Basic Statistics for Business & Economics Ninth Edition LIND MARCHAL WATHEN Basic Statistics for BUSINESS & ECONOMICS The McGraw-Hill/Irwin Series in Operations and Decision Sciences SUPPLY CHAIN MANAGEMENT BUSINESS RESEARCH METHODS Benton Purchasing and Supply Chain Management Third Edition Cooper and Schindler Business Research Methods Twelfth Edition Swink, Melnyk, Cooper, and Hartley Managing Operations across the Supply Chain Third Edition BUSINESS FORECASTING PRODUCT DESIGN Wilson, Keating, and John Galt Solutions, Inc Business Forecasting Seventh Edition Ulrich and Eppinger Product Design and Development Sixth Edition LINEAR STATISTICS AND REGRESSION Slater and Wittry Math for Business and Finance: An Algebraic Approach Second Edition Bowersox, Closs, Cooper, and Bowersox Supply Chain Logistics Management Fourth Edition Burt, Petcavage, and Pinkerton Supply Management Eighth Edition Johnson, Leenders, and Flynn Purchasing and Supply Management Fifteenth Edition Simchi-Levi, Kaminsky, and Simchi-Levi Designing and Managing the Supply Chain: Concepts, Strategies, Case Studies Third Edition PROJECT MANAGEMENT Brown and Hyer Managing Projects: A Team-Based Approach First Edition Larson and Gray Project Management: The Managerial Process Sixth Edition Kutner, Nachtsheim, and Neter Applied Linear Regression Models Fourth Edition BUSINESS SYSTEMS DYNAMICS Sterman Business Dynamics: Systems Thinking and Modeling for a Complex World First Edition OPERATIONS MANAGEMENT Cachon and Terwiesch Matching Supply with Demand: An Introduction to Operations Management Fourth Edition SERVICE OPERATIONS MANAGEMENT Finch Interactive Models for Operations and Supply Chain Management First Edition Fitzsimmons and Fitzsimmons Service Management: Operations, Strategy, Information Technology Ninth Edition Jacobs and Chase Operations and Supply Chain Management Fifteenth Edition MANAGEMENT SCIENCE Jacobs and Chase Operations and Supply Chain Management: The Core Fourth Edition Hillier and Hillier Introduction to Management Science: A Modeling and Case Studies Approach with Spreadsheets Sixth Edition Stevenson and Ozgur Introduction to Management Science with Spreadsheets First Edition MANUFACTURING CONTROL SYSTEMS Jacobs, Berry, Whybark, and Vollmann Manufacturing Planning & Control for Supply Chain Management Sixth Edition Jacobs and Whybark Why ERP? A Primer on SAP Implementation First Edition Schroeder, Goldstein, and Rungtusanatham Operations Management in the Supply Chain: Decisions and Cases Seventh Edition Stevenson Operations Management Twelfth Edition BUSINESS MATH Slater and Wittry Practical Business Math Procedures Twelfth Edition BUSINESS STATISTICS Bowerman, O’Connell, and Murphree Business Statistics in Practice Eighth Edition Bowerman, O’Connell, Murphree, and Orris Essentials of Business Statistics Fifth Edition Doane and Seward Applied Statistics in Business and Economics Fifth Edition Lind, Marchal, and Wathen Basic Statistics for Business and Economics Ninth Edition Lind, Marchal, and Wathen Statistical Techniques in Business and Economics Seventeenth Edition Jaggia and Kelly Business Statistics: Communicating with Numbers Second Edition Jaggia and Kelly Essentials of Business Statistics: Communicating with Numbers First Edition Basic Statistics for BUSINESS & ECONOMICS NINTH EDITION DOUGLAS A LIND Coastal Carolina University and The University of Toledo WILLIAM G MARCHAL The University of Toledo SAMUEL A WATHEN Coastal Carolina University BASIC STATISTICS FOR BUSINESS AND ECONOMICS, NINTH EDITION Published by McGraw-Hill Education, Penn Plaza, New York, NY 10121 Copyright © 2019 by McGraw-Hill Education All rights reserved Printed in the United States of America Previous editions © 2013, 2011, and 2008 No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGrawHill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning Some ancillaries, including electronic and print components, may not be available to customers outside the United States This book is printed on acid-free paper LWI 21 20 19 18 ISBN 978-1-260-18750-2 MHID 1-260-18750-0 Portfolio Manager: Noelle Bathurst Product Developers: Michele Janicek / Ryan McAndrews Marketing Manager: Harper Christopher Content Project Manager: Lori Koetters Buyer: Sandy Ludovissy Design: Matt Backhaus Content Licensing Specialist: Ann Marie Jannette Cover Image: ©Ingram Publishing / SuperStock Compositor: Aptara®, Inc All credits appearing on page or at the end of the book are considered to be an extension of the copyright page Library of Congress Cataloging-in-Publication Data Names: Lind, Douglas A., author | Marchal, William G., author | Wathen,   Samuel Adam author Title: Basic statistics for business and economics / Douglas A Lind, Coastal   Carolina University and The University of Toledo, William G Marchal, The   University of Toledo, Samuel A Wathen, Coastal Carolina Universit Description: Ninth edition | New York, NY : McGraw-Hill Education, [2019] Identifiers: LCCN 2017034976 | ISBN 9781260187502 (alk paper) Subjects: LCSH: Social sciences—Statistical methods |   Economics—Statistical methods | Industrial management—Statistical methods Classification: LCC HA29 L75 2019 | DDC 519.5—dc23 LC record available at  https://lccn.loc.gov/2017034976 The Internet addresses listed in the text were accurate at the time of publication The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites mheducation.com/highered D E D I CATI O N To Jane, my wife and best friend, and our sons, their wives, and our grandchildren: Mike and Sue (Steve and Courtney), Steve and Kathryn (Kennedy, Jake, and Brady), and Mark and Sarah (Jared, Drew, and Nate) Douglas A Lind To Oscar Sambath Marchal, Julian Irving Horowitz, Cecilia Marchal Nicholson, and Andrea William G Marchal To my wonderful family: Barb, Hannah, and Isaac Samuel A Wathen A NOTE FROM THE AUTHORS Over the years, we received many compliments on this text and understand that it’s a favorite among students We accept that as the highest compliment and continue to work very hard to maintain that status The objective of Basic Statistics for Business and Economics is to provide students majoring in management, marketing, finance, accounting, economics, and other fields of business administration with an introductory survey of descriptive and inferential statistics To illustrate the application of statistics, we use many examples and e ­ xercises that focus on business applications, but also relate to the current world of the college student A previous course in statistics is not necessary, and the mathematical requirement is first-year algebra In this text, we show beginning students every step needed to be successful in a basic statistics course This step-by-step approach enhances performance, accelerates preparedness, and significantly improves motivation Understanding the concepts, seeing and doing plenty of examples and exercises, and comprehending the application of statistical methods in business and economics are the focus of this book The first edition of this text was published in 1967 At that time, locating relevant business data was difficult That has changed! Today, locating data is not a problem The number of items you purchase at the grocery store is automatically recorded at the checkout counter Phone companies track the time of our calls, the length of calls, and the identity of the person called Credit card companies maintain information on the number, time and date, and amount of our purchases Medical devices automatically monitor our heart rate, blood pressure, and temperature from remote locations A large amount of business information is recorded and reported almost instantly CNN, USA Today, and MSNBC, for example, all have websites that track stock prices in real time Today, the practice of data analytics is widely applied to “big data.” The practice of data analytics requires skills and knowledge in several areas Computer skills are needed to process large volumes of information Analytical skills are needed to evaluate, summarize, organize, and analyze the information Critical thinking skills are needed to interpret and communicate the results of processing the information Our text supports the development of basic data analytical skills In this edition, we added a new section at the end of each chapter called Data Analytics As you work through the text, this section provides the instructor and student with opportunities to apply statistical knowledge and statistical software to explore several business environments Interpretation of the analytical results is an integral part of these exercises A variety of statistical software is available to complement our text Microsoft Excel includes an add-in with many statistical analyses MegaStat is an add-in available for Microsoft Excel Minitab and JMP are stand-alone statistical software available to download for either PC or Mac computers In our text, Microsoft Excel, Minitab, and MegaStat are used to illustrate statistical software analyses When a software application is presented, the software commands for the application are available in Appendix C We use screen captures within the chapters, so the student becomes familiar with the nature of the software output Because of the availability of computers and software, it is no longer necessary to dwell on calculations We have replaced many of the calculation examples with interpretative ones, to assist the student in understanding and interpreting the statistical results In addition, we place more emphasis on the conceptual nature of the statistical topics While making these changes, we still continue to present, as best we can, the key concepts, along with supporting interesting and relevant examples vi WHAT’S NEW IN THE NINTH EDITION? We have made many changes to examples and exercises throughout the text The section on “Enhancements” to our text details them There are two major changes to the text First, the chapters have been reorganized so that each section corresponds to a learning objective The learning objectives have been revised The second major change responds to user interest in the area of data analytics Our approach is to provide instructors and students with the opportunity to combine statistical knowledge, computer and statistical software skills, and interpretative and critical thinking skills A set of new and revised exercises is included at the end of each chapter in a section titled “Data Analytics.” In these sections, exercises refer to three data sets The North Valley Real Estate sales data set lists 105 homes currently on the market The Lincolnville School District bus data list information on 80 buses in the school district’s bus fleet The authors designed these data so that students will be able to use statistical software to explore the data and find realistic relationships in the variables The Baseball Statistics for the 2016 season is updated from the previous edition The intent of the exercises is to provide the basis of a continuing case analysis We suggest that instructors select one of the data sets and assign the corresponding exercises as each chapter is completed Instructor feedback regarding student performance is important Students should retain a copy of each chapter’s results and interpretations to develop a portfolio of discoveries and findings These will be helpful as students progress through the course and use new statistical techniques to further explore the data The ideal ending for these continuing data analytics exercises is a comprehensive report based on the analytical findings We know that working with a statistics class to develop a very basic competence in data analytics is challenging Instructors will be teaching statistics In addition, instructors will be faced with choosing statistical software and supporting students in developing or enhancing their computer skills Finally, instructors will need to assess student performance based on assignments that include both statistical and written components Using a mentoring approach may be helpful We hope that you and your students find this new feature interesting and engaging vii H OW A R E C H A P TE RS O RGA N I Z E D TO E N GAG E STU D E NTS A N D PRO M OTE LE A R N I N G? Chapter Learning Objectives ©goodluz/Shutterstock MERRILL LYNCH recently completed a study of online investment portfolios for a sample Each chapter begins with a set of learning objectives designed to provide focus for the chapter and motivate student learning These objectives, located in the margins next to the topic, indicate what the student should be able to after completing each section in the chapter of clients For the 70 participants in the study, organize these data into a frequency distribution (See Exercise 43 and LO2-3.) LEARNING OBJECTIVES When you have completed this chapter, you will be able to: LO2-1 Summarize qualitative variables with frequency and relative frequency tables LO2-2 Display a frequency table using a bar or pie chart LO2-3 Summarize quantitative variables with frequency and relative frequency distributions LO2-4 Display a frequency distribution using a histogram or frequency polygon DESCRIBING DATA: FREQUENCY TABLES, FREQUENCY DISTRIBUTIONS, AND GRAPHIC PRESENTATION Chapter Opening Exercise A representative exercise opens LO2-3 the chapter and shows how the chapter CONSTRUCTING FREQUENCY 20 CHAPTER quantitative content can be applied to aSummarize real-world situation variables with frequency and relative frequency distributions Introduction to the Topic Each chapter starts with a review of the important concepts of theLin87500_ch02_019-052.indd previous chapter and provides a link to the material in the current chapter This step-by-step approach increases comprehension by providing continuity across the concepts Example/Solution After important concepts are introduced, a solved example is given This example provides a how-to illustration and shows a relevant business application that helps students answer the question, “How can I apply this concept?” 27 DISTRIBUTIONS In Chapter and earlier in this chapter, we distinguished between qualitative and quantitative data In the previous section, using the Applewood Automotive Group data, we summarized two qualitative variables: the location of the sale and the type of vehicle sold We created INTRODUCTION frequency and relative frequency tables and depicted the results in bar and pie charts The United States automobile retailing industry is highly competitive It is dominated by The Applewood Auto Groupthat data several quantitative variables: megadealerships ownalso andinclude operate 50 or more franchises, employ overthe 10,000 age of the buyer,people, the profit the sale the vehicle, number of dealerships previand earned generateon several billionof dollars in annual and sales.the Many of the top are wants publiclyto owned, with shares on sales the New Stock Exchange ous purchases Suppose Ms Ball summarize last traded month’s byYork profit earned or NASDAQ In 2017, the largest megadealership for each vehicle We can describe profit using a frequency distribution was AutoNation (ticker symbol AN), followed by Penske Auto Group (PAG), Group Automotive, 7/28/17 Inc (ticker symbol GPI), and the privately owned Van Tuyl Group These large corporations use statistics and analytics to summarize FREQUENCY DISTRIBUTION A grouping of quantitative data into mutually exclusive and analyze datathe andnumber information to support their As an exand collectively exhaustive classes showing of observations indecisions each class ample, we will look at the Applewood Auto Group It owns four dealerships and sells a wide range of vehicles These include the popular Korean brands Kia and Hyundai, BMW and Volvo sedans and luxury How we develop a frequency distribution? The following example shows the steps to SUVs, and a full line of Ford and Chevrolet cars and trucks construct a frequency distribution is to tables, charts, Ms.Remember, Kathryn Ball our is a goal member of construct the senior management team at and graphs that will quickly summarize theGroup, data which by showing the location, extreme Applewood Auto has its corporate offices adjacent to Kane ©Darren Brode/Shutterstock is responsible for tracking and analyzing vehicle sales and the profitability values, and shapeMotors of theShe data’s distribution of those vehicles Kathryn would like to summarize the profit earned on the vehicles sold using tables, charts, and graphs that she would review and present to the ownership E X A M P L E group monthly She wants to know the profit per vehicle sold, as well as the lowest and highest amount of profit She is also interested in describing the demographics of the buyMs Kathryn Ballers of What the Applewood Auto wants to summarize the quantitative are their ages? HowGroup many vehicles have they previously purchased from one of theaApplewood What of vehicle they purchase? variable profit with frequencydealerships? distribution andtype display the did distribution with charts The Applewood Auto Group four answer dealerships: and graphs With this information, Ms Balloperates can easily the following ques19 7:44 AM tions: What is the profit eachsells sale? What is the largest maximum profit • typical Tionesta Fordon Lincoln Ford and Lincoln cars andor trucks • is Olean Automotive Inc has theprofit Nissan asAround well as the General on any sale? What the smallest or minimum onfranchise any sale? what value Motors of Chevrolet, Cadillac, and GMC trucks the profits tend brands to cluster? • Sheffield Motors Inc sells Buick, GMC trucks, Hyundai, and Kia S O L U T I O N • Kane Motors offers the Chrysler, Dodge, and Jeep lines as well as BMW and Volvo Every month, Ms Ball collects data from each of the four dealerships To begin, we show the profits each of into the an 180 vehicle sales listed in Table and for enters them Excel spreadsheet Last month the2–4 Applewood This information is calledAuto rawGroup or ungrouped data because it is simplyAacopy listing sold 180 vehicles at the four dealerships of the first few observations appears to the left The variables collected include: TABLE 2–4 Profit on Vehicles Sold Last Month by the Applewood Auto Group • Age—the age of the buyer at the time of the purchase Maximum • Profit—the amount earned by the dealership on the sale of each Self-Reviews Self-Reviews are interspersed throughout each chapter and follow Example/Solution sections They help students monitor their progress and provide immediate reinforcement for that particular technique Answers are in Appendix E $1,387 $2,148 $2,201 $vehicle 963 $ 820 $2,230 $3,043 $2,584 $2,370 1,754 2,207 996 • 1,298 1,266 2,341 1,059 2,666 2,637 Location—the dealership where the vehicle was purchased Vehicle type—SUV, hybrid, or2,991 truck 1,817 2,252 2,813 • 1,410 1,741 sedan, 3,292compact, 1,674 1,426 42 CHAPTER • Previous—the number of vehicles previously purchased at any of the 1,040 1,428 323 1,553 1,772 1,108 1,807 934 2,944 four Applewood dealerships by the consumer 1,273 1,889 352 1,648 1,932 1,295 2,056 2,063 2,147 entire data 2,350 set is available in Connect and in Appendix A.41,973 at the end 482 The 2,071 1,344 2,236 2,083 S E L F - R E V I E W 1,529 2–5 1,166 text 3,082 1,320 1,144 of the 2,116 2,422 1,906 2,928 2,856 2,502 Source: Microsoft Excel The hourly wages of the 15 employees of Matt’s Tire and Auto Repair are organized into 1,951 2,265 1,500 2,446 1,952 1,269 2,989 783 the following table 1,485 LO2-1 2,692 1,323 1,509 1,549 369 2,070 1,717 910 1,538 Hourly Wages Number of Employees Summarize1,206 qualitative 1,760 1,638 2,348 978 2,454 1,797 1,536 2,339 Recall from that techniques used to describe a set of data are called descripvariables with frequency $ Chapter up to $10 1,342 1,919 1,961 2,498 1,238 1,606 1,955 1,957 2,700 tive statistics Descriptive statistics 7organize data to show the general pattern of the and relative frequency   10 up to 12 443 2,357 data, to 2,127 294 values1,818 1,680 2,199to expose 2,240 identify tend 4to concentrate, and extreme2,222 or unusual tables   12 up to where 14 754 2,866 data values 2,430 1,115 1,824 1,827 2,482 table.2,695 2,597 The first technique we discuss is a frequency   14 up to 16 1,621 732 1,704 1,124 1,907 1,915 2,701 1,325 2,742 (a) What1,464 is the table called? 870 1,876 1,532 A grouping 1,938 of qualitative 2,084 data 3,210 2,250 1,837 FREQUENCY TABLE into (b) Develop a cumulative frequency distribution and portray the distribution in amutually cumula- exclusive and 1,174 tive frequency 1,626 collectively 2,010 exhaustive 1,688 classes 1,940 2,279 in each 2,842 showing2,639 the number 377 of observations class polygon (c) On the basis of the cumulative frequency 2,197 polygon, how many 1,412 1,762 2,165 1,822 842 employees 1,220 earn less 2,626 2,434 than $11 per hour? 1,809 1,915 2,231 1,897 2,646 1,963 1,401 1,501 1,640 2,415 2,119 2,389 2,445 1,461 2,059 2,175 1,752 1,821 E X E R C I S E S 1,546 1,766 335 2,886 1,731 2,338 1,118 2,058 2,487 CONSTRUCTING FREQUENCY TABLES 19 The following cumulative frequency and the cumulative relative frequency polygon Minimum for the distribution of hourly wages of a sample of certified welders in the Atlanta, Georgia, area is shown in the graph.  viii 7/28/17 7:44 AM 40 100 30 75 ent ency Lin87500_ch02_019-052.indd 20 36 CHAPTER Frequency Polygon STATISTICS IN ACTION Statistics in Action A frequency polygon also shows the shape o 121 gram It consists of line segments connecting th the class midpoints and the class frequencies T is illustrated in Chart 2–5 We use the profits fro wood Auto Group The midpoint of each class CHAPTER RedLine Productions recently a new video game playability to be tested frequencies onItsthe Y-axis.is Recall that the class cal analysis When developed she by 80 veteran game players class and represents the typical values in that c encountered an unsanitary (a) What is the experiment? of observations in a particular class The profit or an undersup(b) horizontal What iscondition oneaxis possible outcome? and the class frequencies on the vertical axis The class frequencies the Applewood Auto Group is repeated belo (c) are Suppose 65 of the 80 players testing the new game said they liked Is 65 a probability? plied hospital, she improved represented by the heights of theby bars However, there isit.one important differFlorence Nightingale is A SURVEY OF PROBABILITY CONCEPTS Statistics in Action articles are scattered throughknown as the founder of out the text, usually about two per chapter They the nursing profession provide unique, interesting applications and hisHowever, she also saved S E L F - R E V I E W 5–1 many lives by using statistitorical insights in the field of statistics 34 (d) (e) The probability new of game beQuantitative a success is computed to be −1.0 Comment ence based onthat thethe nature the will data data are usually measured using the conditions and then Specifythat one possible event not discrete Therefore, the horizontal axis represents all scales continuous, Profit usedare statistical data to possible values, and the bars are drawn adjacent to each other to show the continudocument the improve$ 200 up to $ 600 ous nature of the data Midpo APPROACHES TO ASSIGNING PROBABILITIES Definitions LO5-2 ment Thus, she was able Assign probabilities using 600 up to 1,000 to convince others There are three ways to assign probability to an event: classical, empirical, a classical, empirical,66 or CHAPTER of athe 1,000 up to and 1,400subjecDefinitions of new terms or terms unique to tive The HISTOGRAM A graph in which the classes are marked onare thebased horizontal axis and classical empirical methods are objective and on 1,800 information subjective approach need forand medical reform, 1,400 up to the class frequencies on theof vertical class frequencies are represented by The subjective method is basedaxis on aThe person’s belief or estimate of an event’s the study of statistics are set apart from the and data particularly in the area 1,800other up to 2,200 the heights of the bars, and the bars are drawn adjacent to each likelihood text and highlighted for easy reference and sanitation a SheWhat developed is the arithmetic mean of the Alaska unemployment 2,200 uprates?  to 2,600 b Find median and the mode for the unemployment rates.  review They also appear in the Glossary at original graphs to the demon2,600 up to(Dec–Mar) 3,000 months c Compute the arithmetic mean and median for just the winter Classical Probability strate that, during the different?  the end of the book Is it much 3,000 up to 3,400 Big Orange is designing anoutcomes information of system for use in “in-cab” more soldiers Classical is based on the Trucking assumption that the an experiment are E Xprobability ACrimean M P L22 EWar, Total communications It must summarize data from eight siteshappening throughout aisregion equally likely Using the classicalcondiviewpoint, the probability of an event com-to died from unsanitary describe typical conditions Compute appropriate measure of month central location Below is the frequency distribution of the profitsanon vehicle sales last at the for puted by dividing the number of favorable outcomes by the number of possible outcomes: theGroup variables wind direction, temperature, and pavement tions than were killed in Applewood Auto Formulas combat EXERCIS Exercises are included after sections within the chapter and at the end of the chapter Section exercises cover the material studied in the section Many exercises have data files available to import into statistical software They are indicated with the FILE icon ­Answers to the odd-numbered exercises are in Appendix D City Wind Direction 40 Birmingham, AL600 up to 1,000 South Jackson, MS 1,000 up to 1,400 Southwest 32 E X A MCHAPTER PLE 1,400 up to 1,800 Meridian, MS South Monroe, LA 1,800 up to 2,200 Southwest 24 Consider an experiment of rolling a six-sided die Tuscaloosa, AL Southwest 2,200 up to 2,600 Pavement Dry (5–1) Wet Wet Dry Dry Trace Wet of Tracethe 11 91 23 92 38 92 93 45 What is the 93 probability 32 appear up toface 3,000up”? 19 Eevent S “an even number of spots2,600 16 up to 3,400 15 Molly’s Candle Shop 3,000 has several retail stores 4in the coastal areas of North and ask180 South Carolina.Solution Many of Molly’s customers her to ship their purchases The folTotal S O L U T I O Software N lowing chart shows the number of packages shipped per day for the last 100 days We can use a statistical software package to find many measures of location example,are: the first class shows that there were days when the number of packThe possible For outcomes 400 800 1,200 shipped was up to Construct ages a histogram What observations can you reach based on the information 1,600 X A histogram? MPLE presented inE the Profi a one-spot four-spot Table 2–4 thea profit on the sales of 180 vehicles at Applewood 30on page 27 shows 28 Auto Group Determine the mean and23the median selling price 18 a two-spot 20 a five-spot SOLUTION 13 CHART 2–5 Frequency Polygon of Profit on 180 Vehicl 10 10 S O LaUthree-spot TIO N scaled a six-spot The class frequencies are along the vertical axis (Y-axis) and either the class As noted previously, $200 up to $600 limits or theThe class midpoints along horizontal axis To illustrate thethe construction median, mean, and the modal amounts of profit are reported in the following 10 25 30 35 $400 To20 construct ainstructions frequency polygon, mov of the histogram, first three are15shot) shown in Chart 2–3 outputthe (highlighted inclasses the screen (Reminder: The to create the Number of Packages appear in the Software Commands Appendix C.) are 180to vehicles There are threeoutput “favorable” outcomes (apoint, two, a$400, four,inand a six) in There the collection of8, the class and then vertically in the study, so using a calculator would be tedious and prone to error six equally likely possible outcomes Therefore: the y values of this point are called the coordin a What is this chart called? are x =Number 800 and y = 11 outcomes The process is contin of ← of favorable b What is the total number packages shipped? 32even ofc.anWhat number = is the class interval? connected in order That is, the point represe ← Total number of possible outcomes 23up to 15 class? d What shipped in the 10 24 is the number=of.5packages one  representing the second class and so on e What is the relative frequency of packages shipped in the 10 up to 15 class? the  f What upfrequency to 15 class? polygon, midpoints of $0 and $3, 16 is the midpoint of the 10 g On how many days were there or 11more packages shipped? the25polygon at zero frequencies These two va Number of Vehicles (class frequency) Probability Computer Output Temperature Number of favorable outcomes Probability Anniston, AL 89 = Profit West 48 Frequency ofAtlanta, an event GA Northwest of possible outcomes 86 Total number $ 200 up to $ 600 Augusta, GA Southwest 92 Frequency Exercises CLASSICAL PROBABILITY Frequency Formulas that are used for the first time are boxed and numbered for reference In addition, key formulas are listed in the back of the text as a reference 38 $ 40 80 1,20 1,60 2,00 2,40 2,80 3,20 Frequency mutually exclusive concept appeared earlier in our study of frequency distri8 The text includes many software examples, The using 16 The following chart shows the number of patientsthe admitted dailyinterval to Memorial subtracting class ofHospital $400 from the butions in Chapter Recall that we create classes so that a particular value is included through the emergency room $400 ­Excel, MegaStat , and Minitab The software results are to the highest midpoint ($3,200) in only one of the classes and there is no overlap between classes Thus, only one of in the fre 200 600 Both 1,000 1,400 and the frequency pol the histogram illustrated in the chapters Instructions for a particular several events can occur at a particular time Profit $characteristics of the data (highs, lows 30 the main software example are in Appendix C the two representations are similar in purpose each class as a rectangle, with the he 20 depicting CHART 2–3 Construction of a Histogram 10 Source: Microsoft Excel Lin87500_ch05_117-154.indd 121 Lin87500_ch02_019-052.indd 34 a b c d Number of Patients 10 What is the midpoint of the up to class? On how many days were up to patients admitted? What is the class interval? What is this chart called? 12 ix 8/16/17 1:01 PM 17 The following frequency distribution reports the number of frequent flier miles, reported in thousands, for employees of Brumley Statistical Consulting Inc during 7/28/17 www.downloadslide.net 586 INDEX Minitab box plots, 98 confidence intervals, 257 correlation coefficient, 372, 377 dot plots, 90 one-sample hypothesis tests, 296–297 one-way ANOVA, 351 prediction intervals, 399 quartiles, 94 random samples, 213 relationship between variables, 402 skewness, 101–103 stepwise regression, 445–447 use of, 12, 31 Mode disadvantages of using, 62 explanation of, 61–62 as measure of location, 54 relative position and, 64–65 Model, of relationship, 429 Monroe, Marilyn, 54 Morton Thiokol, 366 Multicollinearity, 439–441 Multiple linear regression, 429–435 Multiple regression analysis autocorrelation and, 441–442 background on, 419–420 distribution of residuals and, 439 evaluating assumptions of, 436–442 example of, 420–422 homoscedasticity and, 438 independent observations and, 441–442 linear relationships and, 436–437 multicollinearity and, 439–441 qualitative independent variables and, 442–444 review of, 448–453 stepwise regression and, 435, 445–447 uses for, 419, 442 Multiple regression equation adjusted coefficient of determination and, 428 ANOVA table and, 425, 426 coefficient of multiple determination and, 427–428 evaluation of, 425–428 example of, 420–422 explanation of, 419–420, 453 multiple standard error of estimate and, 426–427 Multiple regression model, 430–432 Multiple standard error of estimate, 426–427 Multiplication formula, 142–143 Multiplication rules general, 133–134 special, 132–133 Mutually exclusive events explanation of, 20, 21, 121–122 special rule of addition and, 126, 127 NASDAQ, 20 National Collegiate Athletic Association (NCAA), 137 Negatively skewed distributions, 65, 100 New York Stock Exchange, 20 Nightingale, Florence, 36 Nike, 210 90% confidence intervals, 245, 247 95% confidence intervals, 245, 246, 248, 262, 351 Nixon, Richard, 94 Nominal-scale variables, 7–8, 470 Nonnumeric variables, 21 Nonparametric methods See also Hypothesis tests background on, 470 chi-square limitations and, 487–488 contingency table analysis and, 490–493 goodness-of-fit tests and, 479–483 hypothesis test of population proportion and, 388–390 hypothesis test of unexpected frequencies, 486–487 two-sample tests about proportion and, 474–477 Normal approximation to binomial distribution, 471 Normal curve continuous probability distributions and area under, 191, 192, 196–198, 202–203 finding area under, 196–201 table of area under, 519 Normal probability distributions area under curve and, 192, 196–198, 202–203 characteristics of, 190–191 combining two areas and, 199–200 converted to standard, 192 family of, 190 formula for, 189 means and, 190, 191 residuals and, 439 standard, 192–201 standard deviation and, 79, 191 Normal probability plot, 439 Null hypothesis decision rule and, 279–280 explanation of, 276–277 hypothesis test result and, 280–281 level of significance and, 277–279 www.downloadslide.net INDEX multiple regression and, 430 one-tailed and two-tailed tests and, 281–286 Numeric data See Quantitative variables One-sample hypothesis tests for population mean with known standard deviation, 283–286 with unknown standard deviation, 290–294 One-tailed test example of, 286–287, 389 explanation of, 281–282, 286–287 One-way ANOVA, 348, 351 Ordinal-level data, 8–9 Outcomes, 120, 127 Outliers, 99 p-values, 287–288, 321, 377, 431, 432, 444, 450 Paired samples, 318 Paired t test, 319 Parameter, population, 55, 219 Pearson, Karl, 100, 369, 483 Pearson product-moment correlation coefficient, 369 Pearson’s coefficient of skewness, 100–102 Pearson’s r, 369 Penske Auto Group, 20 Percentiles, 92–94 Perfect correlation, 369 Permutation formula, 143–144 Permutations, 143 Pie charts explanation of, 22–23 frequency tables and, 24 uses for, 25 Pilot studies, 264 Point estimate characteristics of, 173 explanation of, 243, 257 Poisson experiment, 173–174 for population mean, 243–244 Poisson probability distributions application of, 173–177 binomial probability and, 176–177 characteristics of, 174 explanation of, 174 formula for, 174 mean of, 174, 177 table of, 518 variance of, 174 Ponzi scheme, 12 Pooled proportion, 475–477 Pooled variance, 313 587 Population explanation of, parameter of, 55, 219 Population mean compared with unknown population standard deviations, 312–321 confidence intervals for, 244–248 explanation of, 55–56 hypothesis tests for, 283–287, 290–294 point estimate for, 243–244 sample size to estimate, 264–265 two-tailed test for, 283–286 unbiased estimator of, 220 Population parameter, 219 Population proportion confidence interval for, 260–263 hypothesis tests for, 470–473 sample size to estimate, 265–266 Population standard deviation explanation of, 75, 244–248 known, 244–248, 283–287 sample size and, 264 unknown, 252–259, 290–294 Population variance, 73–74 Position See Measures of position Positively skewed distributions, 64, 65, 227–229, 336, 430 Practically significant, 287 Prediction intervals, 397–400 Probability approaches to, 121–122 classical, 121–122 conditional, 134, 137, 138 counting principles and, 142–146 empirical, 122–123 explanation of, 119–120 joint, 129–130, 137, 138 subjective, 124 Probability distributions See also Continuous probability distributions; Discrete probability distributions; Uniform probability distributions application of, 160, 211 binomial, 164–169 characteristics of, 156 cumulative binomial, 171–172 explanation of, 156 F distributions (See F distributions) generation of, 156–158 mean of, 160 Poisson, 173–177 random variables and, 158–160 variance and standard deviation of, 160–162 www.downloadslide.net 588 INDEX Probability rules complement rule of, 128–129 general rule of addition as, 129–131 general rule of multiplication as, 133–134 special rule of addition as, 126–127 special rule of multiplication as, 132–133 Proportions confidence intervals for, 260–263 pooled, 475–477 population, 260–263, 265–266, 470–473 sample, 470 two-sample tests of, 474–477 Pseudo-random numbers, 213 Qualitative variables explanation of, 6, 7, 21 in graphic form, 22–26 in multiple regression, 442–444 ordinal-level data and, 8–9 Quality control See Control charts Quantitative variables continuous, discrete, explanation of, 6, 7, 21 measures of location to describe, 54–67 Quartiles box plots and, 96–99 calculation of, 94–95 explanation of, 92, 93 RAND Corporation, 213 Random numbers in lotteries, 487 pseudo-, 213 Random numbers table, 212, 520 Random samples See also Samples/sampling simple, 212–214 statistical software to create, 249–251 stratified, 215–216 systematic, 215 Random variables continuous, 160, 185–186 discrete, 159 explanation of, 158–159 Random variation, 342–343 Range, 69–70 Range-based approach, 264 Ratio-level data, 10–11 Raw data, 55, 56 Regression analysis See also Linear regression; Multiple regression analysis drawing regression line and, 383–386 explanation of, 366, 380 least squares method and, 380–384 transformation and, 400–403 Regression coefficients evaluation of, 432–435 explanation of, 380, 422 testing individual, 432, 450 Regression equation See also Multiple regression equation ability to predict and, 391–395 explanation of, 380 general form of, 382 hypothesis tests to analyze, 388–390 interval estimates of prediction and, 396–400 method to determine, 383, 388 multiple, 432–434 test of hypothesis to analyze, 388–390 Regression line explanation of, 419 least squares, 384, 399 method to draw, 383–384 slope of, 382 Relative class frequencies, 21, 31 Relative frequency distributions, 31–32, 122, 123 Relative frequency tables discrete random variables and, 159 frequency tables converted to, 21 pie and bar charts and, 24 Residual plots, 436–437 Residuals calculation of, 385 distribution of, 439 variation in, 438 Risk, regression analysis to quantify, 380 Roosevelt, Franklin D., 215 R-square, 392 Rules of probability See Probability rules Sample mean See also Sampling distribution of sample mean central limit theorem and, 225–231 explanation of, 56–57 formula for, 56 Sample proportion, formula to compute, 470 www.downloadslide.net 589 INDEX Sample size confidence intervals and, 263–264 to estimate population mean, 264–265 to estimate population proportion, 265–266 Samples/sampling central limit theorem and, 225–231 cluster, 216–217 dependent, 321–323 determining size of, 243 explanation of, 5, 211 independent, 306–311, 321–323 paired, 318 point estimate for population mean and, 243–244 reasons for, 211–212, 243 simple random, 212–214 stratified random, 215–216 systematic random, 215 use of, Sample standard deviation, 77 Sample statistic, 219 Sample variance, 76–77 Sampling distribution of sample mean central limit theorem and, 225–231 explanation of, 221–223 population standard deviation and, 245 use of, 221–223, 232–233 Sampling error example of, 250–251 explanation of, 219–220, 227 Scatter diagrams correlation analysis and, 367–368, 371, 373 multiple regression and, 436–437, 452 use of, 105, 106 Simple random samples, 212–214 Skewed distributions explanation of, 64, 65 positively, 64, 65, 227–229 Skewness calculation of, 100–103 explanation of, 100 Pearson’s coefficient of, 100–103 software coefficient of, 101 Slope of regression line, 382 testing significance of, 388–390 Software, statistical, 12–13 See also Excel (Microsoft); MegaStat; Minitab Software coefficient of skewness, 101 Southern Technical Institute, 260 Special rule of addition, 126–127 Special rule of multiplication, 132–133 Spurious correlation, 373 Standard deviation Chebyshev’s theorem and, 78–79 of discrete probability distribution, 160–162 Empirical Rule and, 79–80, 193–195 explanation of, 244–245 interpretation and use of, 78–80 normal probability distributions and, 79, 190, 191 population, 75, 244–248, 252–259, 264, 283–287 sample, 77 of uniform distribution, 186 Standard error, 245 Standard error of estimate calculation of, 391–392 explanation of, 391 formula for, 391 multiple, 426–427 prediction and, 395 relationship to coefficients of correlation and determination, 392–394 Standard error of mean, 230 Standardizing, 101 Standard mean, 244 Standard normal probability distribution applications of, 193 areas under normal curve and, 196–201 Empirical Rule and, 193–195 explanation of, 191, 192 normal probability distribution converted into, 192 Standard normal table, 246 Standard normal value, 192 Standard & Poor’s 500 Index, 380 State Farm Mutual Automobile Insurance, Statistic explanation of, 56, 57 sample, 219 Statistical inference applications for, 6, 118 explanation of, 5, 118, 211, 275 multiple regression analysis and, 429–435 pairs of treatment means and, 350–352 sampling and, 215 www.downloadslide.net 590 INDEX Statistically significant, 287 Statistics descriptive, 4, 20, 118 ethics and, 12 explanation of, 3–4 history of, 2–3 inferential, 5–6, 118 misleading, 12 reasons to study, 2–3, 12–13 Stepwise regression, 435, 445–447 Stock market, 380 Strata, 215 Stratified random samples, 215–216 Student’s t distribution, 253, 258, 521–522 Subjective probability, 124 Sum of squares error (SSE), 394, 425 Sum of squares total (SS total), 394 Symbols, pronunciation and meaning of, 82, 110 Symmetric distributions, 64, 100, 190 See also Normal probability distributions Systematic random samples, 215 t distribution characteristics of, 252–253 confidence interval for population mean and, 253–257 development of, 252 hypothesis testing and, 290, 340–341, 389 Student’s, 253, 258, 521–522 t tests for correlation coefficient, 377 Excel procedure for, 315 paired, 319 Table of random numbers, 212–213 Target, Television viewership, 469 Test statistic for comparing two variances, 335–339 explanation of, 279, 284, 291 Tippett, L., 213 Total variation, 342 Travelair.com, 365 Treatment means, inferences about pairs of, 350–352 Treatments, 342–343 Treatment variation, 342–343 Tree diagrams, 138–140 Tukey, John W., 94 Two-sample hypothesis tests dependent samples and, 318–321 independent samples and, 306–311 of means - known σ, 308 two-sample pooled test and, 312–316 Two-sample pooled test, 312–316 Two-sample tests of means, 313 of proportions, 474–477 Two-tailed test critical value of F for, 337 example of, 283–286 explanation of, 281–282 Tyco, 12 Type I error example of, 281 explanation of, 278, 279 statistical software and, 351 Type II error, 278, 279 Unbiased sampling methods, 215 Unequal expected frequencies, 486–487 Uniform probability distributions equation for, 186 examples of, 186–188 explanation of, 185–186 standard deviation of, 186 Univariate data, 104 University of Michigan Institute for Social Research, 422 U.S Postal Service, 69 Van Tuyl Group, 20 Variables continuous, continuous random, 160, 185–186 dependent, 368 (See also Dependent variables) dummy, 442 independent, 368 (See also Independent variables) nominal-scale, 7–8, 470 nonnumeric, 21 qualitative, 6–8, 22–26 quantitative, 6, 7, 21, 54–67 random, 158–160 relationship between two, 104–106, 366, 367 (See also Correlation analysis) types of, 6–7 Variance See also Analysis of variance (ANOVA) of binomial probability distribution, 167 of discrete probability distribution, 160–162 of distribution of differences in means, 308 www.downloadslide.net 591 INDEX explanation of, 70–72 of Poisson distribution, 174 pooled, 313 population, 73–74, 335–339 sample, 76–77 Variance inflation factor (VIF), 440, 441 Variation random, 342–343 in residuals, 438 total, 342 treatment, 342–343 Venn, J., 127 Venn diagrams, 127–131 Volvo, 20 Walmart, Weighted mean, 54, 67 Yates, F., 213 Y-intercept, 382 z distribution, use of, 252, 253, 335 z values (z scores), 192, 198, 232, 233, 245, 258–259, 266 www.downloadslide.net www.downloadslide.net www.downloadslide.net KEY FORMULAS  Lind, Marchal, and Wathen   •  Basic Statistics for Business and Economics, 9th edition CHAPTER CHAPTER • Population mean • Special rule of addition Σx μ = N • Sample mean, raw data x= (3–1) P( A) = − P(~A) Σx n (3–2) (3–3) Range = Maximum value − Minimum value (3–4) σ = Σ(x − μ) N (3–5) σ=√ Σ(x − μ) N (3–6) • Sample variance s2 = Σ(x − x ) n−1 (3–7) • Sample standard deviation s=√ Σ(x − x ) n−1 Lp = (n + 1) sk = Total number of arrangements = ( m)(n) n Pr = (5–7) n! (n − r)! (5–8) n! r !(n − r)! (5–9) • Combination formula nCr = • Mean of a probability distribution (6–1) σ2 = Σ[(x − μ)2P(x)] P 100 (4–1) 3(x − Median) s (4–2) n x−x ∑( [ (n − 1)(n − 2) s ) ] (6–2) • Binomial probability distribution P(x) = nCx πx(1 − π)n − x (6–3) • Mean of a binomial distribution μ = nπ • Software coefficient of skewness sk = (5–6) • Variance of a probability distribution • Pearson’s coefficient of skewness P( A and B) = P( A)P(B ∣ A) μ = Σ[xP(x)] • Location of a percentile (5–5) CHAPTER (3–8) CHAPTER P( A and B) = P( A)P(B) • Permutation formula • Population standard deviation • Special rule of multiplication • Multiplication formula (5–4) • General rule of multiplication • Population variance (5–3) • General rule of addition P( A or B) = P( A) + P(B) − P( A and B) w1 x1 + w2 x2 + + wn xn xw = w1 + w2 + + wn • Range (5–2) • Complement rule • Weighted mean P( A or B) = P( A) + P(B) (6–4) • Variance of a binomial distribution (4–3) σ2 = nπ(1 − π) (6–5) • Poisson probability distribution P(x) = μxe−μ x! (6–6) • Mean of a Poisson distribution μ = nπ (6–7) www.downloadslide.net CHAPTER CHAPTER • Confidence interval for μ, with σ known • Mean of a uniform distribution μ= a+b (7–1) σ=√ (b − a) 12 (7–2) b−a if a ≤ x ≤ b    and elsewhere P(x) = (7–3) P(x) = e −[ σ √2π 2σ2 ] (x−μ)2 z= σ (7–4) (7–5) • Standard error of the mean x n (9–3) p(1 − p) n (9–4) (9–5) • Sample size for a proportion z n = π(1 − π) ( ) E (9–6) CHAPTER 10 σ σX = √n z= (9–2) zσ n=( ) E CHAPTER • z-value, μ and σ known s √n • Sample size for estimating mean p= p ± z √ • Standard normal value x−μ x ± t • Confidence interval for proportion • Normal probability distribution (9–1) • Sample proportion • Uniform probability distribution σ √n • Confidence interval for μ, σ unknown • Standard deviation of a uniform distribution x ± z x−μ σ∕ √n (8–1) • Testing a mean, σ known (8–2) z= x−μ σ∕ √n (10–1) (10–2) • Testing a mean, σ unknown t= x−μ s∕ √n www.downloadslide.net CHAPTER 11 CHAPTER 13 • Variance of the distribution of difference in means σ2x1 − x2 = σ21 n1 + σ22 n2 • Correlation coefficient (11–1) z= σ21 √n • Pooled variance + σ22 (n − 1) sxsy t= x − x2 √ s2p ( 1 + n1 n2 ) t= (11–3) b=r d sd ∕ √n (11–4) • Sum of squares, total s21 s22 (11–5) (13–4) a = y − bx (13–5) b−0 sb (13–6) t= (12–1) SS total = Σ(x − xG ) (12–2) SSE = Σ(x − xc ) (12–3) SST = SS total − SSE 1 (x1 − x2 ) ± t √ MSE ( + ) n1 n2 (13–7) • Coefficient of determination r2 = SSR SSE =1− SS Total SS Total (13–8) • Standard error of estimate SSE sy · x = √ n−2 (13–9) (x − x ) y^ ± tsy · x √ + n Σ(x − x ) (13–11) • Confidence interval (12–4) • Confidence interval for differences in treatment means sy sx Σ( y − y^ ) sy · x = √ n−2 • Sum of squares, treatments (13–3) • Standard error of estimate • Sum of squares, error (13–2) • Test for a zero slope • Test for comparing two variances F= • Intercept of the regression line CHAPTER 12 (13–1) • Slope of the regression line • Paired t test √1 − r y^ = a + bx n1 + n2 − t= • Linear regression equation n2 • Two-sample test of means, unknown but equal σ′s r √n − (11–2) (n1 − 1) s21 + (n2 − 1) s22 s2p = Σ(x − x )( y − y ) • Test for significant correlation • Two-sample test of means, known σ x − x2 r= • Prediction interval (12–5) (x − x ) y^ ± tsy · x √ + + n Σ(x − x ) (13–12) www.downloadslide.net CHAPTER 14 CHAPTER 15 • Multiple regression equation • Test of hypothesis, one proportion y^ = a + b1x1 + b2 x2 + · · · + bk xk (14–1) • Multiple standard error of estimate Σ(y − y^ ) SSE sy · 123…k = √ = n − (k + 1) √ n − (k + 1) (14–2) • Coefficient of multiple determination R2adj = − SS total n−1 F= (14–4) SSR∕k bi − sbi VIF = 1 − R2j (14–5) (14–6) √ pc (1 − pc ) n1 pc = χ2 = • Variance inflation factor n + pc (1 − pc ) (15–2) n2 (14–7) x + x2 n1 + n2 (15–3) • Chi-square test statistic • Expected frequency SSE∕[n − (k + 1)] t= (15–1) p1 − p2 • Testing for a particular regression coefficient √ π(1 − π) • Pooled proportion • Global test of hypothesis z= (14–3) • Adjusted coefficient of determination SSE n − (k + 1) p−π • Two-sample test of proportions SSR R2 = SS total z= fe = ∑[ (fo − fe ) fe ] (Row total)(Column total) Grand total (15–4) (15–5) www.downloadslide.net Student’s t Distribution ␣ –t t Confidence interval ␣ –t Left-tailed test t ␣ t Right-tailed test ␣ –t t Two-tailed test (continued ) 80% 90% 0.10 Level of Significance for One-Tailed Test, ␣ 0.05 0.025 0.01 0.005 df (degrees of freedom) Confidence Intervals, c 95% 98% 99% 99.9% 90% (degrees of freedom) 0.10 Level of Significance for One-Tailed Test, ␣ 0.05 0.025 0.01 0.005 0.0005 0.001 df 0.0005 Confidence Intervals, c 95% 98% 80% 99% 99.9% 0.20 Level of Significance for Two-Tailed Test, ␣ 0.10 0.05 0.02 0.01 0.20 Level of Significance for Two-Tailed Test, ␣ 0.10 0.05 0.02 0.01 3.078 1.886 1.638 1.533 1.476 6.314 2.920 2.353 2.132 2.015 12.706 4.303 3.182 2.776 2.571 31.821 6.965 4.541 3.747 3.365 63.657 9.925 5.841 4.604 4.032 636.619 31.599 12.924 8.610 6.869 36 37 38 39 40 1.306 1.305 1.304 1.304 1.303 1.688 1.687 1.686 1.685 1.684 2.028 2.026 2.024 2.023 2.021 2.434 2.431 2.429 2.426 2.423 2.719 2.715 2.712 2.708 2.704 3.582 3.574 3.566 3.558 3.551 10 1.440 1.415 1.397 1.383 1.372 1.943 1.895 1.860 1.833 1.812 2.447 2.365 2.306 2.262 2.228 3.143 2.998 2.896 2.821 2.764 3.707 3.499 3.355 3.250 3.169 5.959 5.408 5.041 4.781 4.587 41 42 43 44 45 1.303 1.302 1.302 1.301 1.301 1.683 1.682 1.681 1.680 1.679 2.020 2.018 2.017 2.015 2.014 2.421 2.418 2.416 2.414 2.412 2.701 2.698 2.695 2.692 2.690 3.544 3.538 3.532 3.526 3.520 11 12 13 14 15 1.363 1.356 1.350 1.345 1.341 1.796 1.782 1.771 1.761 1.753 2.201 2.179 2.160 2.145 2.131 2.718 2.681 2.650 2.624 2.602 3.106 3.055 3.012 2.977 2.947 4.437 4.318 4.221 4.140 4.073 46 47 48 49 50 1.300 1.300 1.299 1.299 1.299 1.679 1.678 1.677 1.677 1.676 2.013 2.012 2.011 2.010 2.009 2.410 2.408 2.407 2.405 2.403 2.687 2.685 2.682 2.680 2.678 3.515 3.510 3.505 3.500 3.496 16 17 18 19 20 1.337 1.333 1.330 1.328 1.325 1.746 1.740 1.734 1.729 1.725 2.120 2.110 2.101 2.093 2.086 2.583 2.567 2.552 2.539 2.528 2.921 2.898 2.878 2.861 2.845 4.015 3.965 3.922 3.883 3.850 51 52 53 54 55 1.298 1.298 1.298 1.297 1.297 1.675 1.675 1.674 1.674 1.673 2.008 2.007 2.006 2.005 2.004 2.402 2.400 2.399 2.397 2.396 2.676 2.674 2.672 2.670 2.668 3.492 3.488 3.484 3.480 3.476 21 22 23 24 25 1.323 1.321 1.319 1.318 1.316 1.721 1.717 1.714 1.711 1.708 2.080 2.074 2.069 2.064 2.060 2.518 2.508 2.500 2.492 2.485 2.831 2.819 2.807 2.797 2.787 3.819 3.792 3.768 3.745 3.725 56 57 58 59 60 1.297 1.297 1.296 1.296 1.296 1.673 1.672 1.672 1.671 1.671 2.003 2.002 2.002 2.001 2.000 2.395 2.394 2.392 2.391 2.390 2.667 2.665 2.663 2.662 2.660 3.473 3.470 3.466 3.463 3.460 26 27 28 29 30 1.315 1.314 1.313 1.311 1.310 1.706 1.703 1.701 1.699 1.697 2.056 2.052 2.048 2.045 2.042 2.479 2.473 2.467 2.462 2.457 2.779 2.771 2.763 2.756 2.750 3.707 3.690 3.674 3.659 3.646 61 62 63 64 65 1.296 1.295 1.295 1.295 1.295 1.670 1.670 1.669 1.669 1.669 2.000 1.999 1.998 1.998 1.997 2.389 2.388 2.387 2.386 2.385 2.659 2.657 2.656 2.655 2.654 3.457 3.454 3.452 3.449 3.447 31 32 33 34 35 1.309 1.309 1.308 1.307 1.306 1.696 1.694 1.692 1.691 1.690 2.040 2.037 2.035 2.032 2.030 2.453 2.449 2.445 2.441 2.438 2.744 2.738 2.733 2.728 2.724 3.633 3.622 3.611 3.601 3.591 66 67 68 69 70 1.295 1.294 1.294 1.294 1.294 1.668 1.668 1.668 1.667 1.667 1.997 1.996 1.995 1.995 1.994 2.384 2.383 2.382 2.382 2.381 2.652 2.651 2.650 2.649 2.648 3.444 3.442 3.439 3.437 3.435 0.001 (continued-top right ) (continued ) www.downloadslide.net Student’s Student’stt Distribution Distribution ((concluded concluded)) ((continued (continued (continued continued)))) 80% 80% 80% 80% Confidence Confidence Confidence ConfidenceIntervals, Intervals, Intervals, Intervals,cccc 90% 90% 90% 90% 95% 95% 95% 95% 98% 98% 98% 98% 0.10 0.10 0.10 0.10 Level Level Level Levelof of of ofSignificance Significance Significance Significancefor for for forOne-Tailed One-Tailed One-Tailed One-TailedTest, Test, Test, Test,␣␣ ␣ ␣ 0.05 0.025 0.01 0.005 0.0005 0.05 0.05 0.05 0.025 0.025 0.025 0.01 0.01 0.01 0.005 0.005 0.005 0.0005 0.0005 0.0005 df df df df (degrees (degrees (degrees (degrees of of of of freedom) freedom) freedom) freedom) 99% 99% 99% 99% 99.9% 99.9% 99.9% 99.9% Level of Significance for Two-Tailed Test, Level Level Levelof of ofSignificance Significance Significancefor for forTwo-Tailed Two-Tailed Two-TailedTest, Test, Test,␣␣ ␣ ␣ 0.20 0.20 0.20 0.20 0.10 0.10 0.10 0.10 0.05 0.05 0.05 0.05 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.001 0.001 0.001 0.001 71 71 71 71 72 72 72 72 73 73 73 73 74 74 74 74 75 75 75 75 1.294 1.294 1.294 1.294 1.293 1.293 1.293 1.293 1.293 1.293 1.293 1.293 1.293 1.293 1.293 1.293 1.293 1.293 1.293 1.293 1.667 1.667 1.667 1.667 1.666 1.666 1.666 1.666 1.666 1.666 1.666 1.666 1.666 1.666 1.666 1.666 1.665 1.665 1.665 1.665 1.994 1.994 1.994 1.994 1.993 1.993 1.993 1.993 1.993 1.993 1.993 1.993 1.993 1.993 1.993 1.993 1.992 1.992 1.992 1.992 2.380 2.380 2.380 2.380 2.379 2.379 2.379 2.379 2.379 2.379 2.379 2.379 2.378 2.378 2.378 2.378 2.377 2.377 2.377 2.377 2.647 2.647 2.647 2.647 2.646 2.646 2.646 2.646 2.645 2.645 2.645 2.645 2.644 2.644 2.644 2.644 2.643 2.643 2.643 2.643 3.433 3.433 3.433 3.433 3.431 3.431 3.431 3.431 3.429 3.429 3.429 3.429 3.427 3.427 3.427 3.427 3.425 3.425 3.425 3.425 76 76 76 76 77 77 77 77 78 78 78 78 79 79 79 79 80 80 80 80 1.293 1.293 1.293 1.293 1.293 1.293 1.293 1.293 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.665 1.665 1.665 1.665 1.665 1.665 1.665 1.665 1.665 1.665 1.665 1.665 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.992 1.992 1.992 1.992 1.991 1.991 1.991 1.991 1.991 1.991 1.991 1.991 1.990 1.990 1.990 1.990 1.990 1.990 1.990 1.990 2.376 2.376 2.376 2.376 2.376 2.376 2.376 2.376 2.375 2.375 2.375 2.375 2.374 2.374 2.374 2.374 2.374 2.374 2.374 2.374 2.642 2.642 2.642 2.642 2.641 2.641 2.641 2.641 2.640 2.640 2.640 2.640 2.640 2.640 2.640 2.640 2.639 2.639 2.639 2.639 3.423 3.423 3.423 3.423 3.421 3.421 3.421 3.421 3.420 3.420 3.420 3.420 3.418 3.418 3.418 3.418 3.416 3.416 3.416 3.416 81 81 81 81 82 82 82 82 83 83 83 83 84 84 84 84 85 85 85 85 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.663 1.663 1.663 1.663 1.663 1.663 1.663 1.663 1.663 1.663 1.663 1.663 1.990 1.990 1.990 1.990 1.989 1.989 1.989 1.989 1.989 1.989 1.989 1.989 1.989 1.989 1.989 1.989 1.988 1.988 1.988 1.988 2.373 2.373 2.373 2.373 2.373 2.373 2.373 2.373 2.372 2.372 2.372 2.372 2.372 2.372 2.372 2.372 2.371 2.371 2.371 2.371 2.638 2.638 2.638 2.638 2.637 2.637 2.637 2.637 2.636 2.636 2.636 2.636 2.636 2.636 2.636 2.636 2.635 2.635 2.635 2.635 3.415 3.415 3.415 3.415 3.413 3.413 3.413 3.413 3.412 3.412 3.412 3.412 3.410 3.410 3.410 3.410 3.409 3.409 3.409 3.409 86 86 86 86 87 87 87 87 88 88 88 88 89 89 89 89 90 90 90 90 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.663 1.663 1.663 1.663 1.663 1.663 1.663 1.663 1.662 1.662 1.662 1.662 1.662 1.662 1.662 1.662 1.662 1.662 1.662 1.662 1.988 1.988 1.988 1.988 1.988 1.988 1.988 1.988 1.987 1.987 1.987 1.987 1.987 1.987 1.987 1.987 1.987 1.987 1.987 1.987 2.370 2.370 2.370 2.370 2.370 2.370 2.370 2.370 2.369 2.369 2.369 2.369 2.369 2.369 2.369 2.369 2.368 2.368 2.368 2.368 2.634 2.634 2.634 2.634 2.634 2.634 2.634 2.634 2.633 2.633 2.633 2.633 2.632 2.632 2.632 2.632 2.632 2.632 2.632 2.632 3.407 3.407 3.407 3.407 3.406 3.406 3.406 3.406 3.405 3.405 3.405 3.405 3.403 3.403 3.403 3.403 3.402 3.402 3.402 3.402 91 91 91 91 92 92 92 92 93 93 93 93 94 94 94 94 95 95 95 95 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.662 1.662 1.662 1.662 1.662 1.662 1.662 1.662 1.661 1.661 1.661 1.661 1.661 1.661 1.661 1.661 1.661 1.661 1.661 1.661 1.986 1.986 1.986 1.986 1.986 1.986 1.986 1.986 1.986 1.986 1.986 1.986 1.986 1.986 1.986 1.986 1.985 1.985 1.985 1.985 2.368 2.368 2.368 2.368 2.368 2.368 2.368 2.368 2.367 2.367 2.367 2.367 2.367 2.367 2.367 2.367 2.366 2.366 2.366 2.366 2.631 2.631 2.631 2.631 2.630 2.630 2.630 2.630 2.630 2.630 2.630 2.630 2.629 2.629 2.629 2.629 2.629 2.629 2.629 2.629 3.401 3.401 3.401 3.401 3.399 3.399 3.399 3.399 3.398 3.398 3.398 3.398 3.397 3.397 3.397 3.397 3.396 3.396 3.396 3.396 96 96 96 96 97 97 97 97 98 98 98 98 99 99 99 99 100 100 100 100 1.290 1.290 1.290 1.290 1.290 1.290 1.290 1.290 1.290 1.290 1.290 1.290 1.290 1.290 1.290 1.290 1.290 1.290 1.290 1.290 1.661 1.661 1.661 1.661 1.661 1.661 1.661 1.661 1.661 1.661 1.661 1.661 1.660 1.660 1.660 1.660 1.660 1.660 1.660 1.660 1.985 1.985 1.985 1.985 1.985 1.985 1.985 1.985 1.984 1.984 1.984 1.984 1.984 1.984 1.984 1.984 1.984 1.984 1.984 1.984 2.366 2.366 2.366 2.366 2.365 2.365 2.365 2.365 2.365 2.365 2.365 2.365 2.365 2.365 2.365 2.365 2.364 2.364 2.364 2.364 2.628 2.628 2.628 2.628 2.627 2.627 2.627 2.627 2.627 2.627 2.627 2.627 2.626 2.626 2.626 2.626 2.626 2.626 2.626 2.626 3.395 3.395 3.395 3.395 3.394 3.394 3.394 3.394 3.393 3.393 3.393 3.393 3.392 3.392 3.392 3.392 3.390 3.390 3.390 3.390 120 120 120 120 140 140 140 140 160 160 160 160 180 180 180 180 200 200 200 200 ϱϱ ϱ ϱ 1.289 1.289 1.289 1.289 1.288 1.288 1.288 1.288 1.287 1.287 1.287 1.287 1.286 1.286 1.286 1.286 1.286 1.286 1.286 1.286 1.282 1.282 1.282 1.282 1.658 1.658 1.658 1.658 1.656 1.656 1.656 1.656 1.654 1.654 1.654 1.654 1.653 1.653 1.653 1.653 1.653 1.653 1.653 1.653 1.645 1.645 1.645 1.645 1.980 1.980 1.980 1.980 1.977 1.977 1.977 1.977 1.975 1.975 1.975 1.975 1.973 1.973 1.973 1.973 1.972 1.972 1.972 1.972 1.960 1.960 1.960 1.960 2.358 2.358 2.358 2.358 2.353 2.353 2.353 2.353 2.350 2.350 2.350 2.350 2.347 2.347 2.347 2.347 2.345 2.345 2.345 2.345 2.326 2.326 2.326 2.326 2.617 2.617 2.617 2.617 2.611 2.611 2.611 2.611 2.607 2.607 2.607 2.607 2.603 2.603 2.603 2.603 2.601 2.601 2.601 2.601 2.576 2.576 2.576 2.576 3.373 3.373 3.373 3.373 3.361 3.361 3.361 3.361 3.352 3.352 3.352 3.352 3.345 3.345 3.345 3.345 3.340 3.340 3.340 3.340 3.291 3.291 3.291 3.291 www.downloadslide.net Areas under the Normal Curve Example: If z = 1.96, then P(0 to z) = 0.4750 0.4750 z 1.96 z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.1 0.2 0.3 0.4 0.0000 0.0398 0.0793 0.1179 0.1554 0.0040 0.0438 0.0832 0.1217 0.1591 0.0080 0.0478 0.0871 0.1255 0.1628 0.0120 0.0517 0.0910 0.1293 0.1664 0.0160 0.0557 0.0948 0.1331 0.1700 0.0199 0.0596 0.0987 0.1368 0.1736 0.0239 0.0636 0.1026 0.1406 0.1772 0.0279 0.0675 0.1064 0.1443 0.1808 0.0319 0.0714 0.1103 0.1480 0.1844 0.0359 0.0753 0.1141 0.1517 0.1879 0.5 0.6 0.7 0.8 0.9 0.1915 0.2257 0.2580 0.2881 0.3159 0.1950 0.2291 0.2611 0.2910 0.3186 0.1985 0.2324 0.2642 0.2939 0.3212 0.2019 0.2357 0.2673 0.2967 0.3238 0.2054 0.2389 0.2704 0.2995 0.3264 0.2088 0.2422 0.2734 0.3023 0.3289 0.2123 0.2454 0.2764 0.3051 0.3315 0.2157 0.2486 0.2794 0.3078 0.3340 0.2190 0.2517 0.2823 0.3106 0.3365 0.2224 0.2549 0.2852 0.3133 0.3389 1.0 1.1 1.2 1.3 1.4 0.3413 0.3643 0.3849 0.4032 0.4192 0.3438 0.3665 0.3869 0.4049 0.4207 0.3461 0.3686 0.3888 0.4066 0.4222 0.3485 0.3708 0.3907 0.4082 0.4236 0.3508 0.3729 0.3925 0.4099 0.4251 0.3531 0.3749 0.3944 0.4115 0.4265 0.3554 0.3770 0.3962 0.4131 0.4279 0.3577 0.3790 0.3980 0.4147 0.4292 0.3599 0.3810 0.3997 0.4162 0.4306 0.3621 0.3830 0.4015 0.4177 0.4319 1.5 1.6 1.7 1.8 1.9 0.4332 0.4452 0.4554 0.4641 0.4713 0.4345 0.4463 0.4564 0.4649 0.4719 0.4357 0.4474 0.4573 0.4656 0.4726 0.4370 0.4484 0.4582 0.4664 0.4732 0.4382 0.4495 0.4591 0.4671 0.4738 0.4394 0.4505 0.4599 0.4678 0.4744 0.4406 0.4515 0.4608 0.4686 0.4750 0.4418 0.4525 0.4616 0.4693 0.4756 0.4429 0.4535 0.4625 0.4699 0.4761 0.4441 0.4545 0.4633 0.4706 0.4767 2.0 2.1 2.2 2.3 2.4 0.4772 0.4821 0.4861 0.4893 0.4918 0.4778 0.4826 0.4864 0.4896 0.4920 0.4783 0.4830 0.4868 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Business and Economics Fifth Edition Lind, Marchal, and Wathen Basic Statistics for Business and Economics Ninth Edition Lind, Marchal, and Wathen Statistical Techniques in Business and Economics. .. Jaggia and Kelly Business Statistics: Communicating with Numbers Second Edition Jaggia and Kelly Essentials of Business Statistics: Communicating with Numbers First Edition Basic Statistics for BUSINESS. .. sons, their wives, and our grandchildren: Mike and Sue (Steve and Courtney), Steve and Kathryn (Kennedy, Jake, and Brady), and Mark and Sarah (Jared, Drew, and Nate) Douglas A Lind To Oscar Sambath