# Chapter 9, Part A Hypothesis Tests. Learning objectives

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 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 mean when σ is known 4. Able to do hypothesis test about population mean when σ is unknown Slide 2 1

2 Null and Alternative Hypotheses Hypothesis testing can be used to determine whether a statement about the value of a population parameter should or should not be rejected. The null hypothesis, denoted by H, is a tentative assumption about a population parameter. The alternative hypothesis, denoted by H a, is the opposite of what is stated in the null hypothesis. The alternative hypothesis is what the test is attempting to establish. Slide 3 Null and Alternative Hypotheses: Applications Testing Research Hypotheses The research hypothesis should be expressed as the alternative hypothesis. The conclusion that the research hypothesis is true comes from sample data that contradict the null hypothesis. Slide 4 2

3 Null and Alternative Hypotheses: Applications Testing the Validity of a Claim Manufacturers claims are usually given the benefit of the doubt and stated as the null hypothesis. The conclusion that the claim is false comes from sample data that contradict the null hypothesis. Slide 5 Null and Alternative Hypotheses: Applications Testing in Decision-Making Situations A decision maker might have to choose between two courses of action, one associated with the null hypothesis and another associated with the alternative hypothesis. Example: Accepting a shipment of goods from a supplier or returning the shipment of goods to the supplier Slide 6 3

4 Summary of Forms for Null and Alternative Hypotheses about a Population Mean The equality part of the hypotheses always appears in the null hypothesis. In general, a hypothesis test about the value of a population mean µ must take one of the following three forms (where µ is the hypothesized value of the population mean). H : µ µ : a < H µ µ One-tailed (lower-tail) H : µ µ : a > H µ µ One-tailed (upper-tail) H : µ = µ : a H µ µ Two-tailed Slide 7 Null and Alternative Hypotheses Example: Metro EMS A major west coast city provides one of the most comprehensive emergency medical services in the world. Operating in a multiple hospital system with approximately 2 mobile medical units, the service goal is to respond to medical emergencies with a mean time of 12 minutes or less. Slide 8 4

5 Null and Alternative Hypotheses Example: Metro EMS The director of medical services wants to formulate a hypothesis test that could use a sample of emergency response times to determine whether or not the service goal of 12 minutes or less is being achieved. Slide 9 Null and Alternative Hypotheses H : µ < 12 H a : µ > 12 The emergency service is meeting the response goal; no follow-up action is necessary. The emergency service is not meeting the response goal; appropriate follow-up action is necessary. where: µ = mean response time for the population of medical emergency requests Slide 1 5

6 Type I Error Because hypothesis tests are based on sample data, we must allow for the possibility of errors. A Type I error is rejecting H when it is true. The probability of making a Type I error when the null hypothesis is true as an equality is called the level of significance. Applications of hypothesis testing that only control the Type I error are often called significance tests. Slide 11 Type II Error A Type II error is accepting H when it is false. It is difficult to control for the probability of making a Type II error. Statisticians avoid the risk of making a Type II error by using do not reject H and not accept H. Slide 12 6

7 Type I and Type II Errors Population Condition Conclusion Accept H (Conclude µ < 12) H True (µ < 12) Correct Decision H False (µ > 12) Type II Error (β) Reject H (Conclude µ > 12) Type I Error (α) Correct Decision Slide 13 p-value Approach to One-Tailed Hypothesis Testing The p-value is the probability, computed using the test statistic, that measures the support (or lack of support) provided by the sample for the null hypothesis. If the p-value is less than or equal to the level of significance α, the value of the test statistic is in the rejection region. Reject H if the p-value < α. Slide 14 7

8 Lower-Tailed Test About a Population Mean: p-value Approach p-value < α, so reject H. α =.1 p-value =.72 Sampling distribution x of z = µ σ / n z = z α = z Slide 15 Upper-Tailed Test About a Population Mean: p-value Approach Sampling distribution x of z = µ σ / n p-value < α, so reject H. α =.4 p-value =.11 z α = 1.75 z = 2.29 z Slide 16 8

9 Critical Value Approach to One-Tailed Hypothesis Testing The test statistic z has a standard normal probability distribution. We can use the standard normal probability distribution table to find the z-value with an area of α in the lower (or upper) tail of the distribution. The value of the test statistic that established the boundary of the rejection region is called the critical value for the test. The rejection rule is: Lower tail: Reject H if z < -z α Upper tail: Reject H if z > z α Slide 17 Lower-Tailed Test About a Population Mean: Critical Value Approach Reject H α =.1 Sampling distribution x of z = µ σ / n Do Not Reject H z α = 1.28 z Slide 18 9

10 Upper-Tailed Test About a Population Mean: Critical Value Approach Sampling distribution x of z = µ σ / n Do Not Reject H α =.5 Reject H z α = z Slide 19 Steps of Hypothesis Testing Step 1. Develop the null and alternative hypotheses. Step 2. Specify the level of significance α. Step 3. Collect the sample data and compute the test statistic. p-value Approach Step 4. Use the value of the test statistic to compute the p-value. Step 5. Reject H if p-value < α. Slide 2 1

11 Steps of Hypothesis Testing Critical Value Approach Step 4. Use the level of significance to determine the critical value and the rejection rule. Step 5. Use the value of the test statistic and the rejection rule to determine whether to reject H. Slide 21 One-Tailed Tests About a Population Mean: Example: Metro EMS The response times for a random sample of 4 medical emergencies were tabulated. The sample mean is minutes. The population standard deviation is believed to be 3.2 minutes. The EMS director wants to perform a hypothesis test, with a.5 level of significance, to determine whether the service goal of 12 minutes or less is being achieved. Slide 22 11

12 One-Tailed Tests About a Population Mean: p -Value and Critical Value Approaches 1. Develop the hypotheses. H : µ < 12 H a : µ > Specify the level of significance. α =.5 3. Compute the value of the test statistic. x µ z = = = σ / n 3.2/ Slide 23 One-Tailed Tests About a Population Mean: p Value Approach 4. Compute the p value. For z = 2.47, cumulative probability = p value = = Determine whether to reject H. Because p value =.68 < α =.5, we reject H. We are at least 95% confident that Metro EMS is not meeting the response goal of 12 minutes. Slide 24 12

13 One-Tailed Tests About a Population Mean: p Value Approach Sampling distribution x of z = µ σ / n α =.5 p-value =.68 z α = z = 2.47 z Slide 25 One-Tailed Tests About a Population Mean: Critical Value Approach 4. Determine the critical value and rejection rule. For α =.5, z.5 = Reject H if z > Determine whether to reject H. Because 2.47 > 1.645, we reject H. We are at least 95% confident that Metro EMS is not meeting the response goal of 12 minutes. Slide 26 13

14 p-value Approach to Two-Tailed Hypothesis Testing Compute the p-value using the following three steps: 1. Compute the value of the test statistic z. 2. If z is in the upper tail (z > ), find the area under the standard normal curve to the right of z. If z is in the lower tail (z < ), find the area under the standard normal curve to the left of z. 3. Double the tail area obtained in step 2 to obtain the p value. The rejection rule: Reject H if the p-value < α. Slide 27 Critical Value Approach to Two-Tailed Hypothesis Testing The critical values will occur in both the lower and upper tails of the standard normal curve. Use the standard normal probability distribution table to find z α/2 (the z-value with an area of α/2 in the upper tail of the distribution). The rejection rule is: Reject H if z < -z α/2 or z > z α/2. Slide 28 14

15 Example: Glow Toothpaste Two-Tailed Test About a Population Mean: The production line for Glow toothpaste is designed to fill tubes with a mean weight of 6 oz. Periodically, a sample of 3 tubes will be selected in order to check the filling process. Quality assurance procedures call for the continuation of the filling process if the sample results are consistent with the assumption that the mean filling weight for the population of toothpaste tubes is 6 oz.; otherwise the process will be adjusted. oz. Glow Slide 29 Example: Glow Toothpaste Two-Tailed Test About a Population Mean: Assume that a sample of 3 toothpaste tubes provides a sample mean of 6.1 oz. The population standard deviation is believed to be.2 oz. Perform a hypothesis test, at the.3 level of significance, to help determine whether the filling process should continue operating or be stopped and corrected. oz. Glow Slide 3 15

16 Two-Tailed Tests About a Population Mean: p Value and Critical Value Approaches Glow 1. Determine the hypotheses. H : µ = 6 H a : µ Specify the level of significance. α =.3 3. Compute the value of the test statistic. x µ z = = = σ / n.2/ Slide 31 Two-Tailed Tests About a Population Mean: p Value Approach Glow 4. Compute the p value. For z = 2.74, cumulative probability =.9969 p value = 2(1.9969) = Determine whether to reject H. Because p value =.62 < α =.3, we reject H. We are at least 97% confident that the mean filling weight of the toothpaste tubes is not 6 oz. Slide 32 16

17 Two-Tailed Tests About a Population Mean: p-value Approach Glow 1/2 p -value =.31 1/2 p -value =.31 α/2 =.15 z = z α/2 = α/2 =.15 z z = 2.74 z α/2 = 2.17 Slide 33 Two-Tailed Tests About a Population Mean: Critical Value Approach 4. Determine the critical value and rejection rule. For α/2 =.3/2 =.15, z.15 = 2.17 Reject H if z < or z > Determine whether to reject H. Because 2.47 > 2.17, we reject H. We are at least 97% confident that the mean filling weight of the toothpaste tubes is not 6 oz. Glow Slide 34 17

18 Two-Tailed Tests About a Population Mean: Critical Value Approach Glow Sampling distribution x of z = µ σ / n Reject H α/2 =.15 Do Not Reject H Reject H α/2 = z Slide 35 Confidence Interval Approach to Two-Tailed Tests About a Population Mean Select a simple random sample from the population and use the value of the sample mean x to develop the confidence interval for the population mean µ. (Confidence intervals are covered in Chapter 8.) If the confidence interval contains the hypothesized value µ, do not reject H. Otherwise, reject H. Slide 36 18

19 Confidence Interval Approach to Two-Tailed Tests About a Population Mean The 97% confidence interval for µ is σ x ± z α /2 = 6.1 ± 2.17(.2 3) = 6.1 ±.7924 n or to Because the hypothesized value for the population mean, µ = 6, is not in this interval, the hypothesis-testing conclusion is that the null hypothesis, H : µ = 6, can be rejected. Glow Slide 37 In-class exercise #1 (p.355) (one-tail test) #11 (p.355) (two-tail test) Slide 38 19

20 Test Statistic Tests About a Population Mean: σ Unknown t = x µ s / n This test statistic has a t distribution with n -1 degrees of freedom. Slide 39 Tests About a Population Mean: σ Unknown Rejection Rule: p -Value Approach Reject H if p value < α Rejection Rule: Critical Value Approach H : µ > µ Reject H if t < -t α H : µ < µ Reject H if t > t α H : µ = µ Reject H if t < - t α/2 or t > t α/2 Slide 4 2

21 p -Values and the t Distribution The format of the t distribution table provided in most statistics textbooks does not have sufficient detail to determine the exact p-value for a hypothesis test. However, we can still use the t distribution table to identify a range for the p-value. An advantage of computer software packages is that the computer output will provide the p-value for the t distribution. Slide 41 Example: Highway Patrol One-Tailed Test About a Population Mean: σ Unknown A State Highway Patrol periodically samples vehicle speeds at various locations on a particular roadway. The sample of vehicle speeds is used to test the hypothesis H : µ < 65 The locations where H is rejected are deemed the best locations for radar traps. Slide 42 21

22 Example: Highway Patrol One-Tailed Test About a Population Mean: σ Unknown At Location F, a sample of 64 vehicles shows a mean speed of 66.2 mph with a standard deviation of 4.2 mph. Use α =.5 to test the hypothesis. Slide 43 One-Tailed Test About a Population Mean: σ Unknown p Value and Critical Value Approaches 1. Determine the hypotheses. H : µ < 65 H a : µ > Specify the level of significance. α =.5 3. Compute the value of the test statistic. x µ t = = = s / n 4.2/ Slide 44 22

23 One-Tailed Test About a Population Mean: σ Unknown p Value Approach 4. Compute the p value. For t = 2.286, the p value must be less than.25 (for t = 1.998) and greater than.1 (for t = 2.387)..1 < p value < Determine whether to reject H. Because p value < α =.5, we reject H. We are at least 95% confident that the mean speed of vehicles at Location F is greater than 65 mph. Slide 45 One-Tailed Test About a Population Mean: σ Unknown Critical Value Approach 4. Determine the critical value and rejection rule. For α =.5 and d.f. = 64 1 = 63, t.5 = Reject H if t > Determine whether to reject H. Because > 1.669, we reject H. We are at least 95% confident that the mean speed of vehicles at Location F is greater than 65 mph. Location F is a good candidate for a radar trap. Slide 46 23

24 One-Tailed Test About a Population Mean: σ Unknown Reject H Do Not Reject H α =.5 t α = t Slide 47 In-class exercise #23 (p.362) (one-tail test) #24 (p.362) (two-tail test) Slide 48 24

25 End of Chapter 9, Part A Slide 49 25

### Chapter 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

### HYPOTHESIS TESTING: POWER OF THE TEST

HYPOTHESIS TESTING: POWER OF THE TEST The first 6 steps of the 9-step test of hypothesis are called "the test". These steps are not dependent on the observed data values. When planning a research project,

### Chapter 8 Introduction to Hypothesis Testing

Chapter 8 Student Lecture Notes 8-1 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

### An Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10- TWO-SAMPLE TESTS

The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 130) Spring Semester 011 Chapter 10- TWO-SAMPLE TESTS Practice

### Hypothesis Testing. Hypothesis Testing

Hypothesis Testing Daniel A. Menascé Department of Computer Science George Mason University 1 Hypothesis Testing Purpose: make inferences about a population parameter by analyzing differences between observed

### Introduction 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

### Hypothesis 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

### 9-3.4 Likelihood ratio test. Neyman-Pearson lemma

9-3.4 Likelihood ratio test Neyman-Pearson lemma 9-1 Hypothesis Testing 9-1.1 Statistical Hypotheses Statistical hypothesis testing and confidence interval estimation of parameters are the fundamental

### Hypothesis Testing or How to Decide to Decide Edpsy 580

Hypothesis Testing or How to Decide to Decide Edpsy 580 Carolyn J. Anderson Department of Educational Psychology University of Illinois at Urbana-Champaign Hypothesis Testing or How to Decide to Decide

### Chapter 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

### Chapter 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

### The alternative hypothesis,, is the statement that the parameter value somehow differs from that claimed by the null hypothesis. : 0.5 :>0.5 :<0.

Section 8.2-8.5 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

### Null 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

### HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

### Chapter 1 Hypothesis Testing

Chapter 1 Hypothesis Testing Principles of Hypothesis Testing tests for one sample case 1 Statistical Hypotheses They are defined as assertion or conjecture about the parameter or parameters of a population,

### Two Related Samples t Test

Two Related Samples t Test In this example 1 students saw five pictures of attractive people and five pictures of unattractive people. For each picture, the students rated the friendliness of the person

### CHAPTER 11 SECTION 2: INTRODUCTION TO HYPOTHESIS TESTING

CHAPTER 11 SECTION 2: INTRODUCTION TO HYPOTHESIS TESTING MULTIPLE CHOICE 56. In testing the hypotheses H 0 : µ = 50 vs. H 1 : µ 50, the following information is known: n = 64, = 53.5, and σ = 10. The standardized

### Wording 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

### MATH 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

### 1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years

### BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420

BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420 1. Which of the following will increase the value of the power in a statistical test

### 5/31/2013. 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.

### IQ of deaf children example: Are the deaf children lower in IQ? Or are they average? If µ100 and σ 2 225, is the 88.07 from the sample of N59 deaf chi

PSY 511: Advanced Statistics for Psychological and Behavioral Research 1 All inferential statistics have the following in common: Use of some descriptive statistic Use of probability Potential for estimation

### HYPOTHESIS TESTING AND TYPE I AND TYPE II ERROR

HYPOTHESIS TESTING AND TYPE I AND TYPE II ERROR Hypothesis is a conjecture (an inferring) about one or more population parameters. Null Hypothesis (H 0 ) is a statement of no difference or no relationship

### Chapter 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

### Chapter Five: Paired Samples Methods 1/38

Chapter Five: Paired Samples Methods 1/38 5.1 Introduction 2/38 Introduction Paired data arise with some frequency in a variety of research contexts. Patients might have a particular type of laser surgery

### Section 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

### 7 Hypothesis testing - one sample tests

7 Hypothesis testing - one sample tests 7.1 Introduction Definition 7.1 A hypothesis is a statement about a population parameter. Example A hypothesis might be that the mean age of students taking MAS113X

### The Basics of a Hypothesis Test

Overview The Basics of a Test Dr Tom Ilvento Department of Food and Resource Economics Alternative way to make inferences from a sample to the Population is via a Test A hypothesis test is based upon A

### LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.

### Estimation of σ 2, the variance of ɛ

Estimation of σ 2, the variance of ɛ The variance of the errors σ 2 indicates how much observations deviate from the fitted surface. If σ 2 is small, parameters β 0, β 1,..., β k will be reliably estimated

### Sampling 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

### Chapter 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

### Hypothesis Testing. Reminder of Inferential Statistics. Hypothesis Testing: Introduction

Hypothesis Testing PSY 360 Introduction to Statistics for the Behavioral Sciences Reminder of Inferential Statistics All inferential statistics have the following in common: Use of some descriptive statistic

### CHAPTER 9. Hypothesis Tests CONTENTS

FOR BUSINESS AND ECONOMICS STATISTICS CHAPTER 9 Hypothesis Tests CONTENTS STATISTICS IN PRACTICE: JOHN MORRELL & COMPANY 9.1 DEVELOPING NULL AND ALTERNATIVE HYPOTHESES Testing Research Hypotheses Testing

### BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394

BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394 1. Does vigorous exercise affect concentration? In general, the time needed for people to complete

### Module 2 Probability and Statistics

Module 2 Probability and Statistics BASIC CONCEPTS Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The standard deviation of a standard normal distribution

### Hypothesis Testing. Hypothesis Testing CS 700

Hypothesis Testing CS 700 1 Hypothesis Testing! Purpose: make inferences about a population parameter by analyzing differences between observed sample statistics and the results one expects to obtain if

### 6.1 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

### Chapter 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

### Hypothesis testing - Steps

Hypothesis testing - Steps Steps to do a two-tailed test of the hypothesis that β 1 0: 1. Set up the hypotheses: H 0 : β 1 = 0 H a : β 1 0. 2. Compute the test statistic: t = b 1 0 Std. error of b 1 =

### 3.4 Statistical inference for 2 populations based on two samples

3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted

### Chapter 2. Hypothesis testing in one population

Chapter 2. Hypothesis testing in one population Contents Introduction, the null and alternative hypotheses Hypothesis testing process Type I and Type II errors, power Test statistic, level of significance

### Hypothesis Testing Summary

Hypothesis Testing Summary Hypothesis testing begins with the drawing of a sample and calculating its characteristics (aka, statistics ). A statistical test (a specific form of a hypothesis test) is an

### HypoTesting. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Name: Class: Date: HypoTesting Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A Type II error is committed if we make: a. a correct decision when the

### Basic Statistics Self Assessment Test

Basic Statistics Self Assessment Test Professor Douglas H. Jones PAGE 1 A soda-dispensing machine fills 12-ounce cans of soda using a normal distribution with a mean of 12.1 ounces and a standard deviation

### Chapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing

Chapter 8 Hypothesis Testing 1 Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing 8-3 Testing a Claim About a Proportion 8-5 Testing a Claim About a Mean: s Not Known 8-6 Testing

### HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

### Basic concepts and introduction to statistical inference

Basic concepts and introduction to statistical inference Anna Helga Jonsdottir Gunnar Stefansson Sigrun Helga Lund University of Iceland (UI) Basic concepts 1 / 19 A review of concepts Basic concepts Confidence

### THE LOGIC OF HYPOTHESIS TESTING. The general process of hypothesis testing remains constant from one situation to another.

THE LOGIC OF HYPOTHESIS TESTING Hypothesis testing is a statistical procedure that allows researchers to use sample to draw inferences about the population of interest. It is the most commonly used inferential

### Hypothesis 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

### 22. 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?

### Introduction 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

### Hypothesis testing S2

Basic medical statistics for clinical and experimental research Hypothesis testing S2 Katarzyna Jóźwiak k.jozwiak@nki.nl 2nd November 2015 1/43 Introduction Point estimation: use a sample statistic to

### Hypothesis Testing. Bluman Chapter 8

CHAPTER 8 Learning Objectives C H A P T E R E I G H T Hypothesis Testing 1 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 8-5 2 Test for

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

STT315 Practice Ch 5-7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The length of time a traffic signal stays green (nicknamed

### Hypothesis testing for µ:

University of California, Los Angeles Department of Statistics Statistics 13 Elements of a hypothesis test: Hypothesis testing Instructor: Nicolas Christou 1. Null hypothesis, H 0 (always =). 2. Alternative

### A 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

### Two-Sample T-Tests Assuming Equal Variance (Enter Means)

Chapter 4 Two-Sample T-Tests Assuming Equal Variance (Enter Means) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when the variances of

### Chapter Study Guide. Chapter 11 Confidence Intervals and Hypothesis Testing for Means

OPRE504 Chapter Study Guide Chapter 11 Confidence Intervals and Hypothesis Testing for Means I. Calculate Probability for A Sample Mean When Population σ Is Known 1. First of all, we need to find out the

### 8-2 Basics of Hypothesis Testing. Definitions. Rare Event Rule for Inferential Statistics. Null Hypothesis

8-2 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

### 9Tests of Hypotheses. for a Single Sample CHAPTER OUTLINE

9Tests of Hypotheses for a Single Sample CHAPTER OUTLINE 9-1 HYPOTHESIS TESTING 9-1.1 Statistical Hypotheses 9-1.2 Tests of Statistical Hypotheses 9-1.3 One-Sided and Two-Sided Hypotheses 9-1.4 General

### Independent t- Test (Comparing Two Means)

Independent t- Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent t-test when to use the independent t-test the use of SPSS to complete an independent

### Introduction to Hypothesis Testing. Point estimation and confidence intervals are useful statistical inference procedures.

Introduction to Hypothesis Testing Point estimation and confidence intervals are useful statistical inference procedures. Another type of inference is used frequently used concerns tests of hypotheses.

### Chapter 7 Part 2. Hypothesis testing Power

Chapter 7 Part 2 Hypothesis testing Power November 6, 2008 All of the normal curves in this handout are sampling distributions Goal: To understand the process of hypothesis testing and the relationship

### [Chapter 10. Hypothesis Testing]

[Chapter 10. Hypothesis Testing] 10.1 Introduction 10.2 Elements of a Statistical Test 10.3 Common Large-Sample Tests 10.4 Calculating Type II Error Probabilities and Finding the Sample Size for Z Tests

### Two-Sample T-Tests Allowing Unequal Variance (Enter Difference)

Chapter 45 Two-Sample T-Tests Allowing Unequal Variance (Enter Difference) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when no assumption

### Basic Elements of a Hypothesis Test. Hypothesis Testing of Proportions and Small Sample Means. Proportions. Proportions

Hypothesis Testing of Proportions and Small Sample Means Dr. Tom Ilvento FREC 408 Basic Elements of a Hypothesis Test H 0 : H a : : : Proportions The Pepsi Challenge asked soda drinkers to compare Diet

### I. 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

### 1 SAMPLE SIGN TEST. Non-Parametric Univariate Tests: 1 Sample Sign Test 1. A non-parametric equivalent of the 1 SAMPLE T-TEST.

Non-Parametric Univariate Tests: 1 Sample Sign Test 1 1 SAMPLE SIGN TEST A non-parametric equivalent of the 1 SAMPLE T-TEST. ASSUMPTIONS: Data is non-normally distributed, even after log transforming.

### Introduction to Hypothesis Testing OPRE 6301

Introduction to Hypothesis Testing OPRE 6301 Motivation... The purpose of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief, or hypothesis, about

### Testing a claim about a population mean

Introductory Statistics Lectures Testing a claim about a population mean One sample hypothesis test of the mean Department of Mathematics Pima Community College Redistribution of this material is prohibited

### Hypothesis 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

### Difference of Means and ANOVA Problems

Difference of Means and Problems Dr. Tom Ilvento FREC 408 Accounting Firm Study An accounting firm specializes in auditing the financial records of large firm It is interested in evaluating its fee structure,particularly

### Stats Review Chapters 9-10

Stats Review Chapters 9-10 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test

### Ch. 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

### t Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon

t-tests in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com www.excelmasterseries.com

### How 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

### 9.1 Basic Principles of Hypothesis Testing

9. Basic Principles of Hypothesis Testing Basic Idea Through an Example: On the very first day of class I gave the example of tossing a coin times, and what you might conclude about the fairness of the

### Chapter 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

### Hypothesis Testing and Confidence Interval Estimation

Biostatistics for Health Care Researchers: A Short Course Hypothesis Testing and Confidence Interval Estimation Presented ed by: Susan M. Perkins, Ph.D. Division of Biostatistics Indiana University School

### Experimental Design. Power and Sample Size Determination. Proportions. Proportions. Confidence Interval for p. The Binomial Test

Experimental Design Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 To this point in the semester, we have largely

### Correlational Research

Correlational Research Chapter Fifteen Correlational Research Chapter Fifteen Bring folder of readings The Nature of Correlational Research Correlational Research is also known as Associational Research.

### Chapter 7 Notes - Inference for Single Samples. You know already for a large sample, you can invoke the CLT so:

Chapter 7 Notes - Inference for Single Samples You know already for a large sample, you can invoke the CLT so: X N(µ, ). Also for a large sample, you can replace an unknown σ by s. You know how to do a

### 6: Introduction to Hypothesis Testing

6: Introduction to Hypothesis Testing Significance testing is used to help make a judgment about a claim by addressing the question, Can the observed difference be attributed to chance? We break up significance

### General Procedure for Hypothesis Test. Five types of statistical analysis. 1. Formulate H 1 and H 0. General Procedure for Hypothesis Test

Five types of statistical analysis General Procedure for Hypothesis Test Descriptive Inferential Differences Associative Predictive What are the characteristics of the respondents? What are the characteristics

### Water Quality Problem. Hypothesis Testing of Means. Water Quality Example. Water Quality Example. Water quality example. Water Quality Example

Water Quality Problem Hypothesis Testing of Means Dr. Tom Ilvento FREC 408 Suppose I am concerned about the quality of drinking water for people who use wells in a particular geographic area I will test

### Lecture 13 More on hypothesis testing

Lecture 13 More on hypothesis testing Thais Paiva STA 111 - Summer 2013 Term II July 22, 2013 1 / 27 Thais Paiva STA 111 - Summer 2013 Term II Lecture 13, 07/22/2013 Lecture Plan 1 Type I and type II error

### Module 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

### Develop hypothesis and then research to find out if it is true. Derived from theory or primary question/research questions

Chapter 12 Hypothesis Testing Learning Objectives Examine the process of hypothesis testing Evaluate research and null hypothesis Determine one- or two-tailed tests Understand obtained values, significance,

### Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing

Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing 1) Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures

### The Goodness-of-Fit Test

on the Lecture 49 Section 14.3 Hampden-Sydney College Tue, Apr 21, 2009 Outline 1 on the 2 3 on the 4 5 Hypotheses on the (Steps 1 and 2) (1) H 0 : H 1 : H 0 is false. (2) α = 0.05. p 1 = 0.24 p 2 = 0.20

### HYPOTHESIS TESTING III: POPULATION PROPORTIONS, ETC.

HYPOTHESIS TESTING III: POPULATION PROPORTIONS, ETC. HYPOTHESIS TESTS OF POPULATION PROPORTIONS Purpose: to determine whether the proportion in the population with some characteristic is or is not equal

### 12.5: CHI-SQUARE GOODNESS OF FIT TESTS

125: Chi-Square Goodness of Fit Tests CD12-1 125: CHI-SQUARE GOODNESS OF FIT TESTS In this section, the χ 2 distribution is used for testing the goodness of fit of a set of data to a specific probability

About Hypothesis Testing TABLE OF CONTENTS About Hypothesis Testing... 1 What is a HYPOTHESIS TEST?... 1 Hypothesis Testing... 1 Hypothesis Testing... 1 Steps in Hypothesis Testing... 2 Steps in Hypothesis

### Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation

Parkland College A with Honors Projects Honors Program 2014 Calculating P-Values Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating P-Values" (2014). A with Honors Projects.

### 1 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.

### Measuring 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