterval ( ) ( ) + 8 = ± = 0.00± = to We are 90% cofidet that the differece i proportio of defectives for the two machies is betwee -3.97% ad 4.39%. Sice 0 is i this iterval, it is ulikely that the two machies differ i reliability. + BPS - 5th Ed. Chapter 0 9
10 Adjustmet to Cofidece Iterval Plus Four Cofidece Iterval for p p The stadard cofidece iterval approach yields ustable or erratic ifereces. By addig four imagiary observatios (oe success ad oe failure to each sample), the ifereces ca be stabilized. This leads to more accurate iferece of the differece of the populatio proportios. BPS - 5th Ed. Chapter 0 0
11 Adjustmet to Cofidece Iterval Plus Four Cofidece Iterval for p p Add 4 imagiary observatios, oe success ad oe failure to each sample. Compute the plus four proportios. umber of successes + p ~ = ~ umber of successes p = + + Use the plus four proportios i the formula. ~ ( ) ( ) ( ) ~ ~ ~ ~ p p p p p ~ p ± z BPS - 5th Ed. Chapter 0
12 Case Study: Reliability Plus Four 90% Cofidece Iterval ~ p ( ~ p ~ p ) = = ± z ~ p 9 4 ( ~ p ) ~ p ( ~ p ) ~ p 9 = ± = ± = to = = (This is more accurate.) 0 We are 90% cofidet that the differece i proportio of defectives for the two machies is betwee -3.94% ad 4.74%. Sice 0 is i this iterval, it is ulikely that the two machies differ i reliability. BPS - 5th Ed. Chapter 0
13 The Hypotheses for Testig Two Proportios Null: H 0 : p = p Oe sided alteratives H a : p > p H a : p < p Two sided alterative H a : p p BPS - 5th Ed. Chapter 0 3
14 Pooled Sample Proportio If H 0 is true (p =p ), the the two proportios are equal to some commo value p. Istead of estimatig p ad p separately, we will combie or pool the sample iformatio to estimate p. This combied or pooled estimate is called the pooled sample proportio, ad we will use it i place of each of the sample proportios i the expressio for the stadard error SE. = total umber of successes i both samples total umber of observatios i both samples pooled sample proportio BPS - 5th Ed. Chapter 0 4
15 Test Statistic for Two Proportios Use the pooled sample proportio i place of each of the idividual sample proportios i the expressio for the stadard error SE i the test statistic: z = ( ) ( ) + z z = = ( ) ( ) + ( ) + BPS - 5th Ed. Chapter 0 5
16 P-value for Testig Two Proportios H a : p > p P-value is the probability of gettig a value as large or larger tha the observed test statistic (z) value. H a : p < p P-value is the probability of gettig a value as small or smaller tha the observed test statistic (z) value. H a : p p P-value is two times the probability of gettig a value as large or larger tha the absolute value of the observed test statistic (z) value. BPS - 5th Ed. Chapter 0 6
17 BPS - 5th Ed. Chapter 0 7
18 Case Study Summer Jobs A uiversity fiacial aid office polled a simple radom sample of udergraduate studets to study their summer employmet. Not all studets were employed the previous summer. Here are the results: Summer Status Me Wome Employed Not Employed Total Is there evidece that the proportio of male studets who had summer jobs differs from the proportio of female studets who had summer jobs. BPS - 5th Ed. Chapter 0 8
19 Case Study: Summer Jobs The Hypotheses Null: The proportio of male studets who had summer jobs is the same as the proportio of female studets who had summer jobs. [H 0 : p = p ] Alt: The proportio of male studets who had summer jobs differs from the proportio of female studets who had summer jobs. [H a : p p ] BPS - 5th Ed. Chapter 0 9
20 Case Study: Summer Jobs Test Statistic = 797 ad = 73 (both large, so test statistic follows a Normal distributio) Pooled sample proportio: = = stadardized score (test statistic): z = = BPS - 5th Ed. Chapter 0 0
21 Case Study: Summer Jobs. Hypotheses: H 0 : p = p H a : p p. Test Statistic: P-value: P-value = P(Z > 5.07) = (usig a computer) P-value = P(Z > 5.07) < ( ) = (Table A) [sice 5.07 > 3.49 (the largest z-value i the table)] 4. Coclusio: z = = Sice the P-value is smaller tha α = 0.00, there is very strog evidece that the proportio of male studets who had summer jobs differs from that of female studets. BPS - 5th Ed. Chapter 0
Chapter 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 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 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 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 informationSuccessful HE applicants. Information sheet A Number of applicants. Gender Applicants Accepts Applicants Accepts. Age. Domicile
Successful HE applicats Sigificace tests use data from samples to test hypotheses. You will use data o successful applicatios for courses i higher educatio to aswer questios about proportios, for example,
More informationThis chapter focuses on two experimental designs that are crucial to comparative studies: (1) independent samples and (2) matched pair samples.
Chapter 9 & : Comparig Two Treatmets: This chapter focuses o two eperimetal desigs that are crucial to comparative studies: () idepedet samples ad () matched pair samples Idepedet Radom amples from Two
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 informationTABLES AND FORMULAS FOR MOORE Basic Practice of Statistics
TABLES AND FORMULAS FOR MOORE Basic Practice of Statistics Explorig Data: Distributios Look for overall patter (shape, ceter, spread) ad deviatios (outliers). Mea (use a calculator): x = x 1 + x 2 + +
More informationTABLES AND FORMULAS FOR MOORE Basic Practice of Statistics
TABLES AND FORMULAS FOR MOORE Basic Practice of Statistics Explorig Data: Distributios Look for overall patter (shape, ceter, spread) ad deviatios (outliers). Mea (use a calculator): x = x 1 + x 2 + +
More informationSample Size Determination (Two or More Samples)
Sample Sie Determiatio (Two or More Samples) STATGRAPHICS Rev. 963 Summary... Data Iput... Aalysis Summary... 5 Power Curve... 5 Calculatios... 6 Summary This procedure determies a suitable sample sie
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 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 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 informationComparing Two Populations. Topic 15 - Two Sample Inference I. Comparing Two Means. Comparing Two Pop Means. Background Reading
Topic 15 - Two Sample Iferece I STAT 511 Professor Bruce Craig Comparig Two Populatios Research ofte ivolves the compariso of two or more samples from differet populatios Graphical summaries provide visual
More informationMOST PEOPLE WOULD RATHER LIVE WITH A PROBLEM THEY CAN'T SOLVE, THAN ACCEPT A SOLUTION THEY CAN'T UNDERSTAND.
XI-1 (1074) MOST PEOPLE WOULD RATHER LIVE WITH A PROBLEM THEY CAN'T SOLVE, THAN ACCEPT A SOLUTION THEY CAN'T UNDERSTAND. R. E. D. WOOLSEY AND H. S. SWANSON XI-2 (1075) STATISTICAL DECISION MAKING Advaced
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 informationClass 27. Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science. Marquette University MATH 1700
Class 7 Daiel B. Rowe, Ph.D. Departmet of Mathematics, Statistics, ad Computer Sciece Copyright 013 by D.B. Rowe 1 Ageda: Skip Recap Chapter 10.5 ad 10.6 Lecture Chapter 11.1-11. Review Chapters 9 ad 10
More informationAgreement of CI and HT. Lecture 13 - Tests of Proportions. Example - Waiting Times
Sigificace level vs. cofidece level Agreemet of CI ad HT Lecture 13 - Tests of Proportios Sta102 / BME102 Coli Rudel October 15, 2014 Cofidece itervals ad hypothesis tests (almost) always agree, as log
More informationSTATISTICAL INFERENCE
STATISTICAL INFERENCE POPULATION AND SAMPLE Populatio = all elemets of iterest Characterized by a distributio F with some parameter θ Sample = the data X 1,..., X, selected subset of the populatio = sample
More informationFinal Examination Solutions 17/6/2010
The Islamic Uiversity of Gaza Faculty of Commerce epartmet of Ecoomics ad Political Scieces A Itroductio to Statistics Course (ECOE 30) Sprig Semester 009-00 Fial Eamiatio Solutios 7/6/00 Name: I: Istructor:
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 informationENGI 4421 Confidence Intervals (Two Samples) Page 12-01
ENGI 44 Cofidece Itervals (Two Samples) Page -0 Two Sample Cofidece Iterval for a Differece i Populatio Meas [Navidi sectios 5.4-5.7; Devore chapter 9] From the cetral limit theorem, we kow that, for sufficietly
More informationStatistical Inference About Means and Proportions With Two Populations
Departmet of Quatitative Methods & Iformatio Systems Itroductio to Busiess Statistics QM 220 Chapter 10 Statistical Iferece About Meas ad Proportios With Two Populatios Fall 2010 Dr. Mohammad Zaial 1 Chapter
More informationDescribing the Relation between Two Variables
Copyright 010 Pearso Educatio, Ic. Tables ad Formulas for Sulliva, Statistics: Iformed Decisios Usig Data 010 Pearso Educatio, Ic Chapter Orgaizig ad Summarizig Data Relative frequecy = frequecy sum of
More informationSTAT 155 Introductory Statistics Chapter 6: Introduction to Inference. Lecture 18: Estimation with Confidence
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STAT 155 Itroductory Statistics Chapter 6: Itroductio to Iferece Lecture 18: Estimatio with Cofidece 11/14/06 Lecture 18 1 Itroductio Statistical Iferece
More informationStat 200 -Testing Summary Page 1
Stat 00 -Testig Summary Page 1 Mathematicias are like Frechme; whatever you say to them, they traslate it ito their ow laguage ad forthwith it is somethig etirely differet Goethe 1 Large Sample Cofidece
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 information1 Constructing and Interpreting a Confidence Interval
Itroductory Applied Ecoometrics EEP/IAS 118 Sprig 2014 WARM UP: Match the terms i the table with the correct formula: Adrew Crae-Droesch Sectio #6 5 March 2014 ˆ Let X be a radom variable with mea µ ad
More informationStatistics. Chapter 10 Two-Sample Tests. Copyright 2013 Pearson Education, Inc. publishing as Prentice Hall. Chap 10-1
Statistics Chapter 0 Two-Sample Tests Copyright 03 Pearso Educatio, Ic. publishig as Pretice Hall Chap 0- Learig Objectives I this chapter, you lear How to use hypothesis testig for comparig the differece
More informationExpectation and Variance of a random variable
Chapter 11 Expectatio ad Variace of a radom variable The aim of this lecture is to defie ad itroduce mathematical Expectatio ad variace of a fuctio of discrete & cotiuous radom variables ad the distributio
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 informationEconomics Spring 2015
1 Ecoomics 400 -- Sprig 015 /17/015 pp. 30-38; Ch. 7.1.4-7. New Stata Assigmet ad ew MyStatlab assigmet, both due Feb 4th Midterm Exam Thursday Feb 6th, Chapters 1-7 of Groeber text ad all relevat lectures
More informationChapter 1 (Definitions)
FINAL EXAM REVIEW Chapter 1 (Defiitios) Qualitative: Nomial: Ordial: Quatitative: Ordial: Iterval: Ratio: Observatioal Study: Desiged Experimet: Samplig: Cluster: Stratified: Systematic: Coveiece: Simple
More informationProperties and Hypothesis Testing
Chapter 3 Properties ad Hypothesis Testig 3.1 Types of data The regressio techiques developed i previous chapters ca be applied to three differet kids of data. 1. Cross-sectioal data. 2. Time series data.
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 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 informationChapters 5 and 13: REGRESSION AND CORRELATION. Univariate data: x, Bivariate data (x,y).
Chapters 5 ad 13: REGREION AND CORRELATION (ectios 5.5 ad 13.5 are omitted) Uivariate data: x, Bivariate data (x,y). Example: x: umber of years studets studied paish y: score o a proficiecy test For each
More informationSampling Error. Chapter 6 Student Lecture Notes 6-1. Business Statistics: A Decision-Making Approach, 6e. Chapter Goals
Chapter 6 Studet Lecture Notes 6-1 Busiess Statistics: A Decisio-Makig Approach 6 th Editio Chapter 6 Itroductio to Samplig Distributios Chap 6-1 Chapter Goals After completig this chapter, you should
More informationStatistics 20: Final Exam Solutions Summer Session 2007
1. 20 poits Testig for Diabetes. Statistics 20: Fial Exam Solutios Summer Sessio 2007 (a) 3 poits Give estimates for the sesitivity of Test I ad of Test II. Solutio: 156 patiets out of total 223 patiets
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 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 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 informationY i n. i=1. = 1 [number of successes] number of successes = n
Eco 371 Problem Set # Aswer Sheet 3. I this questio, you are asked to cosider a Beroulli radom variable Y, with a success probability P ry 1 p. You are told that you have draws from this distributio ad
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 informationz is the upper tail critical value from the normal distribution
Statistical Iferece drawig coclusios about a populatio parameter, based o a sample estimate. Populatio: GRE results for a ew eam format o the quatitative sectio Sample: =30 test scores Populatio Samplig
More information1 Models for Matched Pairs
1 Models for Matched Pairs Matched pairs occur whe we aalyse samples such that for each measuremet i oe of the samples there is a measuremet i the other sample that directly relates to the measuremet i
More informationClass 23. Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science. Marquette University MATH 1700
Class 23 Daiel B. Rowe, Ph.D. Departmet of Mathematics, Statistics, ad Computer Sciece Copyright 2017 by D.B. Rowe 1 Ageda: Recap Chapter 9.1 Lecture Chapter 9.2 Review Exam 6 Problem Solvig Sessio. 2
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 informationClass 27. Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science. Marquette University MATH 1700
Marquette Uiversity MATH 700 Class 7 Daiel B. Rowe, Ph.D. Departmet of Mathematics, Statistics, a Computer Sciece Copyright 07 by D.B. Rowe Marquette Uiversity MATH 700 Agea: Recap Chapter 0.-0.3 Lecture
More informationSampling Distributions, Z-Tests, Power
Samplig Distributios, Z-Tests, Power We draw ifereces about populatio parameters from sample statistics Sample proportio approximates populatio proportio Sample mea approximates populatio mea Sample variace
More informationAP Statistics Review Ch. 8
AP Statistics Review Ch. 8 Name 1. Each figure below displays the samplig distributio of a statistic used to estimate a parameter. The true value of the populatio parameter is marked o each samplig distributio.
More informationChapter 11: Asking and Answering Questions About the Difference of Two Proportions
Chapter 11: Askig ad Aswerig Questios About the Differece of Two Proportios These otes reflect material from our text, Statistics, Learig from Data, First Editio, by Roxy Peck, published by CENGAGE Learig,
More informationChapter 22: What is a Test of Significance?
Chapter 22: What is a Test of Sigificace? Thought Questio Assume that the statemet If it s Saturday, the it s the weeked is true. followig statemets will also be true? Which of the If it s the weeked,
More informationConfidence Intervals รศ.ดร. อน นต ผลเพ ม Assoc.Prof. Anan Phonphoem, Ph.D. Intelligent Wireless Network Group (IWING Lab)
Cofidece Itervals รศ.ดร. อน นต ผลเพ ม Assoc.Prof. Aa Phophoem, Ph.D. aa.p@ku.ac.th Itelliget Wireless Network Group (IWING Lab) http://iwig.cpe.ku.ac.th Computer Egieerig Departmet Kasetsart Uiversity,
More informationAnnouncements. Unit 5: Inference for Categorical Data Lecture 1: Inference for a single proportion
Housekeepig Aoucemets Uit 5: Iferece for Categorical Data Lecture 1: Iferece for a sigle proportio Statistics 101 Mie Çetikaya-Rudel PA 4 due Friday at 5pm (exteded) PS 6 due Thursday, Oct 30 October 23,
More information1 Constructing and Interpreting a Confidence Interval
Itroductory Applied Ecoometrics EEP/IAS 118 Sprig 2014 WARM UP: Match the terms i the table with the correct formula: Adrew Crae-Droesch Sectio #6 5 March 2014 ˆ Let X be a radom variable with mea µ ad
More informationMathacle. PSet Stats, Concepts In Statistics Level Number Name: Date:
PSet ----- Stats, Cocepts I Statistics 7.3. Cofidece Iterval for a Mea i Oe Sample [MATH] The Cetral Limit Theorem. Let...,,, be idepedet, idetically distributed (i.i.d.) radom variables havig mea µ ad
More informationMA238 Assignment 4 Solutions (part a)
(i) Sigle sample tests. Questio. MA38 Assigmet 4 Solutios (part a) (a) (b) (c) H 0 : = 50 sq. ft H A : < 50 sq. ft H 0 : = 3 mpg H A : > 3 mpg H 0 : = 5 mm H A : 5mm Questio. (i) What are the ull ad alterative
More informationMath 140 Introductory Statistics
8.2 Testig a Proportio Math 1 Itroductory Statistics Professor B. Abrego Lecture 15 Sectios 8.2 People ofte make decisios with data by comparig the results from a sample to some predetermied stadard. These
More informationSimple Random Sampling!
Simple Radom Samplig! Professor Ro Fricker! Naval Postgraduate School! Moterey, Califoria! Readig:! 3/26/13 Scheaffer et al. chapter 4! 1 Goals for this Lecture! Defie simple radom samplig (SRS) ad discuss
More informationOctober 25, 2018 BIM 105 Probability and Statistics for Biomedical Engineers 1
October 25, 2018 BIM 105 Probability ad Statistics for Biomedical Egieers 1 Populatio parameters ad Sample Statistics October 25, 2018 BIM 105 Probability ad Statistics for Biomedical Egieers 2 Ifereces
More informationInstructor: Judith Canner Spring 2010 CONFIDENCE INTERVALS How do we make inferences about the population parameters?
CONFIDENCE INTERVALS How do we make ifereces about the populatio parameters? The samplig distributio allows us to quatify the variability i sample statistics icludig how they differ from the parameter
More informationApril 18, 2017 CONFIDENCE INTERVALS AND HYPOTHESIS TESTING, UNDERGRADUATE MATH 526 STYLE
April 18, 2017 CONFIDENCE INTERVALS AND HYPOTHESIS TESTING, UNDERGRADUATE MATH 526 STYLE TERRY SOO Abstract These otes are adapted from whe I taught Math 526 ad meat to give a quick itroductio to cofidece
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 informationS160 #12. Review of Large Sample Result for Sample Proportion
S160 #12 Samplig Distributio of the Proportio, Part 2 JC Wag February 25, 2016 Review of Large Sample Result for Sample Proportio Recall that for large sample (ie, sample size is large, say p > 5 ad (1
More informationChapter 8: STATISTICAL INTERVALS FOR A SINGLE SAMPLE. Part 3: Summary of CI for µ Confidence Interval for a Population Proportion p
Chapter 8: STATISTICAL INTERVALS FOR A SINGLE SAMPLE Part 3: Summary of CI for µ Cofidece Iterval for a Populatio Proportio p Sectio 8-4 Summary for creatig a 100(1-α)% CI for µ: Whe σ 2 is kow ad paret
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 informationS160 #12. Sampling Distribution of the Proportion, Part 2. JC Wang. February 25, 2016
S160 #12 Samplig Distributio of the Proportio, Part 2 JC Wag February 25, 2016 Outlie 1 Estimatig Proportio Usig Itervals Cofidece Iterval for the Populatio Proportio iclicker Questios 2 JC Wag (WMU) S160
More informationParameter, Statistic and Random Samples
Parameter, Statistic ad Radom Samples A parameter is a umber that describes the populatio. It is a fixed umber, but i practice we do ot kow its value. A statistic is a fuctio of the sample data, i.e.,
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 informationRecall the study where we estimated the difference between mean systolic blood pressure levels of users of oral contraceptives and non-users, x - y.
Testig Statistical Hypotheses Recall the study where we estimated the differece betwee mea systolic blood pressure levels of users of oral cotraceptives ad o-users, x - y. Such studies are sometimes viewed
More informationMIT : Quantitative Reasoning and Statistical Methods for Planning I
MIT 11.220 Sprig 06 Recitatio 4 March 16, 2006 MIT - 11.220: Quatitative Reasoig ad Statistical Methods for Plaig I Recitatio #4: Sprig 2006 Cofidece Itervals ad Hypothesis Testig I. Cofidece Iterval 1.
More informationStatistics Lecture 27. Final review. Administrative Notes. Outline. Experiments. Sampling and Surveys. Administrative Notes
Admiistrative Notes s - Lecture 7 Fial review Fial Exam is Tuesday, May 0th (3-5pm Covers Chapters -8 ad 0 i textbook Brig ID cards to fial! Allowed: Calculators, double-sided 8.5 x cheat sheet Exam Rooms:
More informationUniversity of California, Los Angeles Department of Statistics. Hypothesis testing
Uiversity of Califoria, Los Ageles Departmet of Statistics Statistics 100B Elemets of a hypothesis test: Hypothesis testig Istructor: Nicolas Christou 1. Null hypothesis, H 0 (claim about µ, p, σ 2, µ
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 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 informationConfidence Intervals
Cofidece Itervals Berli Che Deartmet of Comuter Sciece & Iformatio Egieerig Natioal Taiwa Normal Uiversity Referece: 1. W. Navidi. Statistics for Egieerig ad Scietists. Chater 5 & Teachig Material Itroductio
More informationUnderstanding Dissimilarity Among Samples
Aoucemets: Midterm is Wed. Review sheet is o class webpage (i the list of lectures) ad will be covered i discussio o Moday. Two sheets of otes are allowed, same rules as for the oe sheet last time. Office
More informationChapter 7 Student Lecture Notes 7-1
Chapter 7 Studet Lecture otes 7-1 Basic Busiess Statistics (9 th Editio) Chapter 7 Samplig Distributios 24 Pretice-Hall, Ic. Chap 7-1 Chapter Topics Samplig Distributio of the Mea The Cetral Limit Theorem
More informationChapter two: Hypothesis testing
: Hypothesis testig - Some basic cocepts: - Data: The raw material of statistics is data. For our purposes we may defie data as umbers. The two kids of umbers that we use i statistics are umbers that result
More information3/3/2014. CDS M Phil Econometrics. Types of Relationships. Types of Relationships. Types of Relationships. Vijayamohanan Pillai N.
3/3/04 CDS M Phil Old Least Squares (OLS) Vijayamohaa Pillai N CDS M Phil Vijayamoha CDS M Phil Vijayamoha Types of Relatioships Oly oe idepedet variable, Relatioship betwee ad is Liear relatioships Curviliear
More informationπ: ESTIMATES, CONFIDENCE INTERVALS, AND TESTS Business Statistics
π: ESTIMATES, CONFIDENCE INTERVALS, AND TESTS Busiess Statistics CONTENTS The CLT for π Estimatig proportio Hypothesis o the proportio Old exam questio Further study THE CLT FOR π Estimatig, cofidece itervals,
More informationCreative Commons Attribution-NonCommercial-Share Alike License
Author: Breda Guderso, Ph.D., 2015 Licese: Uless otherwise oted, this material is made available uder the terms of the Creative Commos Attributio- NoCommercial-Share Alike 3.0 Uported Licese: http://creativecommos.org/liceses/by-c-sa/3.0/
More informationUCLA STAT 13 Introduction to Statistical Methods for the Life and Health Sciences
UCLA STAT 13 Itroductio to Statistical Methods for the Life ad Health Scieces Istructor: Ivo Diov, Asst. Prof. of Statistics ad Neurolog Sample Size Calculatios & Cofidece Itervals for Proportios Teachig
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 informationChapter 13, Part A Analysis of Variance and Experimental Design
Slides Prepared by JOHN S. LOUCKS St. Edward s Uiversity Slide 1 Chapter 13, Part A Aalysis of Variace ad Eperimetal Desig Itroductio to Aalysis of Variace Aalysis of Variace: Testig for the Equality of
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 informationBecause it tests for differences between multiple pairs of means in one test, it is called an omnibus test.
Math 308 Sprig 018 Classes 19 ad 0: Aalysis of Variace (ANOVA) Page 1 of 6 Itroductio ANOVA is a statistical procedure for determiig whether three or more sample meas were draw from populatios with equal
More informationFrequentist Inference
Frequetist Iferece The topics of the ext three sectios are useful applicatios of the Cetral Limit Theorem. Without kowig aythig about the uderlyig distributio of a sequece of radom variables {X i }, for
More informationLecture 5: Parametric Hypothesis Testing: Comparing Means. GENOME 560, Spring 2016 Doug Fowler, GS
Lecture 5: Parametric Hypothesis Testig: Comparig Meas GENOME 560, Sprig 2016 Doug Fowler, GS (dfowler@uw.edu) 1 Review from last week What is a cofidece iterval? 2 Review from last week What is a cofidece
More informationStatistics 300: Elementary Statistics
Statistics 300: Elemetary Statistics Sectios 7-, 7-3, 7-4, 7-5 Parameter Estimatio Poit Estimate Best sigle value to use Questio What is the probability this estimate is the correct value? Parameter Estimatio
More informationModule 1 Fundamentals in statistics
Normal Distributio Repeated observatios that differ because of experimetal error ofte vary about some cetral value i a roughly symmetrical distributio i which small deviatios occur much more frequetly
More informationHypothesis Testing. Evaluation of Performance of Learned h. Issues. Trade-off Between Bias and Variance
Hypothesis Testig Empirically evaluatig accuracy of hypotheses: importat activity i ML. Three questios: Give observed accuracy over a sample set, how well does this estimate apply over additioal samples?
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 information6 Sample Size Calculations
6 Sample Size Calculatios Oe of the major resposibilities of a cliical trial statisticia is to aid the ivestigators i determiig the sample size required to coduct a study The most commo procedure for determiig
More informationDesign of Engineering Experiments Chapter 2 Basic Statistical Concepts
Desig of Egieerig Experimets Chapter 2 Basic tatistical Cocepts imple comparative experimets The hpothesis testig framework The two-sample t-test Checkig assumptios, validit Motgomer_Chap_2 Portlad Cemet
More informationStatistical inference: example 1. Inferential Statistics
Statistical iferece: example 1 Iferetial Statistics POPULATION SAMPLE A clothig store chai regularly buys from a supplier large quatities of a certai piece of clothig. Each item ca be classified either
More informationFormulas and Tables for Gerstman
Formulas ad Tables for Gerstma Measuremet ad Study Desig Biostatistics is more tha a compilatio of computatioal techiques! Measuremet scales: quatitative, ordial, categorical Iformatio quality is primary
More information