HOMEWORK (due Fri, Nov 19): Chapter 12: #62, 83, 101


 Paula Ellis
 1 years ago
 Views:
Transcription
1 Today: Section 2.2, Lesson 3: What can go wrong with hyothesis testing Section 2.4: Hyothesis tests for difference in two roortions ANNOUNCEMENTS: No discussion today. Check your grades on eee and notify me if any of them are incorrect. Quiz #7 begins Wed after class and ends Friday. Quiz #8 begins Wed before Thanksgiving and ends on Monday after Thanksgiving. That is the last quiz. Jason Kramer will give the lecture this Friday. HOMEWORK (due Fri, Nov 9): Chater 2: #62, 83, 0
2 REVIEW OF HYPOTHESIS TEST FOR ONE PROPORTION ONESIDED TEST, WITH PICTURE H 0 : = 0 versus Ha: > 0 Reject H 0 if value <.05. For what values of z does that haen? Notation: level of significance = α (alha, usually.05) value <.05 corresonds with z >.645 Normal, Mean=0, StDev= Do not reject null hyothesis 0 Value of test statistic Reject null hyothesis
3 AN ILLUSTRATION OF WHAT HAPPENS WHEN Ha IS TRUE A Secific Examle Suose the truth for the oulation roortion is one standard deviation above the null value 0. Then the mean for the standardized scores will be instead of 0. How often would we (correctly) reject the null hyothesis in that case? Answer (urle region) is Picture when the true oulation roortion is s.d. above null value Normal, Mean=, StDev= Do not reject null hyothesis Value of test statistic Reject null hyothesis
4 Section 2.2, Lesson 3 What Can Go Wrong in Hyothesis Testing: The Two Tyes of Errors and Their Probabilities Examle: Case Study.6, asirin and heart attacks. Found statistically significant relationshi; value was < Possible errors: Tye error (false ositive) occurs when: Null hyothesis is actually true, but Conclusion of test is to Reject H 0 and accet H a Tye 2 error (false negative) occurs when: Alternative hyothesis is actually true, but Conclusion is that we cannot reject H 0
5 Heart attack and asirin examle: Null hyothesis: The roortion of men who would have heart attacks if taking asirin = the roortion of men who would have heart attacks if taking lacebo. Alternative hyothesis: The heart attack roortion is lower if men were to take asirin than if they were not to take asirin. Tye error (false ositive): Occurs if there really is no relationshi between taking asirin and heart attack revention, but we conclude that there is a relationshi. Consequence: Good for asirin comanies! Possible bad side effects from asirin, with no redeeming value.
6 Tye 2 error (false negative): Occurs if there really is a relationshi but study failed to find it. Consequence: Miss out on recommending something that could save lives! Which tye of error is more serious? Probably all agree that Tye 2 is more serious. Which could have occurred? Tye error could have occurred. Tye 2 could not have occurred, because we did find a significant relationshi.
7 Asirin Examle: Consequences of the decisions Decision: Truth: H 0 : Asirin doesn t work Ha: Asirin works Which error can occur? Don t conclude asirin works OK Tye 2 error: Asirin could save lives but we don t recognize benefits Tye 2 can only occur if H 0 is not Reject H 0, Conclude asirin works Tye error: Peole take asirin needlessly; may suffer side effects OK Tye can only occur if H 0 is rejected. Which error can occur: Tye error can only occur if asirin doesn t work. Tye 2 error can only occur if asirin does work. rejected. Note that because H 0 was rejected in this study, we could only have made a Tye error, not a Tye 2 error.
8 Some analogies to hyothesis testing: Analogy : Courtroom: Null hyothesis: Defendant is innocent. Alternative hyothesis: Defendant is guilty Note that the two ossible conclusions are not guilty and guilty. The conclusion not guilty is equivalent to don t reject H 0. We don t say defendant is innocent just like we don t accet H 0 in hyothesis testing. Tye error is when defendant is innocent but gets convicted Tye 2 error is when defendant is guilty but does not get convicted. Which one is more serious??
9 Analogy 2: Medical test Null hyothesis: You do not have the disease Alternative hyothesis: You have the disease Tye error: You don't have disease, but test says you do; a "false ositive" Tye 2 error: You do have disease, but test says you do not; a "false negative" Which is more serious??
10 Notes and Definitions: Probability related to Tye error: The conditional robability of making a Tye error, given that H 0 is true, is the level of significance α. In most cases, this is.05. However, it should be adjusted to be lower (.0 is common) if a Tye error is more serious than a Tye 2 error. In robability notation: P(Reject H 0 H 0 is true) = α, usually.05. Normal, Mean=0, StDev= Do not reject null hyothesis 0 Value of test statistic Reject null hyothesis
11 Probability related to Tye 2 error and Power: The conditional robability of making a correct decision, given that H a is true is called the ower of the test. This can only be calculated if a secific value in Ha is secified. Conditional robability of making a Tye 2 error = ower. P(Reject H 0 Ha is true) = ower. P(Do not reject H 0 Ha is true) = ower = β =P(Tye 2 error). Picture when the true oulation roortion is s.d. above null value Normal, Mean=, StDev= Probability of tye 2 error = =.7405 Do not reject null hyothesis = ower.645 Value of test statistic Reject null hyothesis
12 How can we increase ower and decrease P(Tye 2 error)? Power increases if: Samle size is increased (because having more evidence makes it easier to show that the alternative hyothesis is true, if it really is) The level of significance α is increased (because it s easier to reject H 0 when the cutoff oint for the value is larger) The actual difference between the samle estimate and the null value increases (because it s easier to detect a true difference if it s large) We have no control over this one! Tradeoff must be taken into account when choosing α. If α is small it s harder to reject H 0. If α is large it s easier to reject H 0 : If Tye error is more serious, use smaller α. If Tye 2 error is more serious, use larger α.
13 Ways to icture the errors: Truth, decisions, consequences, conditional (row) robabilities: Decision: Truth: Don t reject H 0 Reject H 0 Error can occur: Correct Tye error Tye error can only H 0 α α Tye 2 error Correct H a β = ower ower Error can occur: H 0 not rejected H 0 rejected occur if H 0 true Tye 2 error can only occur if H a is true.
14 SECTION 2.4: Test for difference in 2 roortions Reminder from when we started Chater 9 Five situations we will cover for the rest of this quarter: Parameter name and descrition Poulation arameter Samle statistic For Categorical Variables: One oulation roortion (or robability) ˆ Difference in two oulation roortions 2 ˆ ˆ 2 For Quantitative Variables: One oulation mean µ x Poulation mean of aired differences (deendent samles, aired) µ d d Difference in two oulation means µ (indeendent samles) µ 2 x x2 For each situation will we: Learn about the samling distribution for the samle statistic Learn how to find a confidence interval for the true value of the arameter Test hyotheses about the true value of the arameter
15 Comaring two roortions from indeendent samles Reminder on how we get indeendent samles (Lecture 9): Random samles taken searately from two oulations and same resonse variable is recorded. Examle: Comare roortions who think global warming is a roblem, in two different years. One random samle taken and a variable recorded, but units are categorized to form two oulations. Examle: Comare 2 and over with under 2 for roortion who drink alcohol. Particiants randomly assigned to one of two treatment conditions, and same resonse variable is recorded. Examle: Comare asirin and lacebo grous for roortions who had heart attacks.
16 Hyothesis Test for Difference in Two Proortions Examle: (Source: htt://www.ollingreort.com/enviro.htm) Poll taken in June 2006, just after the May release of An Inconvenient Truth Asked 500 eole In your view, is global warming a very serious roblem, somewhat serious, not too serious, or not a roblem? Results: 65/500 =.4 or 4% answered Very serious Poll taken again with different 500 eole in October, Results: 525/500 =.35 or 35% answered Very serious. Question: Did the oulation roortion that thinks it s very serious go down from 2006 to 2009, or is it chance fluctuation?
17 Notation and numbers for the Examle: Poulation arameter of interest is 2 where: = 2 = roortion of all US adults in May 2006 who thought global warming was a serious roblem. roortion of all US adults in Oct 2009 who thought global warming was a serious roblem. ˆ = samle estimate from May 2006 = X /n = 65/500 =.4 ˆ 2 = samle estimate from Oct 2009 = X 2 /n 2 = 525/500 =.35 Samle statistic is ˆ ˆ 2 =.4.35 =. 06
18 Five stes to hyothesis testing for difference in 2 roortions: See Summary Box on ages STEP : Determine the null and alternative hyotheses. Null hyothesis is H 0 : 2 = 0 (or = 2 ); null value = 0 Alternative hyothesis is one of these, based on context: H a : 2 0 (or 2 ) H a : 2 > 0 (or > 2 ) H a : 2 < 0 (or < 2 ) EXAMPLE: Did the oulation roortion who think global warming is very serious dro from 2006 to 2009? This is the alternative hyothesis. (Note that it s a onesided test.) H 0 : 2 = 0 (no actual change in oulation roortions) H a : 2 > 0 (or > 2 ; 2006 roortion > 2009 roortion)
19 STEP 2: Verify data conditions. If met, summarize data into test statistic. For Difference in Two Proortions: Data conditions: nˆ and n( ˆ ) are both at least 0 for both samles. Test statistic: ˆ z = samle statistic null value (null) standard error Samle statistic = 2 Null value = 0 Null standard error: Comuted assuming null hyothesis is true. If null hyothesis is true, then = 2 We get an estimate for the common value of using both samles, then use that in the standard error formula. Details on next age. ˆ
20 combined samle sizes combined successes ˆ 2 2 = + + = n n X X Null standard error = estimate of ) ( ) ( n n +, using combined estimate ˆ in lace of both and 2. So the test statistic is: ) ˆ)( ˆ( 0 ) ˆ ˆ ( ˆ) ˆ( ˆ) ˆ( 0 ) ˆ ˆ ( n n n n z + = + =
21 Ste 2 for the Examle: Data conditions are met, since both samle sizes are 500. X + X combined successes = = = = = n + n combined samle sizes ˆ.38 2 Null standard error = (. 38)(.38)( + ) = Test statistic: z = samle statistic null value (null) standard error = = 3.39
22 Pictures: On left: Samling distribution of ˆ ˆ 2 when oulation roortions are equal and samle sizes are both 500, showing where the observed value of.06 falls. On right: The same icture, converted to zscores. Samling distribution for hat  2hat, when =2, n=n2=500 Normal, Mean=0, StDev=0.077 Standard normal distribution Normal, Mean=0, StDev= Possible values of hat  2hat Values of z 3.39 Note that area above ˆ ˆ 2 = 0.06 is so small you can t see it!
23 STEP 3: Assuming the null hyothesis is true, find the value. General: value = the robability of a test statistic as extreme as the one observed or more so, in the direction of H a, if the null hyothesis is true. Difference in two roortions, same idea as one roortion. Deends on the alternative hyothesis. See ictures on. 57 Alternative hyothesis: value is: H a : 2 > 0 (a onesided hyothesis) Area above the test statistic z H a : 2 < 0 (a onesided hyothesis) H a : 2 0 (a twosided hyothesis) Area below the test statistic z 2 the area above z = area in tails beyond z and z
24 Examle: Alternative hyothesis is onesided H a : 2 > 0 value = Area above the test statistic z = 3.39 From Table A., value = area above 3.39 =.9997 = STEP 4: Decide whether or not the result is statistically significant based on the value. Examle: Use α of.05, as usual value =.0003 <.05, so: Reject the null hyothesis. Accet the alternative hyothesis The result is statistically significant
25 Ste 5: Reort the conclusion in the context of the situation. Examle: Conclusion: From May 2006 to October 2009 there was a statistically significant decrease in the roortion of US adults who think global warming is very serious. Interretation of the value (for this onesided test): It s a conditional robability. Conditional on the null hyothesis being true (equal oulation roortions), what is the robability that we would observe a samle difference as large as the one observed or larger just by chance? Secific to this examle: If there really were no change in the roortion of the oulation who think global warming is very serious what is the robability of observing a samle roortion in 2009 that is.06 (6%) or more lower than the samle roortion in 2006? Answer: The robability is Therefore, we reject the idea (the hyothesis) that there was no change in the oulation roortion.
Section 12.2, Lesson 3. What Can Go Wrong in Hypothesis Testing: The Two Types of Errors and Their Probabilities
Today: Section 2.2, Lesson 3: What can go wrong with hypothesis testing Section 2.4: Hypothesis tests for difference in two proportions ANNOUNCEMENTS: No discussion today. Check your grades on eee and
More informationChapter 9, Part B Hypothesis Tests. Learning objectives
Chater 9, Part B Hyothesis Tests Slide 1 Learning objectives 1. Able to do hyothesis test about Poulation Proortion 2. Calculatethe Probability of Tye II Errors 3. Understand ower of the test 4. Determinethe
More informationExample for testing one population mean:
Today: Sections 13.1 to 13.3 ANNOUNCEMENTS: We will finish hypothesis testing for the 5 situations today. See pages 586587 (end of Chapter 13) for a summary table. Quiz for week 8 starts Wed, ends Monday
More informationPOL 345: Quantitative Analysis and Politics
POL 345: Quantitative Analysis and Politics Precet Handout 8 Week 10 (Verzani Chaters 7 and 8: 7.5, 8.6.18.6.2) Remember to comlete the entire handout and submit the recet questions to the Blackboard
More informationIt is important to be very clear about our definitions of probabilities.
Use Bookmarks for electronic content links 7.6 Bayesian odds 7.6.1 Introduction The basic ideas of robability have been introduced in Unit 7.3 in the book, leading to the concet of conditional robability.
More informationChapter 21. More About Tests and Intervals. Copyright 2012, 2008, 2005 Pearson Education, Inc.
Chapter 21 More About Tests and Intervals Copyright 2012, 2008, 2005 Pearson Education, Inc. Zero In on the Null Null hypotheses have special requirements. To perform a hypothesis test, the null must be
More informationMonitoring Frequency of Change By Li Qin
Monitoring Frequency of Change By Li Qin Abstract Control charts are widely used in rocess monitoring roblems. This aer gives a brief review of control charts for monitoring a roortion and some initial
More informationLoglikelihood and Confidence Intervals
Stat 504, Lecture 3 Stat 504, Lecture 3 2 Review (contd.): Loglikelihood and Confidence Intervals The likelihood of the samle is the joint PDF (or PMF) L(θ) = f(x,.., x n; θ) = ny f(x i; θ) i= Review:
More informationHypothesis testing allows us to use a sample to decide between two statements made about a Population characteristic.
Hypothesis Testing Hypothesis testing allows us to use a sample to decide between two statements made about a Population characteristic. Population Characteristics are things like The mean of a population
More informationWhat is Adverse Selection. Economics of Information and Contracts Adverse Selection. Lemons Problem. Lemons Problem
What is Adverse Selection Economics of Information and Contracts Adverse Selection Levent Koçkesen Koç University In markets with erfect information all rofitable trades (those in which the value to the
More informationHYPOTHESIS TESTING FOR THE PROCESS CAPABILITY RATIO. A thesis presented to. the faculty of
HYPOTHESIS TESTING FOR THE PROESS APABILITY RATIO A thesis resented to the faculty of the Russ ollege of Engineering and Technology of Ohio University In artial fulfillment of the requirement for the degree
More informationHomework #3 is due Friday by 5pm. Homework #4 will be posted to the class website later this week. It will be due Friday, March 7 th, at 5pm.
Homework #3 is due Friday by 5pm. Homework #4 will be posted to the class website later this week. It will be due Friday, March 7 th, at 5pm. Political Science 15 Lecture 12: Hypothesis Testing Sampling
More informationBeyond the F Test: Effect Size Confidence Intervals and Tests of Close Fit in the Analysis of Variance and Contrast Analysis
Psychological Methods 004, Vol. 9, No., 164 18 Coyright 004 by the American Psychological Association 108989X/04/$1.00 DOI: 10.1037/108989X.9..164 Beyond the F Test: Effect Size Confidence Intervals
More informationHypothesis Testing. Concept of Hypothesis Testing
Quantitative Methods 2013 Hypothesis Testing with One Sample 1 Concept of Hypothesis Testing Testing Hypotheses is another way to deal with the problem of making a statement about an unknown population
More informationConfidence Intervals for CaptureRecapture Data With Matching
Confidence Intervals for CatureRecature Data With Matching Executive summary Caturerecature data is often used to estimate oulations The classical alication for animal oulations is to take two samles
More informationIntroduction to. Hypothesis Testing CHAPTER LEARNING OBJECTIVES. 1 Identify the four steps of hypothesis testing.
Introduction to Hypothesis Testing CHAPTER 8 LEARNING OBJECTIVES After reading this chapter, you should be able to: 1 Identify the four steps of hypothesis testing. 2 Define null hypothesis, alternative
More informationEffects of Math Tutoring
Requestor: Math Deartment Researcher(s): Steve Blohm Date: 6/30/15 Title: Effects of Math Tutoring Effects of Math Tutoring The urose of this study is to measure the effects of math tutoring at Cabrillo
More informationFrequentist vs. Bayesian Statistics
Bayes Theorem Frequentist vs. Bayesian Statistics Common situation in science: We have some data and we want to know the true hysical law describing it. We want to come u with a model that fits the data.
More informationHomework 6 Solutions
Math 17, Section 2 Spring 2011 Assignment Chapter 20: 12, 14, 20, 24, 34 Chapter 21: 2, 8, 14, 16, 18 Chapter 20 20.12] Got Milk? The student made a number of mistakes here: Homework 6 Solutions 1. Null
More informationNormally Distributed Data. A mean with a normal value Test of Hypothesis Sign Test Paired observations within a single patient group
ANALYSIS OF CONTINUOUS VARIABLES / 31 CHAPTER SIX ANALYSIS OF CONTINUOUS VARIABLES: COMPARING MEANS In the last chater, we addressed the analysis of discrete variables. Much of the statistical analysis
More informationSTA102 Class Notes Chapter Hypothesis Testing
10. Hypothesis Testing In this chapter, we continue to study methods for making inference about a population using our sample. In chapter 9, we used CIs, essentially, to answer questions of the type, What
More informationEffect Sizes Based on Means
CHAPTER 4 Effect Sizes Based on Means Introduction Raw (unstardized) mean difference D Stardized mean difference, d g Resonse ratios INTRODUCTION When the studies reort means stard deviations, the referred
More informationCh. 8 Hypothesis Testing
Ch. 8 Hypothesis Testing 8.1 Foundations of Hypothesis Testing Definitions In statistics, a hypothesis is a claim about a property of a population. A hypothesis test is a standard procedure for testing
More informationHypothesis Testing. April 21, 2009
Hypothesis Testing April 21, 2009 Your Claim is Just a Hypothesis I ve never made a mistake. Once I thought I did, but I was wrong. Your Claim is Just a Hypothesis Confidence intervals quantify how sure
More informationLecture Topic 6: Chapter 9 Hypothesis Testing
Lecture Topic 6: Chapter 9 Hypothesis Testing 9.1 Developing Null and Alternative Hypotheses Hypothesis testing can be used to determine whether a statement about the value of a population parameter should
More informationCHAPTER 15: Tests of Significance: The Basics
CHAPTER 15: Tests of Significance: The Basics The Basic Practice of Statistics 6 th Edition Moore / Notz / Fligner Lecture PowerPoint Slides Chapter 15 Concepts 2 The Reasoning of Tests of Significance
More informationThe impact of metadata implementation on webpage visibility in search engine results (Part II) q
Information Processing and Management 41 (2005) 691 715 www.elsevier.com/locate/inforoman The imact of metadata imlementation on webage visibility in search engine results (Part II) q Jin Zhang *, Alexandra
More informationHypothesis Testing. Jungmo Yoon CMC, Claremont McKeena College. Jungmo Yoon (CMC) Testing CMC, / 7
Hypothesis Testing Jungmo Yoon Claremont McKeena College CMC, 2009 Jungmo Yoon (CMC) Testing CMC, 2009 1 / 7 Concepts of Hypothesis Testing A criminal trial as an example of hypothesis testing. A jury
More informationReasoning with Uncertainty More about Hypothesis Testing. Pvalues, types of errors, power of a test
Reasoning with Uncertainty More about Hypothesis Testing Pvalues, types of errors, power of a test PValues and Decisions Your conclusion about any null hypothesis should be accompanied by the Pvalue
More informationSTA 2023H Solutions for Practice Test 4
1. Which statement is not true about confidence intervals? A. A confidence interval is an interval of values computed from sample data that is likely to include the true population value. B. An approximate
More informationHYPOTHESIS TESTING: POWER OF THE TEST
HYPOTHESIS TESTING: POWER OF THE TEST The first 6 steps of the 9step test of hypothesis are called "the test". These steps are not dependent on the observed data values. When planning a research project,
More informationRisk and Return. Sample chapter. e r t u i o p a s d f CHAPTER CONTENTS LEARNING OBJECTIVES. Chapter 7
Chater 7 Risk and Return LEARNING OBJECTIVES After studying this chater you should be able to: e r t u i o a s d f understand how return and risk are defined and measured understand the concet of risk
More informationChapter 7. Estimates and Sample Size
Chapter 7. Estimates and Sample Size Chapter Problem: How do we interpret a poll about global warming? Pew Research Center Poll: From what you ve read and heard, is there a solid evidence that the average
More informationChapter 8: Introduction to Hypothesis Testing
Chapter 8: Introduction to Hypothesis Testing We re now at the point where we can discuss the logic of hypothesis testing. This procedure will underlie the statistical analyses that we ll use for the remainder
More information1 Gambler s Ruin Problem
Coyright c 2009 by Karl Sigman 1 Gambler s Ruin Problem Let N 2 be an integer and let 1 i N 1. Consider a gambler who starts with an initial fortune of $i and then on each successive gamble either wins
More informationModule 5 Hypotheses Tests: Comparing Two Groups
Module 5 Hypotheses Tests: Comparing Two Groups Objective: In medical research, we often compare the outcomes between two groups of patients, namely exposed and unexposed groups. At the completion of this
More informationStatistical Inference
Statistical Inference Idea: Estimate parameters of the population distribution using data. How: Use the sampling distribution of sample statistics and methods based on what would happen if we used this
More informationreductio ad absurdum null hypothesis, alternate hypothesis
Chapter 10 s Using a Single Sample 10.1: Hypotheses & Test Procedures Basics: In statistics, a hypothesis is a statement about a population characteristic. s are based on an reductio ad absurdum form of
More informationMath 62 Statistics Sample Exam Questions
Math 62 Statistics Sample Exam Questions 1. (10) Explain the difference between the distribution of a population and the sampling distribution of a statistic, such as the mean, of a sample randomly selected
More informationMore on the correct use of omnibus tests for normality
Economics Letters 90 (2006) 304 309 www.elsevier.com/locate/econbase More on the correct use of omnibus tests for normality Geoffrey Poitras Simon Fraser University, Burnaby, B.C., Canada VSA ls6 Received
More informationChapter 8. Hypothesis Testing
Chapter 8 Hypothesis Testing Hypothesis In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing
More informationTheoretical comparisons of average normalized gain calculations
PHYSICS EDUCATIO RESEARCH All submissions to PERS should be sent referably electronically to the Editorial Office of AJP, and then they will be forwarded to the PERS editor for consideration. Theoretical
More informationAP STATISTICS 2012 SCORING GUIDELINES
2012 SCORING GUIDELINES Question 4 Intent of Question The primary goal of this question was to assess students ability to identify, set up, perform, and interpret the results of an appropriate hypothesis
More informationCHAPTERS 46: Hypothesis Tests Read sections 4.3, 4.5, 5.1.5, Confidence Interval vs. Hypothesis Test (4.3):
CHAPTERS 46: Hypothesis Tests Read sections 4.3, 4.5, 5.1.5, 6.1.3 Confidence Interval vs. Hypothesis Test (4.3): The purpose of a confidence interval is to estimate the value of a parameter. The purpose
More informationProblem Set 2  Solutions
Ecn 102  Analysis of Economic Data University of California  Davis January 13, 2010 John Parman Problem Set 2  Solutions This problem set will be not be graded and does not need to be turned in. However,
More informationTerminology. 2 There is no mathematical difference between the errors, however. The bottom line is that we choose one type
Hypothesis Testing 10.2.1 Terminology The null hypothesis H 0 is a nothing hypothesis, whose interpretation could be that nothing has changed, there is no difference, there is nothing special taking place,
More information6.1 The Elements of a Test of Hypothesis
University of California, Davis Department of Statistics Summer Session II Statistics 13 August 22, 2012 Date of latest update: August 20 Lecture 6: Tests of Hypothesis Suppose you wanted to determine
More informationTesting Hypotheses About Proportions
Chapter 11 Testing Hypotheses About Proportions Hypothesis testing method: uses data from a sample to judge whether or not a statement about a population may be true. Steps in Any Hypothesis Test 1. Determine
More informationVersions 1a Page 1 of 17
Note to Students: This practice exam is intended to give you an idea of the type of questions the instructor asks and the approximate length of the exam. It does NOT indicate the exact questions or the
More informationTwosample hypothesis testing, I 9.07 3/09/2004
Twosample hypothesis testing, I 9.07 3/09/2004 But first, from last time More on the tradeoff between Type I and Type II errors The null and the alternative: Sampling distribution of the mean, m, given
More informationHow to Conduct a Hypothesis Test
How to Conduct a Hypothesis Test The idea of hypothesis testing is relatively straightforward. In various studies we observe certain events. We must ask, is the event due to chance alone, or is there some
More informationChapter 9: Hypothesis Testing GBS221, Class April 15, 2013 Notes Compiled by Nicolas C. Rouse, Instructor, Phoenix College
Chapter Objectives 1. Learn how to formulate and test hypotheses about a population mean and a population proportion. 2. Be able to use an Excel worksheet to conduct hypothesis tests about population means
More informationI. Basics of Hypothesis Testing
Introduction to Hypothesis Testing This deals with an issue highly similar to what we did in the previous chapter. In that chapter we used sample information to make inferences about the range of possibilities
More informationSTART Selected Topics in Assurance
START Selected Toics in Assurance Related Technologies Table of Contents Understanding Binomial Sequential Testing Introduction Double Samling (Two Stage) Testing Procedures The Sequential Probability
More informationBinomial Random Variables. Binomial Distribution. Examples of Binomial Random Variables. Binomial Random Variables
Binomial Random Variables Binomial Distribution Dr. Tom Ilvento FREC 8 In many cases the resonses to an exeriment are dichotomous Yes/No Alive/Dead Suort/Don t Suort Binomial Random Variables When our
More informationInferential Statistics
Inferential Statistics Sampling and the normal distribution Zscores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are
More informationA null hypothesis must always have μ or p, an equal sign, and the claimed value for the parameter in it!
HOSP 1207 (Business Stats) Learning Centre Formal Hypothesis: Making Decisions with a Single Sample This worksheet continues to build on the previous concepts of inferential statistics, only now, we re
More informationChapter 7. Section Introduction to Hypothesis Testing
Section 7.1  Introduction to Hypothesis Testing Chapter 7 Objectives: State a null hypothesis and an alternative hypothesis Identify type I and type II errors and interpret the level of significance Determine
More informationChapter 8: Hypothesis Testing of a Single Population Parameter
Chapter 8: Hypothesis Testing of a Single Population Parameter THE LANGUAGE OF STATISTICAL DECISION MAKING DEFINITIONS: The population is the entire group of objects or individuals under study, about which
More informationProject Management and. Scheduling CHAPTER CONTENTS
6 Proect Management and Scheduling HAPTER ONTENTS 6.1 Introduction 6.2 Planning the Proect 6.3 Executing the Proect 6.7.1 Monitor 6.7.2 ontrol 6.7.3 losing 6.4 Proect Scheduling 6.5 ritical Path Method
More informationTRANSCRIPT: In this lecture, we will talk about both theoretical and applied concepts related to hypothesis testing.
This is Dr. Chumney. The focus of this lecture is hypothesis testing both what it is, how hypothesis tests are used, and how to conduct hypothesis tests. 1 In this lecture, we will talk about both theoretical
More informationC. The null hypothesis is not rejected when the alternative hypothesis is true. A. population parameters.
Sample Multiple Choice Questions for the material since Midterm 2. Sample questions from Midterms and 2 are also representative of questions that may appear on the final exam.. A randomly selected sample
More informationTESTING OF HYPOTHESIS
TESTING OF HYPOTHESIS Rajender Parsad I.A.S.R.I., Library Avenue, New Delhi 11 12 rajender@iasri.res.in In applied investigations or in experimental research, one may wish to estimate the yield of a new
More informationPopulation Genetics I
Poulation Genetics I The material resented here considers a single diloid genetic locus, ith to alleles A and a; their relative frequencies in the oulation ill be denoted as and q (ith q 1 ). HardyWeinberg
More informationStatistical inference provides methods for drawing conclusions about a population from sample data.
Chapter 15 Tests of Significance: The Basics Statistical inference provides methods for drawing conclusions about a population from sample data. Two of the most common types of statistical inference: 1)
More information6. Statistical Inference: Significance Tests
6. Statistical Inference: Significance Tests Goal: Use statistical methods to check hypotheses such as Women's participation rates in elections in France is higher than in Germany. (an effect) Ethnic divisions
More informationModule 7: Hypothesis Testing I Statistics (OA3102)
Module 7: Hypothesis Testing I Statistics (OA3102) Professor Ron Fricker Naval Postgraduate School Monterey, California Reading assignment: WM&S chapter 10.110.5 Revision: 212 1 Goals for this Module
More informationSociology 6Z03 Topic 15: Statistical Inference for Means
Sociology 6Z03 Topic 15: Statistical Inference for Means John Fox McMaster University Fall 2016 John Fox (McMaster University) Soc 6Z03: Statistical Inference for Means Fall 2016 1 / 41 Outline: Statistical
More informationConfidence Intervals and Hypothesis Testing
Name: Class: Date: Confidence Intervals and Hypothesis Testing Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The librarian at the Library of Congress
More informationAn Analysis of Reliable Classifiers through ROC Isometrics
An Analysis of Reliable Classifiers through ROC Isometrics Stijn Vanderlooy s.vanderlooy@cs.unimaas.nl Ida G. SrinkhuizenKuyer kuyer@cs.unimaas.nl Evgueni N. Smirnov smirnov@cs.unimaas.nl MICCIKAT, Universiteit
More informationBasic Statistics. Probability and Confidence Intervals
Basic Statistics Probability and Confidence Intervals Probability and Confidence Intervals Learning Intentions Today we will understand: Interpreting the meaning of a confidence interval Calculating the
More informationHypothesis Testing. Dr. Bob Gee Dean Scott Bonney Professor William G. Journigan American Meridian University
Hypothesis Testing Dr. Bob Gee Dean Scott Bonney Professor William G. Journigan American Meridian University 1 AMU / BonTech, LLC, JourniTech Corporation Copyright 2015 Learning Objectives Upon successful
More informationTesting: is my coin fair?
Testing: is my coin fair? Formally: we want to make some inference about P(head) Try it: toss coin several times (say 7 times) Assume that it is fair ( P(head)= ), and see if this assumption is compatible
More informationA Trial Analogy for Statistical. Hypothesis Testing. Legal Trial Begin with claim: Statistical Significance Test Hypotheses (statements)
A Trial Analogy for Statistical Slide 1 Hypothesis Testing Legal Trial Begin with claim: Smith is not guilty If this is rejected, we accept Smith is guilty reasonable doubt Present evidence (facts) Evaluate
More informationCBus Voltage Calculation
D E S I G N E R N O T E S CBus Voltage Calculation Designer note number: 3121256 Designer: Darren Snodgrass Contact Person: Darren Snodgrass Aroved: Date: Synosis: The guidelines used by installers
More information22. HYPOTHESIS TESTING
22. HYPOTHESIS TESTING Often, we need to make decisions based on incomplete information. Do the data support some belief ( hypothesis ) about the value of a population parameter? Is OJ Simpson guilty?
More informationPurpose of Hypothesis Testing
Large sample Tests of Hypotheses Chapter 9 1 Purpose of Hypothesis Testing In the last chapter, we studied methods of estimating a parameter (μ, p or p 1 p 2 ) based on sample data: point estimation confidence
More informationPower and Sample Size Determination
Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 Power 1 / 31 Experimental Design To this point in the semester,
More informationA Multivariate Statistical Analysis of Stock Trends. Abstract
A Multivariate Statistical Analysis of Stock Trends Aril Kerby Alma College Alma, MI James Lawrence Miami University Oxford, OH Abstract Is there a method to redict the stock market? What factors determine
More informationChapter 8. Professor Tim Busken. April 20, Chapter 8. Tim Busken. 8.2 Basics of. Hypothesis Testing. Works Cited
Chapter 8 Professor April 20, 2014 In Chapter 8, we continue our study of inferential statistics. Concept: Inferential Statistics The two major activities of inferential statistics are 1 to use sample
More informationLinear Regression with One Regressor
Linear Regression with One Regressor Michael Ash Lecture 10 Analogy to the Mean True parameter µ Y β 0 and β 1 Meaning Central tendency Intercept and slope E(Y ) E(Y X ) = β 0 + β 1 X Data Y i (X i, Y
More informationThe risk of using the Q heterogeneity estimator for software engineering experiments
Dieste, O., Fernández, E., GarcíaMartínez, R., Juristo, N. 11. The risk of using the Q heterogeneity estimator for software engineering exeriments. The risk of using the Q heterogeneity estimator for
More informationThe HIV Epidemic: What kind of vaccine are we looking for?
adia Abuelezam MATH 181 May 5, 2008 The HIV Eidemic: What kind of vaccine are we looking for? 1 Problem Background 33.2 million eole are living with HIV and AIDS worldwide [4]. Human Immunodeficiency Virus
More informationPrice Elasticity of Demand MATH 104 and MATH 184 Mark Mac Lean (with assistance from Patrick Chan) 2011W
Price Elasticity of Demand MATH 104 and MATH 184 Mark Mac Lean (with assistance from Patrick Chan) 2011W The rice elasticity of demand (which is often shortened to demand elasticity) is defined to be the
More informationReview for Exam 2. H 0 : p 1 p 2 = 0 H A : p 1 p 2 0
Review for Exam 2 1 Time in the shower The distribution of the amount of time spent in the shower (in minutes) of all Americans is rightskewed with mean of 8 minutes and a standard deviation of 10 minutes.
More informationagents (believe they) cannot influence the market price agents have all relevant information What happens when neither (i) nor (ii) holds?
Information and strategic interaction Assumtions of erfect cometition: (i) (ii) agents (believe they) cannot influence the market rice agents have all relevant information What haens when neither (i) nor
More informationSection: 101 (10am11am) 102 (11am12pm) 103 (1pm2pm) 104 (1pm2pm)
Stat 0 Midterm Exam Instructor: Tessa ChildersDay 1 May 014 Please write your name and student ID below, and circle your section. With your signature, you certify that you have not observed poor or dishonest
More informationTest of proportion = 0.5 N Sample prop 95% CI z value p value (0.400, 0.466)
STATISTICS FOR THE SOCIAL AND BEHAVIORAL SCIENCES Recitation #10 Answer Key PROBABILITY, HYPOTHESIS TESTING, CONFIDENCE INTERVALS Hypothesis tests 2 When a recent GSS asked, would you be willing to pay
More informationAP Statistics 2004 Scoring Guidelines
AP Statistics 2004 Scoring Guidelines The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use must be sought
More informationMath 140: Introductory Statistics Instructor: Julio C. Herrera Exam 3 January 30, 2015
Name: Exam Score: Instructions: This exam covers the material from chapter 7 through 9. Please read each question carefully before you attempt to solve it. Remember that you have to show all of your work
More informationSampling and Hypothesis Testing
Population and sample Sampling and Hypothesis Testing Allin Cottrell Population : an entire set of objects or units of observation of one sort or another. Sample : subset of a population. Parameter versus
More informationChapter 6: t test for dependent samples
Chapter 6: t test for dependent samples ****This chapter corresponds to chapter 11 of your book ( t(ea) for Two (Again) ). What it is: The t test for dependent samples is used to determine whether the
More informationStatistics II (Discrete Methods: STAT 453/653) Fall 2007 Homework 5 Example Solution
Statistics II (Discrete Methods: STAT 453/653) Fall 007 Homework 5 Eamle Solution Written by: Fares Qeadan, Reviewed by: Ilya Zaliain Deartment of Mathematics Statistics, University of Nevada, Reno Problem
More informationDream Recall and Political Ideology: Results of a Demographic Survey
Dream Recall and Political Ideology: Results of a Demograhic Survey Kelly Bulkeley The Graduate Theological Union This reort resents findings from a survey of 2992 demograhically diverse American adults
More informationThe Lognormal Distribution Engr 323 Geppert page 1of 6 The Lognormal Distribution
Engr 33 Geert age 1of 6 The Lognormal Distribution In general, the most imortant roerty of the lognormal rocess is that it reresents a roduct of indeendent random variables. (Class Handout on Lognormal
More informationProbability & Statistics
Probability & Statistics BITS Pilani K K Birla Goa Campus Dr. Jajati Keshari Sahoo Department of Mathematics TEST OF HYPOTHESIS There are many problems in which, rather then estimating the value of a parameter,
More informationFind Probabilities Using Permutations. Count permutations. Choices for 1st letter
13.2 Find Probabilities Using Permutations Before You used the counting rincile. Now You will use the formula for the number of ermutations. Why? So you can find the number of ossible arrangements, as
More informationAsymmetric Information, Transaction Cost, and. Externalities in Competitive Insurance Markets *
Asymmetric Information, Transaction Cost, and Externalities in Cometitive Insurance Markets * Jerry W. iu Deartment of Finance, University of Notre Dame, Notre Dame, IN 465565646 wliu@nd.edu Mark J. Browne
More informationEE302 Division 1 Homework 2 Solutions.
EE302 Division Homework 2 Solutions. Problem. Prof. Pollak is flying from L to Paris with two lane changes, in New York and London. The robability to lose a iece of luggage is the same,, in L, NY, and
More informationECONOMIC ANALYSIS AND MODELLING OF LOCAL GOVERNMENT MONTHLY EXPENDITURE ON INCOME IN THE SOUTH WEST ZONE OF NIGERIA
IJRRAS 7 () November 0 www.araress.com/volumes/vol7issue/ijrras_7 06.df ECONOMIC ANALYSIS AND MODELLING OF LOCAL GOVERNMENT MONTHLY EXPENDITURE ON INCOME IN THE SOUTH WEST ZONE OF NIGERIA Olawuwo Simeon,
More information