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Statistical techniques in business and economics 15e dr soc Statistical techniques in business and economics 15e dr soc Statistical techniques in business and economics 15e dr soc Statistical techniques in business and economics 15e dr soc Statistical techniques in business and economics 15e dr soc Statistical techniques in business and economics 15e dr soc Statistical techniques in business and economics 15e dr soc Statistical techniques in business and economics 15e dr soc
Lin01803_fm_i-xxx.qxd 11/15/10 11:04 AM Page i S t a t i s t i c a l Te c h n i q u e s i n Business & Economics Fifteenth 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 Lin01803_fm_i-xxx.qxd 11/15/10 3:32 PM Page ii STATISTICAL TECHNIQUES IN BUSINESS & ECONOMICS Published by McGraw-Hill/Irwin, a business unit of The McGraw-Hill Companies, Inc., 1221Avenue of the Americas, New York, NY, 10020 Copyright © 2012, 2010, 2008, 2005, 2002, 1999, 1996, 1993, 1990, 1986, 1982, 1978, 1974, 1970, 1967 by The McGraw-Hill Companies, Inc All rights reserved 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 The McGraw-Hill Companies, Inc., 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 RJE/RJE ISBN MHID ISBN MHID 978-0-07-340180-5 (student edition) 0-07-340180-3 (student edition) 978-0-07-732701-9 (instructor’s edition) 0-07-732701-2 (instructor’s edition) Vice president and editor-in-chief: Brent Gordon Editorial director: Stewart Mattson Publisher: Tim Vertovec Executive editor: Steve Schuetz Executive director of development: Ann Torbert Senior development editor: Wanda J Zeman Vice president and director of marketing: Robin J Zwettler Marketing director: Brad Parkins Marketing manager: Katie White Vice president of editing, design, and production: Sesha Bolisetty Senior project manager: Diane L Nowaczyk Senior buyer: Carol A Bielski Interior designer: JoAnne Schopler Senior photo research coordinator: Keri Johnson Photo researcher: Teri Stratford Lead media project manager: Brian Nacik Media project manager: Ron Nelms Typeface: 9.5/11 Helvetica Neue 55 Compositor: Aptara®, Inc Printer: R R Donnelley Library of Congress Cataloging-in-Publication Data Lind, Douglas A Statistical techniques in business & economics / Douglas A Lind, William G Marchal, Samuel A Wathen — 15th ed p cm — (The McGraw-Hill/Irwin series operations and decision sciences) Includes index ISBN-13: 978-0-07-340180-5 (student ed : alk paper) ISBN-10: 0-07-340180-3 (student ed : alk paper) ISBN-13: 978-0-07-732701-9 (instructor’s ed : alk paper) ISBN-10: 0-07-732701-2 (instructor’s ed : alk paper) Social sciences—Statistical methods Economics—Statistical methods Commercial statistics I Marchal, William G II Wathen, Samuel Adam III Title IV Title: Statistical techniques in business and economics HA29.M268 2012 519.5—dc22 2010045058 www.mhhe.com Lin01803_fm_i-xxx.qxd 11/15/10 3:33 PM Page iii Dedication 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 and Jake), and Mark and Sarah (Jared, Drew, and Nate) Douglas A Lind To John Eric Mouser, his siblings, parents, and Granny William G Marchal To my wonderful family: Isaac, Hannah, and Barb Samuel A Wathen Lin01803_fm_i-xxx.qxd 11/15/10 11:05 AM Page iv A Note from Over the years, we have 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 Statistical Techniques in 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 the many applications of descriptive and inferential statistics We focus on business applications, but we also use many exercises and examples that 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 with a delay of less than 20 minutes Today, skills are needed to deal with a large volume of numerical information First, we need to be critical consumers of information presented by others Second, we need to be able to reduce large amounts of information into a concise and meaningful form to enable us to make effective interpretations, judgments, and decisions All students have calculators and most have either personal computers or access to personal computers in a campus lab Statistical software, such as Microsoft Excel and Minitab, is available on these computers The commands necessary to achieve the software results are available in a special section at the end of each chapter 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 Ionger necessary to dwelI 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 now 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 iv Lin01803_fm_i-xxx.qxd 11/15/10 11:05 AM Page v the Authors What’s New in This Fifteenth Edition? We have made changes to this edition that we think you and your students will find useful and timely • We have revised the learning objectives so they are more specific, added new ones, identified them in the margin, and keyed them directly to sections within the chapter • We have replaced the key example in Chapters to The new example includes more variables and more observations It presents a realistic business situation It is also used later in the text in Chapter 13 • We have added or revised several new sections in various chapters: Chapter now includes a discussion of the exponential distribution Chapter has been reorganized to make it more teachable and improve the flow of the topics Chapter 13 has been reorganized and includes a test of hypothesis for the slope of the regression coefficient Chapter 17 now includes a graphic test for normality and the chisquare test for normality • New exercises and examples use Excel 2007 screenshots and the latest version of Minitab We have also increased the size and clarity of these screenshots • There are new Excel 2007 software commands and updated Minitab commands at the ends of chapters • We have carefully reviewed the exercises within the chapters, those at the ends of chapters, and in the Review Section We have added many new or revised exercises throughout You can still find and assign your favorites that have worked well, or you can introduce fresh examples • Section numbers have been added to more clearly identify topics and more easily reference them • The exercises that contain data files are identified by an icon for easy identification • The Data Exercises at the end of each chapter have been revised The baseball data has been updated to the most current completed season, 2009 A new business application has been added that refers to the use and maintenance of the school bus fleet of the Buena School District • There are many new photos throughout, with updated exercises in the chapter openers v Lin01803_fm_i-xxx.qxd 11/15/10 11:05 AM Page vi How Are Chapters Organized to Chapter Learning Objectives Describing Data: Learning Objectives Numerical Measures When you have completed this chapter, you will be able to: 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 the chapter LO1 Explain the concept of central tendency LO2 Identify and compute the arithmetic mean LO3 Compute and interpret the weighted mean LO4 Determine the median LO5 Identify the mode LO6 Calculate the geometric mean LO7 Explain and apply measures of dispersion Chapter Opening Exercise LO8 Compute and explain the variance and the standard deviation The Kentucky Derby is held the first Saturday in May at Churchill A representative exercise opens the chapter and shows how the chapter content can be applied to a real-world situation LO9 Explain Chebyshev’s Theorem and the Empirical Rule Downs in Louisville, Kentucky The race track is one and one-quarter miles The table in Exercise 82 shows the winners since 1990, their margin of victory, the winning time, and the payoff on a $2 bet LO10 Compute the mean and standard deviation of grouped data Determine the mean and median for the variables winning time and payoff on a $2 bet (See Exercise 82 and LO2 and LO4.) Introduction to the Topic 2.1 Introduction Each chapter starts with a review of the important concepts of the 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 to provide a how-to illustration for students and to show a relevant business or economics-based application that helps answer the question, “What will I use this for?” All examples provide a realistic scenario or application and make the math size and scale reasonable for introductory students Self-Reviews Self-Reviews are interspersed throughout each chapter and closely patterned after the preceding Examples They help students monitor their progress and provide immediate reinforcement for that particular technique vi Self-Review 3–6 The highly competitive automobile retailing industry in the United States has changed dramatically in recent years These changes spurred events such as the: • bankruptcies of General Motors and Chrysler in 2009 • elimination of well-known brands such as Pontiac and Saturn • closing of over 1,500 local dealerships • collapse of consumer credit availability • consolidation dealership groups Traditionally, a local family owned and operated the community dealership, which might have included one or two manufacturers or brands, like Pontiac and GMC Trucks or Chrysler and the popular Jeep line Recently, however, skillfully managed and well-financed companies have been acquiring local dealer- Example Layton Tire and Rubber Company wishes to set a minimum mileage guarantee on its new MX100 tire Tests reveal the mean mileage is 67,900 with a standard deviation of 2,050 miles and that the distribution of miles follows the normal probability distribution Layton wants to set the minimum guaranteed mileage so that no more than percent of the tires will have to be replaced What minimum guaranteed mileage should Layton announce? Solution The facets of this case are shown in the following diagram, where X represents the minimum guaranteed mileage The weights of containers being shipped to Ireland are (in thousands of pounds): 95 (a) (b) (c) 103 105 110 104 What is the range of the weights? Compute the arithmetic mean weight Compute the mean deviation of the weights 105 112 90 Lin01803_fm_i-xxx.qxd 11/15/10 11:05 AM Page vii Engage Students and Promote Learning? The equation for the trend line is: Yˆ ϭ 8.109 ϩ 08991t Statistics in Action Statistics in Action articles are scattered throughout the text, usually about two per chapter They provide unique and interesting applications and historical insights in the field of statistics The slope of the trend line is 08991 This shows that over the 24 quarters the deseasonalized sales increased at a rate of 0.08991 ($ million) per quarter, or $89,910 per quarter The value of 8.109 is the intercept of the trend line on the Y-axis (i.e., for t ϭ 0) Statistics in Action Forecasts are not always correct The reality is that a forecast may just be a best guess as to what will happen What are the reasons forecasts are not correct? One expert lists eight common errors: Margin Notes There are more than 300 concise notes in the margin Each is aimed at reemphasizing the key concepts presented immediately adjacent to it The variance is non-negative and is zero only if all observations are the same STANDARD DEVIATION The square root of the variance Definitions Definitions of new terms or terms unique to the study of statistics are set apart from the text and highlighted for easy reference and review Variance and standard deviation are based on squared deviations from the mean Population Variance The formulas for the population variance and the sample variance are slightly different The population variance is considered first (Recall that a population is the totality of all observations being studied.) The population variance is found by: Formulas Formulas that are used for the first time are boxed and numbered for reference In addition, a formula card is bound into the back of the text, which lists all the key formulas Exercises Exercises are included after sections within the chapter and at the end of the chapter Section exercises cover the material studied in the section POPULATION VARIANCE 2 ϭ ͚(X Ϫ )2 N [3–8] Exercises For Exercises 35–38, calculate the (a) range, (b) arithmetic mean, (c) mean deviation, and (d) interpret the values 35 There were five customer service representatives on duty at the Electronic Super Store during last weekend’s sale The numbers of HDTVs these representatives sold are: 5, 8, 4, 10, and 36 The Department of Statistics at Western State University offers eight sections of basic statistics Following are the numbers of students enrolled in these sections: 34, 46, 52, 29, 41, 38, 36, and 28 Computer Output The text includes many software examples, using Excel, MegaStat®, and Minitab vii Lin01803_fm_i-xxx.qxd 11/15/10 11:06 AM Page viii How Does This Text BY CHAPTER Chapter Summary Chapter Summary I A dot plot shows the range of values on the horizontal axis and the number of observations for each value on the vertical axis A Dot plots report the details of each observation B They are useful for comparing two or more data sets II A stem-and-leaf display is an alternative to a histogram A The leading digit is the stem and the trailing digit the leaf B The advantages of a stem-and-leaf display over a histogram include: Each chapter contains a brief summary of the chapter material, including the vocabulary and the critical formulas Pronunciation Key Pronunciation Key SYMBOL MEANING PRONUNCIATION This tool lists the mathematical symbol, its meaning, and how to pronounce it We believe this will help the student retain the meaning of the symbol and generally enhance course communications Lp Location of percentile L sub p Q1 First quartile Q sub Q3 Third quartile Q sub Chapter Exercises Chapter Exercises 27 A sample of students attending Southeast Florida University is asked the number of social activities in which they participated last week The chart below was prepared from the sample data Generally, the end-of-chapter exercises are the most challenging and integrate the chapter concepts The answers and worked-out solutions for all odd-numbered exercises appear at the end of the text For exercises with more than 20 observations, the data can be found on the text’s website These files are in Excel and Minitab formats Data Set Exercises Software examples using Excel, MegaStat®, and Minitab are included throughout the text, but the explanations of the computer input commands for each program are placed at the end of the chapter This allows students to focus on the statistical techniques rather than on how to input data 44 Refer to the Real Estate data, which reports information on homes sold in the Goodyear, Arizona, area during the last year Prepare a report on the selling prices of the homes Be sure to answer the following questions in your report a Develop a box plot Estimate the first and the third quartiles Are there any outliers? b Develop a scatter diagram with price on the vertical axis and the size of the home on the horizontal Does there seem to be a relationship between these variables? Is the relationship direct or inverse? c Develop a scatter diagram with price on the vertical axis and distance from the center of the city on the horizontal axis Does there seem to be a relationship between these variables? Is the relationship direct or inverse? 45 Refer to the Baseball 2009 data, which reports information on the 30 Major League Baseball teams for the 2009 season Refer to the variable team salary a Select the variable that refers to the year in which the stadium was built (Hint: Subtract the year in which the stadium was built from the current year to find the age of the stadium and work this variable.) Develop a box plot Are there any outliers? Which stadiums are outliers? b Select the variable team salary and draw a box plot Are there any outliers? What are the quartiles? Write a brief summary of your analysis How the salaries of the New York Yankees compare with the other teams? Software Commands The Excel Commands for the descriptive statistics on page 69 are: a From the CD, retrieve the Applewood data b From the menu bar, select Data and then Data Analysis Select Descriptive Statistics and then click OK viii Activities Data Set Exercises The last several exercises at the end of each chapter are based on three large data sets These data sets are printed in Appendix A in the text and are also on the text’s website These data sets present the students with real-world and more complex applications Software Commands The Minitab commands for the descriptive summary on page 84 are: Lin01803_fm_i-xxx.qxd 11/15/10 11:06 AM Page ix Reinforce Student Learning? Answers to Self-Review The worked-out solutions to the Self-Reviews are provided at the end of each chapter Chapter 2–1 Answers to Self-Review a Qualitative data, because the customers’ response to the taste test is the name of a beverage b Frequency table It shows the number of people who prefer each beverage c 2–3 40 Frequency 30 20 10 2–4 Cola-Plus Coca-Cola Pepsi Lemon-Lime Beverage BY SECTION Section Reviews After selected groups of chapters (1–4, 5–7, and 9, 10–12, 13 and 14, 15 and 16, and 17 and 18), a Section Review is included Much like a review before an exam, these include a brief overview of the chapters, a glossary of key terms, and problems for review 2–5 The review also includes continuing cases and several small cases that let students make decisions using tools and techniques from a variety of chapters Practice Test The Practice Test is intended to give students an idea of content that might appear on a test and how the test might be structured The Practice Test includes both objective questions and problems covering the material studied in the section a 20 20 A Review of Chapters 1–4 This section is a review of the major concepts and terms introduced in Chapters 1–4 Chapter began by describing the meaning and purpose of statistics Next we described the different types of variables and the four levels of measurement Chapter was concerned with describing a set of observations by organizing it into a frequency distribution and then portraying the frequency distribution as a histogram or a frequency polygon Chapter began by describing measures of location, such as the mean, weighted mean, median, geometric mean, and mode This chapter also included measures of dispersion, or spread Discussed in this section were the range, mean deviation, variance, and standard deviation Chapter included several graphing techniques such as dot plots, box plots, and scatter diagrams We also discussed the coefficient of skewness, which reports the lack of symmetry in a set of data Throughout this section we stressed the importance of statistical software, such as Excel and Minitab Many computer outputs in these chapters demonstrated how quickly and effectively a large data set can be organized into a frequency distribution, several of the measures of location or measures or variation calculated, and the information presented in graphical form Glossary Chapter Descriptive statistics The techniques used to describe the important characteristics of a set of data This includes organizing the data values into a frequency distribution, computing measures of location, and computing mea- Cases c Class frequencies d The largest concentration of commissions is $1,500 up to $1,600 The smallest commission is about $1,400 and the largest is about $1,800 The typical amount earned is $15,500 a 26 ϭ 64 Ͻ 73 Ͻ 128 ϭ 27 So seven classes are recommended b The interval width should be at least (488 Ϫ 320)͞7 ϭ 24 Class intervals of 25 or 30 feet are both reasonable c If we use a class interval of 25 feet and begin with a lower limit of 300 feet, eight classes would be necessary A class interval of 30 feet beginning with 300 feet is also reasonable This alternative requires only seven classes a 45 b .250 c .306, found by 178 ϩ 106 ϩ 022 90 degrees is 10 degrees more than a temperature of 80 degrees, and so on Nominal measurement The “lowest” level of measurement If data are classified into categories and the order of those categories is not important, it is the nominal level of E l d ( l f l ) d Cases A Century National Bank The following case will appear in subsequent review sections Assume that you work in the Planning Department of the Century National Bank and report to Ms Lamberg You will need to some data analysis and prepare a short written report Remember, Mr Selig is the president of the bank, so you will want to ensure that your report is complete and accurate A copy of the data appears in Appendix A.6 Century National Bank has offices in several cities in the Midwest and the southeastern part of the United States Mr Dan Selig, president and CEO, would like to know the characteristics of his checking account customers What is the balance of a typical customer? How many other bank services the checking account customers use? Do the customers use the ATM service and, if so, how often? What about debit cards? Who uses them, and how often are they used? To better understand the customers, Mr Selig asked Ms Wendy Lamberg, director of planning, to select a sample of customers and prepare a report To begin, she has appointed a team from her staff You are the head of the team and responsible for preparing the report You select a random sample of 60 customers In addition to the balance in each account at the end of last month, you determine: (1) the number of ATM (auto- median balances for the four branches Is there a difference among the branches? Be sure to explain the difference between the mean and the median in your report Determine the range and the standard deviation of the checking account balances What the first and third quartiles show? Determine the coefficient of skewness and indicate what it shows Because Mr Selig does not deal with statistics daily, include a brief description and interpretation of the standard deviation and other measures B Wildcat Plumbing Supply Inc.: Do We Have Gender Differences? Wildcat Plumbing Supply has served the plumbing needs of Southwest Arizona for more than 40 years The company was founded by Mr Terrence St Julian and is run today by his son Cory The company has grown from a handful of employees to more than 500 today Cory is concerned about several positions within the company where he has men and women doing essentially the same job but at different pay To investigate, he collected the information below Suppose you are a student intern in the Accounting Department and have been given the task to write a report Practice Test There is a practice test at the end of each review section The tests are in two parts The first part contains several objective questions, usually in a fill-in-the-blank format The second part is problems In most cases, it should take 30 to 45 minutes to complete the test The problems require a calculator Check the answers in the Answer Section in the back of the book Part 1—Objective The science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making effective decisions is called Methods of organizing, summarizing, and presenting data in an informative way is called The entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest is called the List the two types of variables The number of bedrooms in a house is an example of a (discrete variable, continuous variable, qualitative variable—pick one) The jersey numbers of Major League Baseball players is an example of what level of measurement? The classification of students by eye color is an example of what level of measurement? The sum of the differences between each value and the mean is always equal to what value? A set of data contained 70 observations How many classes would you suggest in order to construct a frequency distribution? 10 What percent of the values in a data set are always larger than the median? 10 11 The square of the standard deviation is the 11 12 The standard deviation assumes a negative value when (All the values are negative, when at least half the values are negative, or never—pick one.) 12 13 Which of the following is least affected by an outlier? (mean, median, or range—pick one) 13 Part 2—Problems The Russell 2000 index of stock prices increased by the following amounts over the last three years 18% 4% 2% What is the geometric mean increase for the three years? ix Lin01803_ndx_831-850.qxd 840 11/10/10 5:11 PM Page 840 Index Percent defective (p) chart, 737–740 Percentiles, 111, 113–114 Permutation formula, 172–174 Permutations, 173 Pie charts, 25–27 Point estimates, 298–299 Poisson probability distributions, 207–209 binomial probability estimation, 210–211 characteristics, 208–209 definition, 207 exponential distribution and, 247 formula, 208 mean, 208 tables, 209, 770 variance, 208 Pooled proportion, 379 Pooled variance, 383 Population mean, 58–59 confidence intervals for, 299, 310 with known standard deviation, 300–303 with unknown standard deviation, 306–308 hypothesis tests for comparing three or more, 416–418 with equal population standard deviations, 383–386 with known standard deviation, 341–345 one-tailed test, 345 with unequal population standard deviations, 388–390 with unknown standard deviation, 348–352, 383–390 point estimates, 298–299 sample size for estimating, 317–318 two-tailed test for, 341–344 Population proportion, 314 hypothesis tests for, 356–358 sample size for estimating, 318–319 Population standard deviation, 82, 300–303, 306–308 Population variance, 80–81, 412–415 Populations definition, finite, 204, 320 inferences in multiple regression, 523–530 parameters, 59, 274 relationship to samples, strata, 270–271 Positively skewed distributions, 70, 119–120 Posterior probability, 167–168 PPI; see Producer Price Index Prediction intervals, 492, 493–494 Prior probability, 167 Probability approaches, 151 Bayes’ Theorem, 167–170 classical, 148–149 conditional, 160 counting principles combination formula, 174–175 multiplication formula, 171–172 permutation formula, 172–174 definition, 146 empirical, 149–150 events, 147 experiments, 146 joint, 156 objective, 148 outcomes, 146–147 posterior, 167–168 prior, 167 special rule of multiplication, 159–160 subjective, 150–151 Probability distributions binomial; see Binomial probability distributions characteristics, 187 continuous; see Continuous probability distributions definition, 187 discrete; see Discrete probability distributions F distributions; see F distributions generating, 187–188 hypergeometric, 204–206 normal; see Normal probability distributions Poisson, 207–209 uniform, 223–226 Probability rules complement rule, 154 general rule of addition, 155–157 general rule of multiplication, 160–161 special rule of addition, 153–155 Probability theory, 145 Processes; see Quality control Producer Price Index (PPI), 574, 589, 594 Producer’s risk, 743 Proportions confidence intervals for, 313–316 control limits, 737 definition, 314 hypothesis tests for one-sample, 356–358 two-sample, 378–381 Lin01803_ndx_831-850.qxd 11/10/10 5:11 PM Page 841 841 Index pooled, 379 population, 314, 318–319 sample, 314 Pseudo-random numbers, 266 Purchasing power of dollar, 594–595 P-values, 345–346, 354–355, 473 Q Qualitative variables; see also Nominal level data definition, in multiple regression, 537–539 Quality control acceptance sampling, 742–745 attribute sampling, 744 Baldrige National Quality Award, 723–724 causes of variation, 724–725 control charts; see Control charts diagnostic charts, 725–728 fishbone diagrams, 727–728 history, 721–722 Pareto charts, 725–727 six sigma, 724 statistical (SQC), 721, 722–723 statistical process control, 721 Quantitative variables continuous, definition, discrete, Quartiles, 111–112, 116 R RAND Corporation, 266 Random numbers finding, 266 in lotteries, 656 pseudo-, 266 tables, 268, 771 Random samples; see Sampling Random variables continuous, 190 definition, 189 discrete, 190 Random variation, 419 Range, 75–76 Range charts, 733–734 Ranked-data analysis Kruskal-Wallis test, 698–702 rank-order correlation, 704–707 sign test; see Sign tests Spearman’s coefficient of rank correlation, 704–706 Wilcoxon rank-sum test, 695–697 Wilcoxon signed-rank test, 690–693 Rank-order correlation, 704–707 Ratio level data, 12–13, 61 Ratio-to-moving-average method, 622–626 Raw data, 30 Real estate data set, 754–756 Real income, 593 Regression analysis, 462, 476; see also Linear regression; Multiple regression Regression coefficients, 513–514, 525–530 Regression equation, 476, 478 Regression line, 479–480 Relative class frequencies, 24–25 Relative frequencies, 149–150 Relative frequency distributions, 34–35 Residual plots, 532–533 Residuals calculating, 480–481 correlated, 631–635 variation in, 533–534 Ritz-Carlton Hotel Corporation, 723 Rockwell International, 462 Roosevelt, Franklin D., 270, 372 Royal Viking, 222 Rules of probability; see Probability rules S Sample mean, 60 sampling distribution of, 275–277 central limit theorem, 279–280, 284 standard deviation, 285 use of, 286–288 z values, 287 Sample proportion, 314 standard error of, 737 Sample standard deviation, 83–84 Sample statistics, 60, 274 Sample variance, 83 Lin01803_ndx_831-850.qxd 842 11/10/10 5:11 PM Page 842 Index Samples definition, dependent, 392–397, 690 independent; see Independent samples paired, 392–395 relationship to population, sizes, 316–317 use of, 7–8 Sampling acceptance, 742–745 attribute, 744 cluster, 271 reasons for, 7–8, 266–267 with replacement, 204 without replacement, 204 simple random, 267–268 stratified random, 270–271 systematic random, 270 Sampling distribution of sample mean, 275–277 central limit theorem, 279–280, 284 standard deviation, 285 use of, 286–288 Sampling error, 274–275 Scatter diagrams, 124–125, 463, 532 School district bus data set, 759–760 Seasonal indexes, 621–626 Seasonal variation, 607–608, 621 Seasonally adjusted data, 627–630 Secular trends, 605–606 Serial correlation; see Autocorrelation Shewhart, Walter A., 721 Sign tests, 681–685 hypothesis tests for median, 688–689 using normal approximation to binomial, 686–687 Significance, statistical, 346 Significance level, 337 Simple aggregate index, 580–581 Simple average of price indexes, 579–580 Simple indexes, 577 Simple random samples, 267–268 Six sigma, 724 Skewed distributions, 70–71, 119–120 Skewness coefficient of, 120–122 Pearson’s coefficient of, 120 software coefficient of, 120–121 Slope, of regression line, 478, 483–485 Smith Barney, 111–112, 113–114 Smucker’s, 60 Software, statistical, 14–16; see also Excel; MegaStat; Minitab Software coefficient of skewness, 120–121 Southwest Airlines, 740 SPC; see Statistical process control Spearman, Charles, 704 Spearman’s coefficient of rank correlation, 704–706 Special rule of addition, 153–155 Special rule of multiplication, 159–160 Spread; see Dispersion Spurious correlations, 469 SQC; see Statistical quality control SSB; see Sum of squares due to blocks SSE; see Sum of squares error SSI; see Sum of squares interaction SST; see Sum of squares treatment Standard & Poor’s 500 Index, 479–480, 574, 590, 617 Standard deviation Chebyshev’s theorem, 85–86 definition, 80 of discrete probability distribution, 191–193 Empirical Rule, 86–87, 231–232 of grouped data, 88, 89–90 of normal distribution, 227–228 population, 82, 300–303, 306–308 sample, 83–84 software example, 84 of uniform distribution, 224 use of, 85 Standard error finite-population correction factor, 320–321 of mean, 285, 730 of sample proportion, 737 Standard error of estimate definition, 486 formula, 487, 490 multiple, 520–521 relationship to coefficients of correlation and determination, 488–490 Standard normal distribution, 229–231 applications of, 231, 233–236 Lin01803_ndx_831-850.qxd 11/10/10 5:11 PM Page 843 Index computing probabilities, 230 probabilities table, 230, 764 Standard normal values, 229–230 Standardizing, 120–121 Starbucks, 77–78 State Farm Insurance, Statistic definition, 60 test, 338 Statistical inference; see Inferential statistics Statistical process control (SPC), 721 Statistical quality control (SQC), 721, 722–723 Statistical significance, 346 Statistics computer applications, 14–16 definition, 4, descriptive, history, 10, 307 inferential, 6–7, 145 misleading, 14 reasons for studying, 2–4 Stem-and-leaf displays, 105–108 Stems, 105 Stepwise regression, 530, 542–544 Stock indexes; see Dow Jones Industrial Average; NASDAQ; Standard & Poor’s 500 Index Strata, 270–271 Stratified random samples, 270–271 Student’s t distribution, 307, 527, 765–766 Subjective probability, 150–151 Sum of squared residuals, 480–481 Sum of squares due to blocks (SSB), 432 Sum of squares error (SSE), 421, 489 with interaction, 437, 438 two-way, 432–433 Sum of squares interaction (SSI), 438 Sum of squares total (SS total), 421 Sum of squares treatment (SST), 421, 423 Sutter Home Winery, 267 Symmetric distributions, 69–70, 86, 119; see also Normal probability distributions Systematic random samples, 270 843 T t distribution characteristics, 307 confidence interval for population mean, 307–308 development of, 307 Student’s, 307, 527, 765–766 use of, 308–309 t tests for coefficient of correlation, 472–475 paired, 293 Taster’s Choice, 681–682 Test statistic, 338 Time series cyclical variations, 606–607 definition, 605 deseasonalized data, 627–630 Durbin-Watson statistic, 631–635 irregular variations, 608 least squares method, 616–617 linear trend equation, 615–616 moving-average method, 608–611 nonlinear trends, 618–620 seasonal indexes, 621–626 seasonal variation, 607–608, 621 secular trends, 605–606 weighted moving average, 611–614 Tippett, L., 266 Total variation, 418 in Y, 488–489 Transformations, 495–497 Treatment means, 423, 426–428 Treatment variation, 418–419 Treatments, 417 Tree diagrams, 164–165 Tukey, John W., 105 Two-factor experiments, 433 Two-sample hypothesis tests dependent samples, 392–395 independent samples, 372–376 dependent samples vs., 395–397 standard deviations equal, 383–386 standard deviations known, 383–390 standard deviations unequal, 388–390 paired t test, 293 for proportion, 378–381 Two-tailed tests of significance, 341–344 Lin01803_ndx_831-850.qxd 844 11/10/10 5:11 PM Page 844 Index Two-way analysis of variance, 430–433 with interaction, 435–440 Tyco, 14 Type I error, 337 Type II error, 337–338, 359–362 U UCL; see Upper control limit Unexplained variation, 489 Ungrouped data, 30 Uniform probability distributions, 223–226 United States Postal Service, 74 Univariate data, 124 University of Michigan, 683 University of Michigan Institute for Social Research, 515 University of Wisconsin-Stout, 723 Unweighted indexes, 579–581 Upper control limit (UCL), 730, 731 USA Today, 3, 10 V Value indexes, 585–586 Variable control charts, 729–733 Variables blocking, 431–432 dependent, 464 dummy, 537–539 independent, 464 multicollinearity, 534–536 qualitative, 537–539 selecting, 525–530 measurement levels, 9–13 qualitative, 8, 537–539 quantitative, random, 189–190 relationship between two, 124–127 types, 8–9 Variance; see also Analysis of variance (ANOVA) of binomial probability distribution, 197–198 definition, 79–80 of discrete probability distribution, 191 of distribution of differences, 373–374 Kruskal-Wallis test, 698–702 of Poisson distribution, 208 pooled, 383 population, 80–81 sample, 83 Variance inflation factor (VIF), 535–536 Variation; see also Dispersion assignable, 725 causes, 724–725 chance, 725 explained, 488–489 irregular, 608 random, 419 seasonal; see Seasonal variation total, 418, 488–489 treatment, 418–419 unexplained, 489 Venn, J., 154 Venn diagrams, 154 Veterans Affairs Cooperative Studies Program, 724 VIF; see Variance inflation factor Volvo, 22 W Wallis, W A., 698 Walmart, Weighted indexes Fisher’s ideal index, 584 Laspeyres price index, 581–582, 583 Paasche’s price index, 582–583 Weighted mean, 63 Weighted moving average, 611–614 Wells, H G., Wendy’s, 63 Wilcoxon, Frank, 690 Wilcoxon rank-sum test, 695–697 Wilcoxon signed-rank test, 690–693 critical values, 692–693, 772 Williams, Ted, 88 World War II, 208, 339, 721 X Xerox, 723 Y Yates, F., 266 Y-intercept, 478 Z z distribution as test statistic, 338 use of, 308–309 z values (scores), 229, 230, 287 Zogby International, 266 Lin01803_ndx_831-850.qxd 11/10/10 5:11 PM Page 845 Lin01803_ndx_831-850.qxd 11/10/10 5:11 PM Page 846 Lin01803_ndx_831-850.qxd 11/10/10 5:11 PM Page 847 Lin01803_ndx_831-850.qxd 11/10/10 5:11 PM Page 848 Lin01803_ndx_831-850.qxd 11/10/10 5:11 PM Page 849 Lin01803_ndx_831-850.qxd 11/10/10 5:11 PM Page 850 Lin01803_keyform.qxd 10/28/10 KEY FORMULAS 1:36 PM Page Lind, Marchal, and Wathen • CHAPTER Statistical Techniques in Business and Economics, 15th edition CHAPTER CHAPTER 10 sk ϭ ͚X ϭ N [3–1] n X Ϫ X b3 c a d (n Ϫ 1)( n Ϫ 2) a s (b Ϫ a)2 12 _ [3–2] P( A or B) ϭ P( A) ϩ P(B) [5–2] P( A) ϭ Ϫ P(~A) [5–3] • Complement rule • Weighted mean w X ϩ w2X2 ϩ и и и ϩ wn Xn Xw ϭ 1 w1 ϩ w2 ϩ и и и ϩ wn _ [3–3] P( A or B) ϭ P( A) ϩ P(B) Ϫ P( A and B) n GM ϭ (X1)(X2)(X3) # # # (Xn) [3–4] P(x) ϭ [5–4] • Special rule of multiplication P( A and B) ϭ P( A)P(B) • Geometric mean rate of increase [5–5] Value at end of period GM ϭ n Ϫ 1.0 B Value at start of period [3–5] P( A and B) ϭ P( A)P(B͉ A) • Range Range ϭ Largest value Ϫ Smallest value • Mean deviation P( A1) P(BΗ A1) P( A1)P(BΗ A1) ϩ P( A2)P(BΗ A2) ͚(X Ϫ )2 N [5–7] n Pr ϭ ϭ ͱ n! (n Ϫ r)! [3–9] ͚(X Ϫ X )2 nϪ1 [3–10] sϭB ϭ n! r!(n Ϫ r)! ϭ ͚[xP(x)] 2 ϭ ͚[(x Ϫ )2P(x)] g (X Ϫ X )2 nϪ1 [3–11] Xϭ 2 ϭ n(1 Ϫ ) [3–13] • Location of a percentile Lp ϭ (n ϩ 1) P 100 XϮz 1n s _ XϮt [6–3] P(x) ϭ 3( X Ϫ Median) s (n1 Ϫ 1) s21 ϩ (n2 Ϫ 1) s 22 n1 ϩ n2 Ϫ _ tϭ [9–1] xeϪ x! X n [9–3] ͱ [9–4] [6–7] z b E ϭ n [6–8] _ X1 Ϫ X 1 s2p ϩ n1 n2 [11–6] X1 Ϫ X s21 s2 ϩ A n1 n2 [11–7] [(s21/n1) ϩ (s 22 /n2 )]2 (s21/n1)2 (s 22 /n 2)2 ϩ n1 Ϫ n2 Ϫ [11–8] • Paired t test • Sample size for estimating mean nϭ a [11–5] • Degrees of freedom for unequal variance test df ϭ p(1 Ϫ p) n [11–3] • Two-sample tests of means, unknown and unequal s • Confidence interval for proportion pϮz ͱ tϭ _ tϭ [9–5] z n ϭ (1 Ϫ ) a b E d sd ր͙n [11–9] CHAPTER 12 • Sample size for a proportion • Test for comparing two variances • Mean of a Poisson distribution [4–2] ͱ • Two-sample test of means, unknown but equal [9–2] ͙n pϭ [6–6] [11–4] p1 Ϫ p2 pc(1 Ϫ pc) p c(1 Ϫ p c ) ϩ n1 n2 [6–4] [6–5] X1 ϩ X2 n1 ϩ n2 • Pooled variance • Sample proportion • Poisson probability distribution • Pearson’s coefficient of skewness sk ϭ (SCx)(NϪSCnϪx) NCn [4–1] [8–2] • Confidence interval for , with known [6–2] • Hypergeometric probability distribution P(x) ϭ CHAPTER zϭ s2p ϭ • Sample standard deviation, grouped data g f(M Ϫ X )2 sϭB nϪ1 ͙n [8–1] CHAPTER • Variance of a binomial distribution [11–2] • Pooled proportion • Confidence interval for , unknown ϭ n [3–12] XϪ / 1n • Mean of a binomial distribution g fM n [7–7] • z-value, and known zϭ [6–1] [11–1] • Two-sample test of proportions Ϫ ϭ X [5–10] 21 22 ϩ n1 n2 X1 Ϫ X2 21 2 ϩ A n1 n2 pc ϭ [5–9] • Binomial probability distribution P(x) ϭ nCx x(1 Ϫ )n Ϫ x • Sample mean, grouped data zϭ [7–6] • Finding a probability using the exponential distribution • Variance of a probability distribution • Sample standard deviation 2x 1Ϫx2 ϭ [7–5] • Standard error of mean • Mean of a probability distribution _ XϪ • Two-sample test of means, known CHAPTER • Sample variance s2 ϭ • Variance of the distribution of difference in means P( x) ϭ leϪlx • Number of combinations nCr [10–4] /͙n CHAPTER 11 CHAPTER [3–8] [10–3] Xc Ϫ 1 [7–4] [5–8] • Number of permutations • Population standard deviation ͚(X Ϫ )2 N (XϪ) R 22 pϪ (1 Ϫ ) n _ zϭ • Exponential distribution • Population variance 2 ϭ ͙2 eϪ B P ( Arrival time x ) ϭ Ϫ eϪl x Total arrangements ϭ ( m)(n) [3–7] • Type II error [5–6] • Multiplication formula _ ͚Η X Ϫ X Η MD ϭ n P( A1ΗB) ϭ [3–6] ͱ and elsewhere zϭ • Bayes’ Theorem zϭ [7–3] • Standard normal value • General rule of multiplication [10–2] • Test of hypothesis, one proportion • Normal probability distribution • General rule of addition • Geometric mean if a Յ x Յ b [10–1] /͙n XϪ s/ 1n tϭ [7–2] bϪa P(x) ϭ XϪ • Testing a mean, unknown • Uniform probability distribution • Special rule of addition ͚X Xϭ n ͱ ϭ zϭ [7–1] • Standard deviation of a uniform distribution [4–3] CHAPTER • Sample mean, raw data _ aϩb ϭ • Software coefficient of skewness • Population mean • Testing a mean, known • Mean of a uniform distribution [9–6] Fϭ s21 s22 [12–1] Lin01803_keyform.qxd 10/28/10 1:36 PM Page • Sum of squares, total • Real income • Prediction interval SS total ϭ g (X Ϫ XG) [12–2] Yˆ Ϯ t(sy · x) • Sum of squares, error SSE ϭ g (X Ϫ Xc)2 [12–3] ͱ 1ϩ (X Ϫ X )2 _ ϩ n ͚(X Ϫ X )2 • Multiple regression equation Deflated sales ϭ Yˆ ϭ a ϩ b1X1 ϩ b2X2 ϩ · · · ϩ bk X k ͱ _ (X1 Ϫ X2) Ϯ t MSE n1 ϩ n1 [14–1] sY · 123 · · · k ϭ [12–5] g(Y Ϫ Yˆ )2 B n Ϫ (k ϩ 1) SSB ϭ k g(Xb Ϫ XG) R2 ϭ [12–6] SSR SS total [12–7] SSE n Ϫ (k ϩ 1) Radj ϭ Ϫ SS total nϪ1 • Sum of squares, interaction SSI ϭ n͞bk ©© (Xij Ϫ Xi Ϫ X.j ϩ XG)2 [12–8] • Sum of squares error, with interaction [12–9] rϭ b Ϫ0 tϭ i sbi g (X Ϫ X )(Y Ϫ Y ) (n Ϫ 1) sx sy [13–1] VIF ϭ Ϫ R 2j r nϪ2 tϭ ͙ ͙1 Ϫ r [13–2] [14–4] log Yˆ ϭ log a ϩ log b(t ) [16–2] • Correction factor for adjusting quarterly means 4.00 Correction factor ϭ Total of four means • Slope of the regression line dϭ [13–4] Pϭ x • Intercept of the regression line tϭ2 [13–5] [14–6] bϪ0 tϭ sb [13–6] B ͚(Y Ϫ Yˆ )2 nϪ2 [13–7] r2 ϭ SSR SSE ϭ1Ϫ SS Total SS Total [13–8] 2 ϭ a c [15–2] Pϭ ͚ptq0 (100) ͚p0q0 [15–4] Pϭ ͚ptqt (100) ͚p0qt [15–5] • Fisher’s ideal index [15–6] ͱ (X Ϫ X ) _ ϩ n ͚(X Ϫ X )2 [13–9] Vϭ ͚ptqt (100) ͚p0q0 [15–7] ϭ Ϫ LCL ϭ X Ϫ A2 R [19–4] Ϫ LCL ϭ D3 R [19–5] • Mean proportion defective Sum of the number defective Total number of items sampled [19–6] [17–1] UCL and LCL ϭ p Ϯ ͱ p(1 Ϫ p) n [19–8] • Control limits, c-bar chart UCL and LCL ϭ Ϫ c Ϯ 3͙ Ϫ c [19–9] [17–2] CHAPTER 20 (ON THE WEBSITE: www.mhhe.com/lind15e) • Expected monetary value CHAPTER 18 • Sign test, n Ͼ 10 EMV(Ai ) ϭ ͚[P(Sj ) · V(Ai , Sj )] [18–1] zϭ ͱ n1(n1 ϩ n2 ϩ 1) n1n2(n1 ϩ n2 ϩ 1) 12 [20–1] • Expected opportunity loss EOL(Ai ) ϭ ͚[P(S j) · R(Ai, Sj )] • Wilcoxon rank-sum test WϪ • Value index _ (fo Ϫ fe)2 d fe (X Ϯ 50) Ϫ zϭ [15–3] ͙(Laspeyres’ price index)(Paasche’s price index) • Confidence interval Yˆ Ϯ t(sy · x) [15–1] [19–1] • Control limits, proportion • Expected frequency • Paasche’s price index • Coefficient of determination • Control limits, mean ϭ Ϫ UCL ϭ X ϩ A2R pϭ CHAPTER 17 [14–7] • Laspeyres’ price index • Standard error of estimate et2 • Chi-square test statistic ͚pt (100) ͚p0 Pϭ • Test for a zero slope [18–7] ϭ ͚X X ϭ k Ϫ UCL ϭ D4R [16–4] n a • Simple aggregate index a ϭ Y Ϫ bX sy · x ϭ ͚Pi n nϪ2 Ϫ rs2 • Control limits, range tϭ • Simple average of price relatives sy bϭrs [16–3] a (et Ϫ etϪ1) [14–5] • Simple index pt (100) p0 ͱ • Grand mean (Row total)(Column total) fe ϭ Grand total Pϭ [18–6] CHAPTER 19 n CHAPTER 15 [13–3] 6͚d n(n2 Ϫ 1) • Hypothesis test, rank correlation • Log trend equation • Linear regression equation Yˆ ϭ a ϩ bX [15–10] [16–1] • Variance inflation factor • Test for significant correlation $1 (100) CPI • Durbin-Watson statistic SSR /k Fϭ SSE /[n Ϫ (k ϩ 1)] • Correlation coefficient rs ϭ Ϫ Yˆ ϭ a ϩ bt • Testing for a particular regression coefficient CHAPTER 13 • Spearman coefficient of rank correlation [15–9] • Linear trend • Global test of hypothesis SSE ϭ SS total Ϫ SS factor A Ϫ SS factor B Ϫ SSI ΅ [18–5] t ϭ rs [14–3] • Adjusted coefficient of determination SSE ϭ SS total Ϫ SST Ϫ SSB Actual sales (100) Index CHAPTER 16 • Coefficient of multiple determination • Sum of squares, two-way ANOVA ΄ 12 (͚R1)2 (͚R2 )2 (͚Rk)2 ϩ ϩ · · ·ϩ n(n ϩ 1) n1 n2 nk Ϫ 3(n ϩ 1) Purchasing power ϭ [14–2] • Sum of squares, blocks Hϭ • Purchasing power • Multiple standard error of estimate • Confidence interval for differences in treatment means _ [15–8] • Using an index as a deflator CHAPTER 14 [12–4] Money income (100) CPI Real income ϭ [13–10] • Sum of squares, treatments SST ϭ SS total Ϫ SSE • Kruskal-Wallis test _ [20–2] • Expected value of perfect information [18–4] EVPI ϭ Expected value under conditions of certainty Ϫ Expected value of optimal decision under conditions of uncertainty [20–3] Lin01803_endsheet.indd Page 11/10/10 6:10 PM F-497 208/MHBR192/ Lin 01803_ disk1of1/ 007340 1803/L in0 1803_p agefile s 208/MHBR192/Lin01803_disk1of1/0073401803/Lin01803_pagefiles Student’s t Distribution ␣ –t t Confidence interval ␣ –t Left-tailed test t ␣ t Right-tailed test ␣ –t t Two-tailed test (continued ) 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% 80% 99.9% Back endsheets Color: Pages: (degrees of freedom) 0.10 Level of Significance for One-Tailed Test, ␣ 0.05 0.025 0.01 0.005 99% 99.9% 0.0005 0.001 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 ) ISBN: 0073401803 Author: Lind, Marchal, Wathen Title: Statistical Techniques in Business & Economics Fifteenth edition 90% df 0.0005 Confidence Intervals, c 95% 98% 80% (continued ) Lin01803_endsheet.indd Page 11/10/10 6:10 PM F-497 208/MHBR192/ Lin 01803_ disk1of1/ 007340 1803/L in0 1803_p agefile s 208/MHBR192/Lin01803_disk1of1/0073401803/Lin01803_pagefiles Student’s t Distribution (concluded ) Areas under the Normal Curve (continued ) 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% 80% 99% Example: If z = 1.96, then P(0 to z) = 0.4750 99.9% z Level of Significance for Two-Tailed Test, ␣ 0.20 0.10 0.05 0.02 0.01 0.001 71 72 73 74 75 1.294 1.293 1.293 1.293 1.293 1.667 1.666 1.666 1.666 1.665 1.994 1.993 1.993 1.993 1.992 2.380 2.379 2.379 2.378 2.377 2.647 2.646 2.645 2.644 2.643 3.433 3.431 3.429 3.427 3.425 76 77 78 79 80 1.293 1.293 1.292 1.292 1.292 1.665 1.665 1.665 1.664 1.664 1.992 1.991 1.991 1.990 1.990 2.376 2.376 2.375 2.374 2.374 2.642 2.641 2.640 2.640 2.639 3.423 3.421 3.420 3.418 3.416 81 82 83 84 85 1.292 1.292 1.292 1.292 1.292 1.664 1.664 1.663 1.663 1.663 1.990 1.989 1.989 1.989 1.988 2.373 2.373 2.372 2.372 2.371 2.638 2.637 2.636 2.636 2.635 3.415 3.413 3.412 3.410 3.409 86 87 88 89 90 1.291 1.291 1.291 1.291 1.291 1.663 1.663 1.662 1.662 1.662 1.988 1.988 1.987 1.987 1.987 2.370 2.370 2.369 2.369 2.368 2.634 2.634 2.633 2.632 2.632 3.407 3.406 3.405 3.403 3.402 91 92 93 94 95 1.291 1.291 1.291 1.291 1.291 1.662 1.662 1.661 1.661 1.661 1.986 1.986 1.986 1.986 1.985 2.368 2.368 2.367 2.367 2.366 2.631 2.630 2.630 2.629 2.629 3.401 3.399 3.398 3.397 3.396 96 97 98 99 100 1.290 1.290 1.290 1.290 1.290 1.661 1.661 1.661 1.660 1.660 1.985 1.985 1.984 1.984 1.984 2.366 2.365 2.365 2.365 2.364 2.628 2.627 2.627 2.626 2.626 3.395 3.394 3.393 3.392 3.390 120 140 160 180 200 ϱ 1.289 1.288 1.287 1.286 1.286 1.282 1.658 1.656 1.654 1.653 1.653 1.645 1.980 1.977 1.975 1.973 1.972 1.960 2.358 2.353 2.350 2.347 2.345 2.326 2.617 2.611 2.607 2.603 2.601 2.576 3.373 3.361 3.352 3.345 3.340 3.291 ISBN: 0073401803 Author: Lind, Marchal, Wathen Title: Statistical Techniques in Business & Economics Fifteenth edition Back endsheets Color: Pages: 6, 0.4750 0.0005 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 0.4898 0.4922 0.4788 0.4834 0.4871 0.4901 0.4925 0.4793 0.4838 0.4875 0.4904 0.4927 0.4798 0.4842 0.4878 0.4906 0.4929 0.4803 0.4846 0.4881 0.4909 0.4931 0.4808 0.4850 0.4884 0.4911 0.4932 0.4812 0.4854 0.4887 0.4913 0.4934 0.4817 0.4857 0.4890 0.4916 0.4936 2.5 2.6 2.7 2.8 2.9 0.4938 0.4953 0.4965 0.4974 0.4981 0.4940 0.4955 0.4966 0.4975 0.4982 0.4941 0.4956 0.4967 0.4976 0.4982 0.4943 0.4957 0.4968 0.4977 0.4983 0.4945 0.4959 0.4969 0.4977 0.4984 0.4946 0.4960 0.4970 0.4978 0.4984 0.4948 0.4961 0.4971 0.4979 0.4985 0.4949 0.4962 0.4972 0.4979 0.4985 0.4951 0.4963 0.4973 0.4980 0.4986 0.4952 0.4964 0.4974 0.4981 0.4986 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990 ... 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. .. assessment and learning program that provides individualized instruction in Business Statistics, Business Math, and Accounting Available online in partnership with McGrawHill/lrwin, ALEKS interacts... Understanding the importance and value of AACSB accreditation, Statistical Techniques in Business & Economics recognizes the curricula guidelines detailed in the AACSB standards for business accreditation