Hypothesis Testing (unknown σ)


 Eleanore Conley
 2 years ago
 Views:
Transcription
1 Hypothesis Testing (unknown σ) Business Statistics Recall: Plan for Today Null and Alternative Hypotheses Types of errors: type I, type II Types of correct decisions: type A, type B Level of Significance and Power of the Test Hypothesis testing with unknown σ Examples 1
2 Null and Alternative hypothesis Hypothesis : A statement about the value of a population parameter. In case of two hypotheses, the statement assumed to be true is called the null hypothesis (notation H0) and the contradictory statement is called the alternative hypothesis (notation Ha). Hypothesis testing : Based on sample evidence, a procedure for determining whether the hypothesis stated is a reasonable statement and should not be rejected, or is unreasonable and should be rejected. Null and Alternative Hypotheses The null hypothesis (H0) : It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt. The alternative hypothesis (Ha): It is a claim about the population that is contradictory to H0 and what we conclude when we reject H0. 2
3 How to formulate the conclusion The conclusions are made in reference to the null hypothesis. We either reject the null hypothesis, or else we fail to reject the null hypothesis. If we reject the null hypothesis, it means that our data support the alternative hypotheses. If we fail to reject H0, it does not mean that it is proven to be true. It only means that our data fits within its scope. Errors and Correct Decisions Example: buying a laundry detergent. Two choices: Tide and generic detergent VS 3
4 Example: laundry detergents (continued) H0: there is no difference in performance Ha: Tide performs better H0 is true Type A correct decision. Decision: no difference in performance (and it is true). You bought generic product and saved money. Type I error (false positive). Decision: Tide performs better (in reality, no difference) You bought Tide and wasted $$ H0 is false Type II error (false negative). Decision: no difference (false, as Tide performs better). You bought generic product, got inferior results. Type B correct decision. Decision: Tide is better (true) You bought Tide and got better results Video on hypothesis testing with example: 4
5 Alpha and beta α is the level of significance of the test It equals the probability of making a type I error. 1 α equals the probability of making type A correct decision β is the probability of making a type II error. 1 β is called the Power of the Test. It equals the probability of making type B correct decision. Hypothesis testing when σ is not known When the population standard deviation, σ, is not known, we use the sample standard deviation, s, instead. And instead of the normal distribution, we use the Student s t distribution. For the classical approach, we will use Table 2 (Critical Values of Student s t Distribution), and for the pvalue approach we will use Table 3 (called pvalues for Student s t Distribution) with df = n 1 5
6 Hypothesis testing (classical approach) 1. State the hypotheses H0 and Ha. 2. Compute the test statistic t = x μ s n 3. Find the critical value(s) in the table. 4. Draw a bellshaped curve and indicate the region(s) of rejection. 5. Place the test statistic onto the graph. 6. State your decision. Tails and critical values H a : μ μ 0 a twotailed test with the critical values ±t( df, α 2) H a : μ > μ 0 a righttailed test with the critical value t(df, α) H a : μ < μ 0 a lefttailed test with the critical value t(df, α) 6
7 Hypothesis testing (pvalue approach) 1. State the hypotheses H0 and Ha. 2. Compute the test statistic t = x μ s n 3. Is this a left, right, or a twotailed test? 4. Find the corresponding pvalue in the table. 5. Compare the pvalue with the level of significance α. 6. State your decision. What is the pvalue? Righttailed test: the area to the right of t Lefttailed test: the area to the left of t Twotailed test: twice the area mathcaptain.com 7
8 Comparing the pvalue and α: If the pvalue is smaller than the level of significance α, it means that the test statistic is in the region of rejection. In this case, decision: reject H0. If the pvalue is larger than the level of significance α, it means that the test statistic is in the region of acceptance. In this case, decision: fail to reject H0. Example: righttailed test A company that makes Orange Soda claims that on the average its soda cans contain no more than 39 grams of sugar. A random sample of 12 cans tested in a lab yielded the following sugar contents (in grams): Can we disprove the company s claim at a 5% level of significance? Assume that the amount of sugar in cans is normally distributed. 8
9 Example: Orange Soda (classical approach) 1. H 0 : μ 39 g H a : μ > 39 g 2. Compute from sample: x = g, s = g Test statistic: t = / 12 = Since α = 0.05, we have the critical value t df, α = t 11, 0.05 = Plot the curve! 5. Where is t? (in the region of rejection) 6. Decision: reject H0 Example: Orange Soda (the pvalue approach) 1. H 0 : μ 39 g H a : μ > 39 g 2. Test statistic t = This is a righttailed test. 4. From Table 3 with df = 11: pvalue = (always pick the bigger value) 5. Compare: pvalue = < 0.05 = α 6. Decision: Reject H0 9
10 Example: lefttailed test A restaurant owner has counted the number of clients in his restaurant during 14 randomly selected Fridays: He wants to test the claim that the average number of clients in the restaurant on Fridays is actually smaller than 186, using a 2.5% level of significance. Assume that the number of clients is normally distributed. Example: restaurant (classical approach) 1. H 0 : μ 186 H a : μ < Compute from the sample: x = and s = Test statistic: t = = α = 0.025, the critical value: t df, α = t 13, = Plot the curve 5. Where is t? (in the region of acceptance) 6. Decision: Fail to reject H0 10
11 Example: restaurant (the pvalue approach) 1. H 0 : μ 186 H a : μ < Test statistic: t = This is a lefttailed test. 4. Use Table 3 to find with df = 13 pvalue = (take the larger value) 5. Compare: pvalue = > = α 6. Decision: Fail to reject H0 Example: twotailed test According to a website, the average weekly wage of government workers is $1038. A sample of randomly chosen 11 government workers is taken and their weekly wages are recorded: $1080 $990 $1540 $960 $920 $880 $1220 $1630 $940 $1270 $1160 Test at a 10% level of significance whether the average weekly wage of government workers is actually different from $1038. Assume a normal distribution of wages. 11
12 Example: wages (classical approach) 1. H 0 : μ = $1038 H a : μ $ Compute from the sample: x = $ and s = $252.6 Test statistic: t = = α = 0.1, the critical values: ±t df, α/2 = ±t 10, 0.05 = ± Plot the curve 5. Where is t? (in the region of acceptance) 6. Decision: Fail to reject H0 Example: wages (the pvalue approach) 1. H 0 : μ = $1038 H a : μ $ Test statistic: t = This is a twotailed test with positive t. 4. Find the pvalue from Table 3 with df = 10: pvalue = 2 * = (because twotailed!) 5. Compare: pvalue = > 0.1 = α 6. Decision: Fail to reject H0 The decision would be different if we would ve forgotten to multiply by 2. 12
13 Example: practice An article in the San Jose Mercury News claims that students in the California state university system take an average of 4.5 years to finish their undergraduate degrees. Suppose you suspect that the average time is longer. You conduct a survey of 30 students and obtain a sample mean of 4.8 years and a sample standard deviation of 0.9 years. Test the claim at a 5% level of significance. (Do both, the classical, and the pvalue approaches.) Example: practice A website claims that in Toronto, the average water/garbage bill for a single family house is $650 per year. A researcher wants to test this claim by randomly choosing 50 single family houses. The average water/garbage bill in his sample turns out to be equal to $705 per year with a standard deviation of $195. Can he claim that the average annual water/garbage bill for a single family house in Toronto is actually different from $650 at a 2% level of significance? 13
14 Example: practice A telephone company claims that the mean duration of all longdistance phone calls made by its residential customers is at least 11 minutes. Here is a random sample of 16 longdistance calls, in minutes: Assuming the duration of longdistance calls is normally distributed, test at a 10% level of significance whether the mean duration of all longdistance calls is actually less than 11 minutes. 14
Hypothesis 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 informationWording of Final Conclusion. Slide 1
Wording of Final Conclusion Slide 1 8.3: Assumptions for Testing Slide 2 Claims About Population Means 1) The sample is a simple random sample. 2) The value of the population standard deviation σ is known
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 7. Hypothesis Testing with One Sample
Chapter 7 Hypothesis Testing with One Sample 7.1 Introduction to Hypothesis Testing Hypothesis Tests A hypothesis test is a process that uses sample statistics to test a claim about the value of a population
More informationHypothesis Testing with One Sample. Introduction to Hypothesis Testing 7.1. Hypothesis Tests. Chapter 7
Chapter 7 Hypothesis Testing with One Sample 71 Introduction to Hypothesis Testing Hypothesis Tests A hypothesis test is a process that uses sample statistics to test a claim about the value of a population
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 informationSection 7.1. Introduction to Hypothesis Testing. Schrodinger s cat quantum mechanics thought experiment (1935)
Section 7.1 Introduction to Hypothesis Testing Schrodinger s cat quantum mechanics thought experiment (1935) Statistical Hypotheses A statistical hypothesis is a claim about a population. Null hypothesis
More informationHypothesis Testing  One Mean
Hypothesis Testing  One Mean A hypothesis is simply a statement that something is true. Typically, there are two hypotheses in a hypothesis test: the null, and the alternative. Null Hypothesis The hypothesis
More informationHypothesis Testing. Bluman Chapter 8
CHAPTER 8 Learning Objectives C H A P T E R E I G H T Hypothesis Testing 1 Outline 81 Steps in Traditional Method 82 z Test for a Mean 83 t Test for a Mean 84 z Test for a Proportion 85 2 Test for
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 informationThe topics in this section concern with the second course objective.
3.2 Hypothesis Testing The topics in this section concern with the second course objective. In practice, a decision is often made according to the result of a statistical analysis, actually a statistical
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 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 informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
STA2023 Module 10 Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A hypothesis test is to be performed. Determine the null and alternative
More informationChapter III. Testing Hypotheses
Chapter III Testing Hypotheses R (Introduction) A statistical hypothesis is an assumption about a population parameter This assumption may or may not be true The best way to determine whether a statistical
More informationPROBLEM SET 1. For the first three answer true or false and explain your answer. A picture is often helpful.
PROBLEM SET 1 For the first three answer true or false and explain your answer. A picture is often helpful. 1. Suppose the significance level of a hypothesis test is α=0.05. If the pvalue of the test
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 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 informationMCQ TESTING OF HYPOTHESIS
MCQ TESTING OF HYPOTHESIS MCQ 13.1 A statement about a population developed for the purpose of testing is called: (a) Hypothesis (b) Hypothesis testing (c) Level of significance (d) Teststatistic MCQ
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 informationStatistical Inference and ttests
1 Statistical Inference and ttests Objectives Evaluate the difference between a sample mean and a target value using a onesample ttest. Evaluate the difference between a sample mean and a target value
More informationChapter Additional: Standard Deviation and Chi Square
Chapter Additional: Standard Deviation and Chi Square Chapter Outline: 6.4 Confidence Intervals for the Standard Deviation 7.5 Hypothesis testing for Standard Deviation Section 6.4 Objectives Interpret
More informationMath 10 MPS Homework 6 Answers to additional problems
Math 1 MPS Homework 6 Answers to additional problems 1. What are the two types of hypotheses used in a hypothesis test? How are they related? Ho: Null Hypotheses A statement about a population parameter
More informationMATH 10: Elementary Statistics and Probability Chapter 9: Hypothesis Testing with One Sample
MATH 10: Elementary Statistics and Probability Chapter 9: Hypothesis Testing with One Sample Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of
More informationHypothesis testing: Examples. AMS7, Spring 2012
Hypothesis testing: Examples AMS7, Spring 2012 Example 1: Testing a Claim about a Proportion Sect. 7.3, # 2: Survey of Drinking: In a Gallup survey, 1087 randomly selected adults were asked whether they
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 informationCHAPTER 9 HYPOTHESIS TESTING
CHAPTER 9 HYPOTHESIS TESTING A hypothesis test is a formal way to make a decision based on statistical analysis. A hypothesis test has the following general steps: Set up two contradictory hypotheses.
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 informationHypothesis Testing Population Mean
Ztest About One Mean ypothesis Testing Population Mean The Ztest about a mean of population we are using is applied in the following three cases: a. The population distribution is normal and the population
More informationThe alternative hypothesis,, is the statement that the parameter value somehow differs from that claimed by the null hypothesis. : 0.5 :>0.5 :<0.
Section 8.28.5 Null and Alternative Hypotheses... The null hypothesis,, is a statement that the value of a population parameter is equal to some claimed value. :=0.5 The alternative hypothesis,, is the
More informationSTA218 Introduction to Hypothesis Testing
STA218 Introduction to Hypothesis Testing Al Nosedal. University of Toronto. Fall 2015 October 29, 2015 Who wants to be a millionaire? Let s say that one of you is invited to this popular show. As you
More informationHypothesis Testing. Chapter Introduction
Contents 9 Hypothesis Testing 553 9.1 Introduction............................ 553 9.2 Hypothesis Test for a Mean................... 557 9.2.1 Steps in Hypothesis Testing............... 557 9.2.2 Diagrammatic
More informationChapter 8 Introduction to Hypothesis Testing
Chapter 8 Student Lecture Notes 81 Chapter 8 Introduction to Hypothesis Testing Fall 26 Fundamentals of Business Statistics 1 Chapter Goals After completing this chapter, you should be able to: Formulate
More informationThe ChiSquare Distributions
MATH 183 The ChiSquare Distributions Dr. Neal, WKU The chisquare distributions can be used in statistics to analyze the standard deviation " of a normally distributed measurement and to test the goodness
More informationChapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 81 Overview 82 Basics of Hypothesis Testing
Chapter 8 Hypothesis Testing 1 Chapter 8 Hypothesis Testing 81 Overview 82 Basics of Hypothesis Testing 83 Testing a Claim About a Proportion 85 Testing a Claim About a Mean: s Not Known 86 Testing
More informationChapter 9: Hypothesis Tests of a Single Population
Chapter 9: Hypothesis Tests of a Single Population Department of Mathematics Izmir University of Economics Week 12 20142015 Introduction In this chapter we will focus on Example developing hypothesis
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 informationA) to D) to B) to E) to C) to Rate of hay fever per 1000 population for people under 25
Unit 0 Review #3 Name: Date:. Suppose a random sample of 380 married couples found that 54 had two or more personality preferences in common. In another random sample of 573 married couples, it was found
More informationHypothesis Testing: Single Mean and Single Proportion
Chapter 9 Hypothesis Testing: Single Mean and Single Proportion 9.1 Hypothesis Testing: Single Mean and Single Proportion 1 9.1.1 Student Learning Objectives By the end of this chapter, the student should
More information82 Basics of Hypothesis Testing. Definitions. Rare Event Rule for Inferential Statistics. Null Hypothesis
82 Basics of Hypothesis Testing Definitions This section presents individual components of a hypothesis test. We should know and understand the following: How to identify the null hypothesis and alternative
More informationStatistics for Management IISTAT 362Final Review
Statistics for Management IISTAT 362Final Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. The ability of an interval estimate to
More informationNull Hypothesis H 0. The null hypothesis (denoted by H 0
Hypothesis test 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 a claim about a property
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 informationChapter 9 Introduction to Hypothesis Testing
Chapter 9 Introduction to Hypothesis Testing 9.2  Hypothesis Testing Hypothesis testing is an eample of inferential statistics We use sample information to draw conclusions about the population from which
More informationThird Midterm Exam (MATH1070 Spring 2012)
Third Midterm Exam (MATH1070 Spring 2012) Instructions: This is a one hour exam. You can use a notesheet. Calculators are allowed, but other electronics are prohibited. 1. [40pts] Multiple Choice Problems
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 informationLecture 13: Kolmogorov Smirnov Test & Power of Tests
Lecture 13: Kolmogorov Smirnov Test & Power of Tests S. Massa, Department of Statistics, University of Oxford 2 February 2016 An example Suppose you are given the following 100 observations. 0.160.680.320.85
More informationHypothesis Tests for a Population Proportion
Hypothesis Tests for a Population Proportion MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2015 Review: Steps of Hypothesis Testing 1. A statement is made regarding
More information1 Confidence intervals
Math 143 Inference for Means 1 Statistical inference is inferring information about the distribution of a population from information about a sample. We re generally talking about one of two things: 1.
More informationHypothesis Testing I
ypothesis Testing I The testing process:. Assumption about population(s) parameter(s) is made, called null hypothesis, denoted. 2. Then the alternative is chosen (often just a negation of the null hypothesis),
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 informationChapter 9, Part A Hypothesis Tests. Learning objectives
Chapter 9, Part A Hypothesis Tests Slide 1 Learning objectives 1. Understand how to develop Null and Alternative Hypotheses 2. Understand Type I and Type II Errors 3. Able to do hypothesis test about population
More informationChapter Five. Hypothesis Testing: Concepts
Chapter Five The Purpose of Hypothesis Testing... 110 An Initial Look at Hypothesis Testing... 112 Formal Hypothesis Testing... 114 Introduction... 114 Null and Alternate Hypotheses... 114 Procedure for
More informationCHAPTER 10: HYPOTHESIS TESTING WITH TWO SAMPLES
CHAPTER 10: HYPOTHESIS TESTING WITH TWO SAMPLES Exercise 1. Exercise 2. Exercise 3. Indicate if the hypothesis test is for a. independent group means, population standard deviations, and/or variances known
More informationStatistics Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Statistics Final Exam Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Assume that X has a normal distribution, and find the indicated
More informationStat 210 Exam Four. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Stat 210 Exam Four Read these directions carefully. As usual, you may pick any part of one problem to omit by writing OMIT in the answer blank (any one multiple choice or any one part of the other problems).
More informationFor instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on the average.
Hypothesis Testing: Single Mean and Single Proportion Introduction One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question
Stats: Test Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Provide an appropriate response. ) Given H0: p 0% and Ha: p < 0%, determine
More informationMAT X Hypothesis Testing  Part I
MAT 2379 3X Hypothesis Testing  Part I Definition : A hypothesis is a conjecture concerning a value of a population parameter (or the shape of the population). The hypothesis will be tested by evaluating
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 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 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 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 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 informationUnit 21 Student s t Distribution in Hypotheses Testing
Unit 21 Student s t Distribution in Hypotheses Testing Objectives: To understand the difference between the standard normal distribution and the Student's t distributions To understand the difference between
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 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 informationPractice Set 8b ST Spring 2014
Practice Set 8b ST 20  Spring 204 The following problem set will help you work with hypothesis testing.. Ex 8.7 (p. 400. Add the following parts: (c Explain why the assumption that interpupillary distance
More informationNull and Alternative Hypotheses
OpenStaxCNX module m47033 1 Null and Alternative Hypotheses OpenStax College This work is produced by OpenStaxCNX and licensed under the Creative Commons Attribution License 3.0 The actual test begins
More informationConnexions module: m
Connexions module: m17025 1 Hypothesis Testing: Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Unknown Population Standard Deviations Susan Dean Barbara
More informationHypothesis Testing  II
3σ 2σ +σ +2σ +3σ Hypothesis Testing  II Lecture 9 0909.400.01 / 0909.400.02 Dr. P. s Clinic Consultant Module in Probability & Statistics in Engineering Today in P&S 3σ 2σ +σ +2σ +3σ Review: Hypothesis
More informationPower & Effect Size power Effect Size
Power & Effect Size Until recently, researchers were primarily concerned with controlling Type I errors (i.e. finding a difference when one does not truly exist). Although it is important to make sure
More informationOneSample ttest. Example 1: Mortgage Process Time. Problem. Data set. Data collection. Tools
OneSample ttest Example 1: Mortgage Process Time Problem A faster loan processing time produces higher productivity and greater customer satisfaction. A financial services institution wants to establish
More informationAMS 5 HYPOTHESIS TESTING
AMS 5 HYPOTHESIS TESTING Hypothesis Testing Was it due to chance, or something else? Decide between two hypotheses that are mutually exclusive on the basis of evidence from observations. Test of Significance
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 informationStatistiek I. ttests. John Nerbonne. CLCG, Rijksuniversiteit Groningen. John Nerbonne 1/35
Statistiek I ttests John Nerbonne CLCG, Rijksuniversiteit Groningen http://wwwletrugnl/nerbonne/teach/statistieki/ John Nerbonne 1/35 ttests To test an average or pair of averages when σ is known, we
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 informationIntroductory Statistics Hypothesis Testing Review( Critical Value Approach)
MULTIPLE CHOICE. Introductory Statistics Hypothesis Testing Review( Critical Value Approach) Determine the critical value(s) for a onemean ztest. 1) A lefttailed test with α = 0.02. A) ±1.96 B) ±2.054
More informationClassical Hypothesis Testing and GWAS
Department of Computer Science Brown University, Providence sorin@cs.brown.edu September 15, 2014 Outline General Principles Classical statistical hypothesis testing involves the test of a null hypothesis
More informationMath 251: Practice Questions for Test III Hints and Answers.. Then. P (67 x 69) = P (.33 z.33) = =.2586.
Math 251: Practice Questions for Test III Hints and Answers III.A: The Central Limit Theorem and Sampling Distributions. III.A.1 The heights of 18yearold men are approximately normally distributed with
More informationHypothesis Testing Level I Quantitative Methods. IFT Notes for the CFA exam
Hypothesis Testing 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 3 2. Hypothesis Testing... 3 3. Hypothesis Tests Concerning the Mean... 10 4. Hypothesis Tests
More informationTests of Hypotheses: Means
Tests of Hypotheses: Means We often use inferential statistics to make decisions or judgments about the value of a parameter, such as a population mean. For example, we might need to decide whether the
More informationUnit 24 Hypothesis Tests about Means
Unit 24 Hypothesis Tests about Means Objectives: To recognize the difference between a paired t test and a twosample t test To perform a paired t test To perform a twosample t test A measure of the amount
More information1. What are the two types of hypotheses used in a hypothesis test? How are they related?
Math 10  Homework 6 Part A 1. What are the two types of hypotheses used in a hypothesis test? How are they related? 2. Describe the two types of error possible in a hypothesis test decision. True or False?
More informationIntroduction to Hypothesis Testing. Hypothesis Testing. Step 1: State the Hypotheses
Introduction to Hypothesis Testing 1 Hypothesis Testing A hypothesis test is a statistical procedure that uses sample data to evaluate a hypothesis about a population Hypothesis is stated in terms of the
More informationHypothesis Testing 1
Hypothesis Testing 1 Statistical procedures for addressing research questions involves formulating a concise statement of the hypothesis to be tested. The hypothesis to be tested is referred to as the
More informationChapter 8 Hypothesis Testing
Chapter 8 Hypothesis Testing Chapter problem: Does the MicroSort method of gender selection increase the likelihood that a baby will be girl? MicroSort: a genderselection method developed by Genetics
More information5/31/2013. Chapter 8 Hypothesis Testing. Hypothesis Testing. Hypothesis Testing. Outline. Objectives. Objectives
C H 8A P T E R Outline 8 1 Steps in Traditional Method 8 2 z Test for a Mean 8 3 t Test for a Mean 8 4 z Test for a Proportion 8 6 Confidence Intervals and Copyright 2013 The McGraw Hill Companies, Inc.
More informationHypothesis Testing. Chapter 7
Hypothesis Testing Chapter 7 Hypothesis Testing Time to make the educated guess after answering: What the population is, how to extract the sample, what characteristics to measure in the sample, After
More informationE205 Final: Version B
Name: Class: Date: E205 Final: Version B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of a local nightclub has recently surveyed a random
More informationAn Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 9  FUNDAMENTALS OF HYPOTHESIS TESTING: ONESAMPLE TESTS
The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 302) Spring Semester 20 Chapter 9  FUNDAMENTALS OF HYPOTHESIS
More information6/19/13 Practice problems on ch 8 and ch 11
6/19/13 Practice problems on ch 8 and ch 11 For all hypotheses test you must do the following: z/t test a. State the hypotheses and identify the claim. b. Find the critical values. c. Compute the test
More informationThe calculations lead to the following values: d 2 = 46, n = 8, s d 2 = 4, s d = 2, SEof d = s d n s d n
EXAMPLE 1: Paired ttest and tinterval DBP Readings by Two Devices The diastolic blood pressures (DBP) of 8 patients were determined using two techniques: the standard method used by medical personnel
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
STATISTICS/GRACEY EXAM 3 PRACTICE/CH. 89 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the Pvalue for the indicated hypothesis test. 1) A
More informationMath 251, Review Questions for Test 3 Rough Answers
Math 251, Review Questions for Test 3 Rough Answers 1. (Review of some terminology from Section 7.1) In a state with 459,341 voters, a poll of 2300 voters finds that 45 percent support the Republican candidate,
More information9.1 Hypothesis Testing
9.1 Hypothesis Testing Define: 1. Null Hypothesis 2. Alternative Hypothesis Null Hypothesis: H 0, statement that the population proportion, or population mean is EQUAL TO a number population proportion
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 informationMeasuring the Power of a Test
Textbook Reference: Chapter 9.5 Measuring the Power of a Test An economic problem motivates the statement of a null and alternative hypothesis. For a numeric data set, a decision rule can lead to the rejection
More informationChapter 08. Introduction
Chapter 08 Introduction Hypothesis testing may best be summarized as a decision making process in which one attempts to arrive at a particular conclusion based upon "statistical" evidence. A typical hypothesis
More informationChiSquare Tests TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson
Math Objectives Students will recognize that chisquared tests are for counts of categorical data. Students will identify the appropriate chisquared test to use for a given situation: 2 Goodness of Fit
More information