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

 To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video
Save this PDF as:

Size: px
Start display at page:

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

## Transcription

1 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 standard deviation of a sampling distribution. When the population s standard deviation, σ, is known to us, use SD ( ), where n is the sample size. 2. Calculate z-statistic for a value of sample mean z = where is the sample mean and is the population mean 3. Find out probability using Z-table (A-32/33 in Appendix C) Q11.1 The weight of potato chips in a medium-size bag is stated to be 10 ounces (label). The amount that the packaging machine puts in these bags is believed to have a Normal distribution N (10.2, 0.12). Answer the following questions [Question 7 for Chapter 11, p.346]: a) What fraction of all bags sold are underweight? P (w<10) = P ( z< = P (z< ) P (z< -1.67) = (by checking Z-table) More precisely, P (z< ) = P (z<1.6667) = (using excel NORMDIST function). b) Some of the chips are sold in bargain packs of 3 bags. What s the probability that none of the 3 is underweight? The probability of none of 3 bags is underweight = p (bag 1 NOT underweight) x p (bag 2 NOT underweight) x p (bag 3 NOT underweight) = [1- p (bag 1 underweight)] x [1- p (bag 2 underweight)] x [1- p (bag 3 underweight)] = ( ) x ( )x ( ) = c) What s the probability that the mean weight of the 3 bags is below the stated weight? SD ( ) = z = p (Z<-2.899) = = Chaodong Han OPRE504 Page 1 of 6

2 d) What s the probability that the mean weight per bag of a 24-bag case of potato chips is below 10 ounces? SD ( ) = z = = The probability to see z-score of is almost impossible. P =0.000 Q11.2 Refer to the example in the Textbook (Sharpe 2011, p.324) II. Hypothesis Test for Means without Knowing Population s σ However, since the population parameters are not always known, we can only use SE ( ), to approximate the standard deviation of the sampling distribution, where s is the standard deviation of the sample we happen to use and n is the sample size and the degree of freedom (df) is n State hypotheses (H 0 and H a ) and determine whether a two-tailed or one-tailed test 2. Based on level and degree of freedom (df= n-1), find out the critical value and determine the rejection region(s) using Student s T-Table (A-34 in Appendix C) 3. Calculate standard error of the sampling distribution SE ( ), s = standard deviation of the sample, n = sample size 4. Calculate Student s t-statistic for the sample t = 5. Compare t and : if t, reject H0; if t <, fail to reject H0. Q11.3 Suppose we would like to know whether the mean GMAT score for all MBA students is 600. Now you take a random sample of 36 MBA students and find that the average GMAT score for this sample is 640 and the standard deviation for this sample 120. State your hypothesis and conduct the test. If an alpha level α of 5% is used, what s your conclusion? If an alpha level α of 10% is used, what is your conclusion? Step 1: State Hypotheses H 0 : μ = 600 Chaodong Han OPRE504 Page 2 of 6

3 H a : μ 600 This is a two-tailed test. Step 2: Find Critical Value Using Two-Tailed T Table Based on α=5%, df= 36-1=35: = 2.03 Rejection regions are 2.03 and due to a two-tailed test Step 3: Calculate the Standard Error for the Sampling Distribution SE ( ) = 20 Step 4: Calculate Student s t-statistic for the Sample t 35 = = = 2 Step 5: Compare the calculated t-statistic with critical value and make your judgment Since t 35 < and falls outside the rejection regions, we fail to reject H 0 that the average GMAT score is 640 and conclude that the average GMAT score for all MBA students may not differ from 640 at the 5% significance level. REPEAT STEP 2 AND STEP 5 FOR THE NEW α: Step 2: Find out the Critical Value associated with α=10% using two-tailed T table = 1.69 Step 5: Compare the calculated t-statistic with critical value and make your judgment Since t 35 > and falls in the rejection region, we reject H 0 that the average GMAT score is 640 and conclude that the average GMAT score for all MBA students may differ from 640 at 10% significance level. Q11.4 Suppose we would like to know whether the mean GMAT score for all MBA students is greater than 600. Now you take a random sample of 36 MBA students and find that the average GMAT score for this sample is 640 and the standard deviation for this sample 120. State your hypothesis and conduct the test. If an alpha level α = 5% is used, what s your conclusion? If an alpha level α = 1% is used, what is your conclusion? Step 1: State Hypothesis Chaodong Han OPRE504 Page 3 of 6

4 H 0 : μ = 600 H a : μ > 600 This is a one-tailed test (upper tail). Step 2: Find Critical Value Using One-Tailed T-Table Based on α=5%, df= 36-1=35: = 1.69 Rejection regions are 1.69 due to a one-tailed test Using Excel formula: TINV (0.10, 35) = 1.69 because TINV only works with 2-tailed T. From the T table, we note that two-tailed 10% is equivalent to one-tailed 5%. Therefore, we need to double alpha levels to use TINV function for a one-tailed test. Step 3: Calculate the Standard Error for the Sampling Distribution SE ( ) = 20 Step 4: Calculate Student s t-statistic for the Sample t 35 = = = 2 Step 5: Compare the calculated t-statistic with critical value and make your judgment Since t 35 > and falls within the rejection region, we reject H 0 that the average GMAT score is 640 and conclude that the average GMAT score for all MBA students may differ from 640 at the 5% significance level. REPEAT STEP 2 AND STEP 5 FOR THE NEW α: Step 2: Find out the Critical Value associated with α=1% using one-tailed T-table = Step 5: Compare the calculated t-statistic with the Critical Value and make your judgment Since t 35 < and falls outside the rejection region, we fail to reject H 0 that the average GMAT score is 600 and conclude that the average GMAT score for all MBA students may not differ from 600 at 1% significance level. Textbook Examples of Hypothesis Tests for Means Guided Example Insurance Profits Revisited (pp ); This is also one-tailed test with lower tail. Chaodong Han OPRE504 Page 4 of 6

5 III Confidence Intervals for Means Model: One-sample t-interval = Estimate Marginal Error (ME) ME = X SE (, CI = X SE (, SE ( =, where n= sample size, df = n-1 1. Determine level for confidence interval (CI): = 1-CI 2. Calculate Standard Error of the Sampling Distribution: SE ( 3. Find out the critical value using Two-Tailed T-Table (, df= n-1) 4. CI = X SE (, SE ( Q11.5 The average gasoline price per gallon for a random sample of 30 stations in a region is \$4.49 with a standard deviation of \$0.29. [Textbook, Q13, p.346]. a) Find a 95% confidence interval for the mean price of gasoline for all stations in that region Given n = 30, = 4.49, s= 0.29, and 95% confidence interval 1. = = SE ( = = = CI = X SE ( = X = CI = (4.382, 4.598) if rounded to tenth cents b) Find a 90% CI for mean price of gasoline for all stations in that region Given n = 30, = 4.49, s= 0.29, and 90% confidence interval 1. = = SE ( = = = CI = X SE ( = X = CI = (4.400, 4.580) c) If we had the sample statistics from a sample of 60 stations, what would be the 95% confidence interval? Given n = 60, = 4.49, s= 0.29, and 95% confidence interval 1. = = SE ( = = = CI = X SE ( = X = CI = (4.415, 4.565) Chaodong Han OPRE504 Page 5 of 6

6 IV Determine Sample Size CI upper = Mean Estimate + Marginal Error (ME) CI lower = Mean Estimate - ME ME = CI upper Mean Estimate SE (, ME = x ( = 1- confidence interval) [ Z is used because we don t know n and need to find it] n = Q11.6 Police departments often try to control traffic speed by placing speed-measuring machines on roads that tell motorists how fast they are driving. Traffic safety experts must determine where machines should be placed. In one recent test, police recorded the average speed clocked by cars driving on one busy street close to an elementary school. For a sample of 25 clocked speeds, it was determined that the average amount over the speed limit for the 25 clocked speeds was 11.6 mph with a standard deviation of 8 mph. The 95% confidence interval estimate for this sample is 8.30 mph to mph [Sharpe 2011, Q57-58, p.353] a) What is the margin of error for this problem? Given CI = (8.30, 14.90) and the mean estimate = 11.6 mph, ME = Upper Limit Mean Estimate = = 3.3 mph b) The researchers commented that the interval was too wide. Explain what should be done to reduce the margin of error to no more than ±2 mph. Given n is unknown, s = 8, = = 0.05, Z * = 1.96 n= = x 8 2 = clocked speeds c) To ensure that error rates are estimated accurately, the researchers want to take a large enough sample that will ensure that usable and accurate interval estimates of how much the machines may be off in measuring actual speeds. Specifically, the researchers want the margin of error for a single speed measurement to be no more than ±1.5 mph at the 95% confidence interval. How may the researchers obtain a reasonable estimate of the standard deviation of error in the measured speeds? Conduct a pilot study or use findings from previous studies d) Suppose the standard deviation of for the error in the measured speeds is believed to be 4 mph from a pilot study, what should be the sample size for next study to ensure that the margin of error is no larger than ±1 mph. 1.0 = 1.96* ( ), n = = x 4 2 = Chaodong Han OPRE504 Page 6 of 6

### 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

### Chapter 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

### 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

### T-test in SPSS Hypothesis tests of proportions Confidence Intervals (End of chapter 6 material)

T-test in SPSS Hypothesis tests of proportions Confidence Intervals (End of chapter 6 material) Definition of p-value: The probability of getting evidence as strong as you did assuming that the null hypothesis

### Test 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

### Statistics 104: Section 7

Statistics 104: Section 7 Section Overview Reminders Comments on Midterm Common Mistakes on Problem Set 6 Statistical Week in Review Comments on Midterm Overall, the midterms were good with one notable

### Third 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

### MAT140: Applied Statistical Methods Summary of Calculating Confidence Intervals and Sample Sizes for Estimating Parameters

MAT140: Applied Statistical Methods Summary of Calculating Confidence Intervals and Sample Sizes for Estimating Parameters Inferences about a population parameter can be made using sample statistics 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

### Chapter 23 Inferences About Means

Chapter 23 Inferences About Means Chapter 23 - Inferences About Means 391 Chapter 23 Solutions to Class Examples 1. See Class Example 1. 2. We want to know if the mean battery lifespan exceeds the 300-minute

### Hypothesis 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

### 4) The role of the sample mean in a confidence interval estimate for the population mean is to: 4)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Assume that the change in daily closing prices for stocks on the New York Stock Exchange is a random

### Psychology 60 Fall 2013 Practice Exam Actual Exam: Next Monday. Good luck!

Psychology 60 Fall 2013 Practice Exam Actual Exam: Next Monday. Good luck! Name: 1. The basic idea behind hypothesis testing: A. is important only if you want to compare two populations. B. depends on

### A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

CHAPTER 5. A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING 5.1 Concepts When a number of animals or plots are exposed to a certain treatment, we usually estimate the effect of the treatment

### MCQ 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) Test-statistic MCQ

### 12 Hypothesis Testing

CHAPTER 12 Hypothesis Testing Chapter Outline 12.1 HYPOTHESIS TESTING 12.2 CRITICAL VALUES 12.3 ONE-SAMPLE T TEST 247 12.1. Hypothesis Testing www.ck12.org 12.1 Hypothesis Testing Learning Objectives Develop

### 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 =

### Estimation of the Mean and Proportion

1 Excel Manual Estimation of the Mean and Proportion Chapter 8 While the spreadsheet setups described in this guide may seem to be getting more complicated, once they are created (and tested!), they will

### 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

### 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

### Probability, Binomial Distributions and Hypothesis Testing Vartanian, SW 540

Probability, Binomial Distributions and Hypothesis Testing Vartanian, SW 540 1. Assume you are tossing a coin 11 times. The following distribution gives the likelihoods of getting a particular number of

### 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

### 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

### Practice problems for Homework 12 - confidence intervals and hypothesis testing. Open the Homework Assignment 12 and solve the problems.

Practice problems for Homework 1 - confidence intervals and hypothesis testing. Read sections 10..3 and 10.3 of the text. Solve the practice problems below. Open the Homework Assignment 1 and solve the

### Statistics I for QBIC. Contents and Objectives. Chapters 1 7. Revised: August 2013

Statistics I for QBIC Text Book: Biostatistics, 10 th edition, by Daniel & Cross Contents and Objectives Chapters 1 7 Revised: August 2013 Chapter 1: Nature of Statistics (sections 1.1-1.6) Objectives

### 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.

### Statistics Review PSY379

Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses

### 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

### 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

### 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

### 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

### 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.

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

### 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

### Regression Analysis: A Complete Example

Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty

### 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

### 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 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

### Elements of Hypothesis Testing (Summary from lecture notes)

Statistics-20090 MINITAB - Lab 1 Large Sample Tests of Hypothesis About a Population Mean We use hypothesis tests to make an inference about some population parameter of interest, for example the mean

### 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

### Mind on Statistics. Chapter 13

Mind on Statistics Chapter 13 Sections 13.1-13.2 1. Which statement is not true about hypothesis tests? A. Hypothesis tests are only valid when the sample is representative of the population for the question

### 5.1 Identifying the Target Parameter

University of California, Davis Department of Statistics Summer Session II Statistics 13 August 20, 2012 Date of latest update: August 20 Lecture 5: Estimation with Confidence intervals 5.1 Identifying

### 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

### THE FIRST SET OF EXAMPLES USE SUMMARY DATA... EXAMPLE 7.2, PAGE 227 DESCRIBES A PROBLEM AND A HYPOTHESIS TEST IS PERFORMED IN EXAMPLE 7.

THERE ARE TWO WAYS TO DO HYPOTHESIS TESTING WITH STATCRUNCH: WITH SUMMARY DATA (AS IN EXAMPLE 7.17, PAGE 236, IN ROSNER); WITH THE ORIGINAL DATA (AS IN EXAMPLE 8.5, PAGE 301 IN ROSNER THAT USES DATA FROM

### 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.

### Lesson 9 Hypothesis Testing

Lesson 9 Hypothesis Testing Outline Logic for Hypothesis Testing Critical Value Alpha (α) -level.05 -level.01 One-Tail versus Two-Tail Tests -critical values for both alpha levels Logic for Hypothesis

### Sample Size Determination

Sample Size Determination Population A: 10,000 Population B: 5,000 Sample 10% Sample 15% Sample size 1000 Sample size 750 The process of obtaining information from a subset (sample) of a larger group (population)

### 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 26: Tests of Significance

Chapter 26: Tests of Significance Procedure: 1. State the null and alternative in words and in terms of a box model. 2. Find the test statistic: z = observed EV. SE 3. Calculate the P-value: The area under

### In the past, the increase in the price of gasoline could be attributed to major national or global

Chapter 7 Testing Hypotheses Chapter Learning Objectives Understanding the assumptions of statistical hypothesis testing Defining and applying the components in hypothesis testing: the research and null

### 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 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.

### 1 Hypotheses test about µ if σ is not known

1 Hypotheses test about µ if σ is not known In this section we will introduce how to make decisions about a population mean, µ, when the standard deviation is not known. In order to develop a confidence

### Suppose we want to compare the average effectiveness of two treatments in a completely randomized experiment. In this case, the parameters µ 1

AP Statistics: 10.2: Comparing Two Means Name: Suppose we want to compare the average effectiveness of two treatments in a completely randomized experiment. In this case, the parameters µ 1 and µ 2 are

### An Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 9 - FUNDAMENTALS OF HYPOTHESIS TESTING: ONE-SAMPLE 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

### Chapter 9: Hypothesis Tests of a Single Population

Chapter 9: Hypothesis Tests of a Single Population Department of Mathematics Izmir University of Economics Week 12 2014-2015 Introduction In this chapter we will focus on Example developing hypothesis

### Study Guide for the Final Exam

Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make

### Homework 5 Solutions

Math 130 Assignment Chapter 18: 6, 10, 38 Chapter 19: 4, 6, 8, 10, 14, 16, 40 Chapter 20: 2, 4, 9 Chapter 18 Homework 5 Solutions 18.6] M&M s. The candy company claims that 10% of the M&M s it produces

### Linear 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

### Math 108 Exam 3 Solutions Spring 00

Math 108 Exam 3 Solutions Spring 00 1. An ecologist studying acid rain takes measurements of the ph in 12 randomly selected Adirondack lakes. The results are as follows: 3.0 6.5 5.0 4.2 5.5 4.7 3.4 6.8

### 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

### Need for Sampling. Very large populations Destructive testing Continuous production process

Chapter 4 Sampling and Estimation Need for Sampling Very large populations Destructive testing Continuous production process The objective of sampling is to draw a valid inference about a population. 4-

### Two-sample hypothesis testing, I 9.07 3/09/2004

Two-sample 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

### Hypothesis 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

### BE ALERT FOR CORRECTIONS TO THIS KEY

A statistical hypothesis test acts on data to arrive at a decision to either reject or not reject a stated null hypothesis. One important focus is to design a test achieving a given alpha. Then there is

### 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

### 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

### SPSS on two independent samples. Two sample test with proportions. Paired t-test (with more SPSS)

SPSS on two independent samples. Two sample test with proportions. Paired t-test (with more SPSS) State of the course address: The Final exam is Aug 9, 3:30pm 6:30pm in B9201 in the Burnaby Campus. (One

### 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

### 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

### 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

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

Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly

### 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

### KSTAT MINI-MANUAL. Decision Sciences 434 Kellogg Graduate School of Management

KSTAT MINI-MANUAL Decision Sciences 434 Kellogg Graduate School of Management Kstat is a set of macros added to Excel and it will enable you to do the statistics required for this course very easily. To

### 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

### 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

### Unit 26 Estimation with Confidence Intervals

Unit 26 Estimation with Confidence Intervals Objectives: To see how confidence intervals are used to estimate a population proportion, a population mean, a difference in population proportions, or a difference

### STA 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

### Chapter 16 Multiple Choice Questions (The answers are provided after the last question.)

Chapter 16 Multiple Choice Questions (The answers are provided after the last question.) 1. Which of the following symbols represents a population parameter? a. SD b. σ c. r d. 0 2. If you drew all possible

### 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,

### AP STATISTICS 2009 SCORING GUIDELINES (Form B)

AP STATISTICS 2009 SCORING GUIDELINES (Form B) Question 5 Intent of Question The primary goals of this question were to assess students ability to (1) state the appropriate hypotheses, (2) identify and

### When σ Is Known: Recall the Mystery Mean Activity where x bar = 240.79 and we have an SRS of size 16

8.3 ESTIMATING A POPULATION MEAN When σ Is Known: Recall the Mystery Mean Activity where x bar = 240.79 and we have an SRS of size 16 Task was to estimate the mean when we know that the situation is Normal

### 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

### Practice Problems and Exams

Practice Problems and Exams 1 The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 1302) Spring Semester 2009-2010

### Chapter 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

### Chapter 5 Review The Normal Probability and Standardization

Chapter 5 Review The Normal Probability and Standardization MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Approximately

### 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

### 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

### Example 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 586-587 (end of Chapter 13) for a summary table. Quiz for week 8 starts Wed, ends Monday

### 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

### Let m denote the margin of error. Then

S:105 Statistical Methods and Computing Sample size for confidence intervals with σ known t Intervals Lecture 13 Mar. 6, 009 Kate Cowles 374 SH, 335-077 kcowles@stat.uiowa.edu 1 The margin of error The

### Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS

Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS Choose the single best answer for each question. Discuss questions with classmates, TAs and Professor Whitten. Raise your hand to check

### Chapter 7 Review. Confidence Intervals. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Chapter 7 Review Confidence Intervals MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Suppose that you wish to obtain a confidence interval for

### 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

### 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

### Sociology 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

### Basic 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

### CONFIDENCE INTERVALS FOR MEANS AND PROPORTIONS

LESSON SEVEN CONFIDENCE INTERVALS FOR MEANS AND PROPORTIONS An interval estimate for μ of the form a margin of error would provide the user with a measure of the uncertainty associated with the point estimate.

### 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