Kroger weekly ad laporte indiana

Data Analysis & Business Intelligence

Question:

Describe the concepts of prior probability, conditional probability, joint probability, and posterior probability.
Explain Bayes’ Theorem and provide a numerical example related to a real-life situation.
Note:

1. Need to write at least 2 paragraphs

2. Need to include the information from the textbook as the reference.

3. Need to include at least 1 peer reviewed article as the reference.

4. Please find the textbook and related power point in the attachment

Statistical Techniques in Business & Economics

LIND

MARCHAL

WATHEN

Seventeenth Edition

Statistical Techniques in

BUSINESS & ECONOMICS

The McGraw-Hill/Irwin Series in Operations and Decision Sciences

SUPPLY CHAIN MANAGEMENT

Benton Purchasing and Supply Chain Management Third 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 Fourteenth 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 Fifth Edition

SERVICE OPERATIONS MANAGEMENT

Fitzsimmons and Fitzsimmons Service Management: Operations, Strategy, Information Technology Eighth Edition

MANAGEMENT SCIENCE

Hillier and Hillier Introduction to Management Science: A Modeling and Case Studies Approach with Spreadsheets Fifth 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

BUSINESS RESEARCH METHODS

Cooper and Schindler Business Research Methods Twelfth Edition

BUSINESS FORECASTING

Wilson, Keating, and John Galt Solutions, Inc. Business Forecasting Sixth Edition

LINEAR STATISTICS AND REGRESSION

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 Third Edition

Finch Interactive Models for Operations and Supply Chain Management First Edition

Jacobs and Chase Operations and Supply Chain Management Fourteenth Edition

Jacobs and Chase Operations and Supply Chain Management: The Core Third 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 Sixth Edition

Stevenson Operations Management Eleventh Edition

Swink, Melnyk, Cooper, and Hartley Managing Operations across the Supply Chain Second Edition

PRODUCT DESIGN

Ulrich and Eppinger Product Design and Development Fifth Edition

BUSINESS MATH

Slater and Wittry Math for Business and Finance: An Algebraic Approach First Edition

Slater and Wittry Practical Business Math Procedures Eleventh Edition

Slater and Wittry Practical Business Math Procedures, Brief Edition Eleventh Edition

BUSINESS STATISTICS

Bowerman, O’Connell, and Murphree Business Statistics in Practice Seventh Edition

Bowerman, O’Connell, Murphree, and Orris Essentials of Business Statistics Fourth Edition

Doane and Seward Applied Statistics in Business and Economics Fourth Edition

Lind, Marchal, and Wathen Basic Statistics for Business and Economics Eighth Edition

Lind, Marchal, and Wathen Statistical Techniques in Business and Economics Seventeenth Edition

Jaggia and Kelly Business Statistics: Communicating with Numbers First Edition

Jaggia and Kelly Essentials of Business Statistics: Communicating with Numbers First Edition

Statistical Techniques in

BUSINESS & ECONOMICS

S E V E N T E E N T H E D I T I O N

DOUGLAS A. LIND Coastal Carolina University and The University of Toledo

WILLIAM G. MARCHAL The University of Toledo

SAMUEL A. WATHEN Coastal Carolina University

STATISTICAL TECHNIQUES IN BUSINESS & ECONOMICS, SEVENTEENTH EDITION Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2018 by McGraw-Hill Education. All rights reserved. Printed in the United States of America. Previous editions © 2015, 2012, and 2010. 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 McGraw- Hill 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.

1 2 3 4 5 6 7 8 9 LWI 21 20 19 18 17 16

ISBN 978-1-259-66636-0 MHID 1-259-66636-0

Chief Product Officer, SVP Products & Markets: G. Scott Virkler Vice President, General Manager, Products & Markets: Marty Lange Vice President, Content Design & Delivery: Betsy Whalen Managing Director: Tim Vertovec Senior Brand Manager: Charles Synovec Director, Product Development: Rose Koos Product Developers: Michele Janicek / Ryan McAndrews Senior Director, Digital Content Development: Douglas Ruby Marketing Manager: Trina Maurer Director, Content Design & Delivery: Linda Avenarius Program Manager: Mark Christianson Content Project Managers: Harvey Yep (Core) / Bruce Gin (Assessment) Buyer: Susan K. Culbertson Design: Matt Backhaus Cover Image: © Corbis / Glow Images Content Licensing Specialists: Melissa Homer (Image) / Beth Thole (Text) Typeface: 9.5/11 Proxima Nova Compositor: Aptara®, Inc. Printer: LSC Communications

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: Statistical techniques in business & economics/Douglas A. Lind, Coastal Carolina University and The University of Toledo, William G. Marchal, The University of Toledo, Samuel A. Wathen, Coastal Carolina University. Other titles: Statistical techniques in business and economics Description: Seventeenth Edition. | Dubuque, IA : McGraw-Hill Education, [2017] | Revised edition of the authors’ Statistical techniques in business & economics, [2015] Identifiers: LCCN 2016054310| ISBN 9781259666360 (alk. paper) | ISBN 1259666360 (alk. paper) Subjects: LCSH: Social sciences—Statistical methods. | Economics—Statistical methods. | Commercial statistics. Classification: LCC HA29 .M268 2017 | DDC 519.5—dc23 LC record available at https://lccn.loc.gov/2016054310

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

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, 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

vi

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 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 descriptive and infer- ential statistics. To illustrate the application of statistics, we use many examples and exercises 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, accel- erates 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 automati- cally 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 opportu- nities to apply statistical knowledge and statistical software to explore several busi- ness 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 down- load 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 pre- sented, 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 interpre- tative 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 con- cepts, along with supporting interesting and relevant examples.

A N O T E F R O M T H E A U T H O R S

vii

WHAT’S NEW IN THE SEVENTEENTH EDITION? We have made many changes to examples and exercises throughout the text. The sec- tion on “Enhancements” to our text details them. The major change to the text is in response to user interest in the area of data analytics. Our approach is to provide in- structors 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 chapters 1 through 18 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 lists information on 80 buses in the school district’s bus fleet. The authors de- signed 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 exer- cises 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, instruc- tors will be faced with choosing statistical software and supporting students in develop- ing or enhancing their computer skills. Finally, instructors will need to assess student performance based on assignments that include both statistical and written compo- nents. Using a mentoring approach may be helpful.

We hope that you and your students find this new feature interesting and engaging.

HOW ARE CHAPTERS ORGANIZED TO ENGAGE STUDENTS AND PROMOTE LEARNING?

Chapter Learning Objectives Each chapter begins with a set of learning objectives designed to pro- vide focus for the chapter and motivate student learning. These objectives, lo- cated in the margins next to the topic, indicate what the student should be able to do after completing each sec- tion in the chapter.

Chapter Opening Exercise A representative exercise opens the chapter and shows how the chapter content can be applied to a real-world situation.

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.

MERRILL LYNCH recently completed a study of online investment portfolios for a sample of clients. For the 70 participants in the study, organize these data into a frequency distribution. (See Exercise 43 and LO2-3.)

Describing Data: FREQUENCY TABLES, FREQUENCY DISTRIBUTIONS,

AND GRAPHIC PRESENTATION2

Source: © rido/123RF

Lin66360_ch02_018-050.indd 18 1/6/17 4:52 AM

Introduction to the Topic Each chapter starts with a review of the important concepts of the previ- ous chapter and provides a link to the material in the current chapter. This step-by-step approach increases com- prehension by providing continuity across the concepts.

DESCRIBING DATA: FREQUENCY TABLES, FREQUENCY DISTRIBUTIONS, AND GRAPHIC PRESENTATION 19

INTRODUCTION The United States automobile retailing industry is highly competitive. It is dominated by megadealerships that own and operate 50 or more franchises, employ over 10,000 people, and generate several billion dollars in annual sales. Many of the top dealerships

are publicly owned with shares traded on the New York Stock Exchange or NASDAQ. In 2014, the largest megadealership was AutoNation (ticker symbol AN), followed by Penske Auto Group (PAG), Group 1 Automotive, Inc. (ticker symbol GPI), and the privately owned Van Tuyl Group.

These large corporations use statistics and analytics to summarize and analyze data and information to support their decisions. As an ex- ample, we will look at the Applewood Auto group. It owns four dealer- ships and sells a wide range of vehicles. These include the popular Korean brands Kia and Hyundai, BMW and Volvo sedans and luxury SUVs, and a full line of Ford and Chevrolet cars and trucks.

Ms. Kathryn Ball is a member of the senior management team at Applewood Auto Group, which has its corporate offices adjacent to Kane Motors. She is responsible for tracking and analyzing vehicle sales and

the profitability of those vehicles. Kathryn would like to summarize the profit earned on the vehicles sold with tables, charts, and graphs that she would review 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 buyers. What are their ages? How many vehicles have they previously purchased from one of the Apple- wood dealerships? What type of vehicle did they purchase?

The Applewood Auto Group operates four dealerships:

• Tionesta Ford Lincoln sells Ford and Lincoln cars and trucks. • Olean Automotive Inc. has the Nissan franchise as well as the General Motors

brands of Chevrolet, Cadillac, and GMC Trucks. • Sheffield Motors Inc. sells Buick, GMC trucks, Hyundai, and Kia. • Kane Motors offers the Chrysler, Dodge, and Jeep line as well as BMW and Volvo.

Every month, Ms. Ball collects data from each of the four dealerships and enters them into an Excel spreadsheet. Last month the Applewood Auto Group sold 180 vehicles at the four dealerships. A copy of the first few observations appears to the left. The variables collected include:

• Age—the age of the buyer at the time of the purchase. • Profit—the amount earned by the dealership on the sale of each

vehicle. • Location—the dealership where the vehicle was purchased. • Vehicle type—SUV, sedan, compact, hybrid, or truck. • Previous—the number of vehicles previously purchased at any of the

four Applewood dealerships by the consumer.

The entire data set is available at the McGraw-Hill website (www.mhhe .com/lind17e) and in Appendix A.4 at the end of the text.

Source: © Justin Sullivan/Getty Images

CONSTRUCTING FREQUENCY TABLES Recall from Chapter 1 that techniques used to describe a set of data are called descrip- tive statistics. Descriptive statistics organize data to show the general pattern of the data, to identify where values tend to concentrate, and to expose extreme or unusual data values. The first technique we discuss is a frequency table.

LO2-1 Summarize qualitative variables with frequency and relative frequency tables.

FREQUENCY TABLE A grouping of qualitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class.

Lin66360_ch02_018-050.indd 19 1/6/17 4:52 AM

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?”

DESCRIBING DATA: DISPLAYING AND EXPLORING DATA 95

INTRODUCTION Chapter 2 began our study of descriptive statistics. In order to transform raw or un- grouped data into a meaningful form, we organize the data into a frequency distribution. We present the frequency distribution in graphic form as a histogram or a frequency polygon. This allows us to visualize where the data tend to cluster, the largest and the smallest values, and the general shape of the data.

In Chapter 3, we first computed several measures of location, such as the mean, median, and mode. These measures of location allow us to report a typical value in the set of observations. We also computed several measures of dispersion, such as the range, variance, and standard deviation. These measures of dispersion allow us to de- scribe the variation or the spread in a set of observations.

We continue our study of descriptive statistics in this chapter. We study (1) dot plots, (2) stem-and-leaf displays, (3) percentiles, and (4) box plots. These charts and statistics give us additional insight into where the values are concentrated as well as the general shape of the data. Then we consider bivariate data. In bivariate data, we observe two variables for each individual or observation. Examples include the number of hours a student studied and the points earned on an examination; if a sampled product meets quality specifications and the shift on which it is manufactured; or the amount of electric- ity used in a month by a homeowner and the mean daily high temperature in the region for the month. These charts and graphs provide useful insights as we use business analytics to enhance our understanding of data.

DOT PLOTS Recall for the Applewood Auto Group data, we summarized the profit earned on the 180 vehicles sold with a frequency distribution using eight classes. When we orga- nized the data into the eight classes, we lost the exact value of the observations. A dot plot, on the other hand, groups the data as little as possible, and we do not lose the identity of an individual observation. To develop a dot plot, we display a dot for each observation along a horizontal number line indicating the possible values of the data. If there are identical observations or the observations are too close to be shown individually, the dots are “piled” on top of each other. This allows us to see the shape of the distribution, the value about which the data tend to cluster, and the largest and smallest observations. Dot plots are most useful for smaller data sets, whereas histo- grams tend to be most useful for large data sets. An example will show how to con- struct and interpret dot plots.

LO4-1 Construct and interpret a dot plot.

E X A M P L E

The service departments at Tionesta Ford Lincoln and Sheffield Motors Inc., two of the four Applewood Auto Group dealerships, were both open 24 days last month. Listed below is the number of vehicles serviced last month at the two dealerships. Construct dot plots and report summary statistics to compare the two dealerships.

Tionesta Ford Lincoln

Monday Tuesday Wednesday Thursday Friday Saturday

23 33 27 28 39 26 30 32 28 33 35 32 29 25 36 31 32 27 35 32 35 37 36 30

Lin66360_ch04_094-131.indd 95 1/10/17 7:41 PM

Self-Reviews Self-Reviews are interspersed throughout each chapter and follow Example/Solution sec- tions. They help students mon- itor their progress and provide immediate reinforcement for that particular technique. An- swers are in Appendix E.

106 CHAPTER 4

calculate quartiles. Excel 2013 and Excel 2016 offer both methods. The Excel function, Quartile.exc, will result in the same answer as Equation 4–1. The Excel function, Quar- tile.inc, will result in the Excel Method answers.

The Quality Control department of Plainsville Peanut Company is responsible for checking the weight of the 8-ounce jar of peanut butter. The weights of a sample of nine jars pro- duced last hour are:

7.69 7.72 7.8 7.86 7.90 7.94 7.97 8.06 8.09

(a) What is the median weight? (b) Determine the weights corresponding to the first and third quartiles.

S E L F - R E V I E W 4–2

11. Determine the median and the first and third quartiles in the following data.

46 47 49 49 51 53 54 54 55 55 59

12. Determine the median and the first and third quartiles in the following data.

5.24 6.02 6.67 7.30 7.59 7.99 8.03 8.35 8.81 9.45 9.61 10.37 10.39 11.86 12.22 12.71 13.07 13.59 13.89 15.42

13. The Thomas Supply Company Inc. is a distributor of gas-powered generators. As with any business, the length of time customers take to pay their invoices is im- portant. Listed below, arranged from smallest to largest, is the time, in days, for a sample of The Thomas Supply Company Inc. invoices.

13 13 13 20 26 27 31 34 34 34 35 35 36 37 38 41 41 41 45 47 47 47 50 51 53 54 56 62 67 82

a. Determine the first and third quartiles. b. Determine the second decile and the eighth decile. c. Determine the 67th percentile.

14. Kevin Horn is the national sales manager for National Textbooks Inc. He has a sales staff of 40 who visit college professors all over the United States. Each Saturday morning he requires his sales staff to send him a report. This re- port includes, among other things, the number of professors visited during the previous week. Listed below, ordered from smallest to largest, are the number of visits last week.

38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57 59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79

a. Determine the median number of calls. b. Determine the first and third quartiles. c. Determine the first decile and the ninth decile. d. Determine the 33rd percentile.

E X E R C I S E S

Lin66360_ch04_094-131.indd 106 1/10/17 7:41 PM

viii

ix

Statistics in Action Statistics in Action articles are scattered through- out the text, usually about two per chapter. They provide unique, interesting applications and his- torical insights in the field of statistics.

144 CHAPTER 5

The General Rule of Addition The outcomes of an experiment may not be mutually exclusive. For example, the Florida Tourist Commission selected a sample of 200 tourists who visited the state during the year. The survey revealed that 120 tourists went to Disney World and 100 went to Busch Gardens near Tampa. What is the probability that a person selected visited either Disney World or Busch Gardens? If the special rule of addition is used, the probability of selecting a tourist who went to Disney World is .60, found by 120/200. Similarly, the probability of a tourist going to Busch Gardens is .50. The sum of these probabilities is 1.10. We know, however, that this probability cannot be greater than 1. The explanation is that many tour- ists visited both attractions and are being counted twice! A check of the survey responses revealed that 60 out of 200 sampled did, in fact, visit both attractions.

To answer our question, “What is the probability a selected person visited either Disney World or Busch Gardens?” (1) add the probability that a tourist visited Disney World and the probability he or she visited Busch Gardens, and (2) subtract the proba- bility of visiting both. Thus:

P(Disney or Busch) = P(Disney) + P(Busch) − P(both Disney and Busch) = .60 + .50 − .30 = .80

When two events both occur, the probability is called a joint probability. The prob- ability (.30) that a tourist visits both attractions is an example of a joint probability.

© Rostislav Glinsky/Shutterstock.com

The following Venn diagram shows two events that are not mutually exclusive. The two events overlap to illustrate the joint event that some people have visited both attractions.

A sample of employees of Worldwide Enterprises is to be surveyed about a new health care plan. The employees are classified as follows:

Classification Event Number of Employees

Supervisors A 120 Maintenance B 50 Production C 1,460 Management D 302 Secretarial E 68

(a) What is the probability that the first person selected is: (i) either in maintenance or a secretary? (ii) not in management? (b) Draw a Venn diagram illustrating your answers to part (a). (c) Are the events in part (a)(i) complementary or mutually exclusive or both?

S E L F - R E V I E W 5–3

STATISTICS IN ACTION

If you wish to get some attention at the next gath- ering you attend, announce that you believe that at least two people present were born on the same date—that is, the same day of the year but not necessarily the same year. If there are 30 people in the room, the probability of a duplicate is .706. If there are 60 people in the room, the probability is .994 that at least two people share the same birthday. With as few as 23 people the chances are even, that is .50, that at least two people share the same birthday. Hint: To compute this, find the probability everyone was born on a different day and use the complement rule. Try this in your class.

Lin66360_ch05_132-174.indd 144 1/10/17 7:41 PM

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. They also appear in the Glossary at the end of the book.

A SURVEY OF PROBABILITY CONCEPTS 145

P (Disney) = .60 P (Busch) = .50

P (Disney and Busch) = .30

JOINT PROBABILITY A probability that measures the likelihood two or more events will happen concurrently.

So the general rule of addition, which is used to compute the probability of two events that are not mutually exclusive, is:

GENERAL RULE OF ADDITION P(A or B) = P(A) + P(B) − P(A and B) [5–4]

For the expression P(A or B), the word or suggests that A may occur or B may occur. This also includes the possibility that A and B may occur. This use of or is sometimes called an inclusive. You could also write P(A or B or both) to emphasize that the union of the events includes the intersection of A and B.

If we compare the general and special rules of addition, the important difference is determining if the events are mutually exclusive. If the events are mutually exclusive, then the joint probability P(A and B) is 0 and we could use the special rule of addition. Other- wise, we must account for the joint probability and use the general rule of addition.

E X A M P L E

What is the probability that a card chosen at random from a standard deck of cards will be either a king or a heart?

S O L U T I O N

We may be inclined to add the probability of a king and the probability of a heart. But this creates a problem. If we do that, the king of hearts is counted with the kings and also with the hearts. So, if we simply add the probability of a king (there are 4 in a deck of 52 cards) to the probability of a heart (there are 13 in a deck of 52 cards) and report that 17 out of 52 cards meet the requirement, we have counted the king of hearts twice. We need to subtract 1 card from the 17 so the king of hearts is counted only once. Thus, there are 16 cards that are either hearts or kings. So the probability is 16/52 = .3077.

Card Probability Explanation

King P(A) = 4/52 4 kings in a deck of 52 cards Heart P(B) = 13/52 13 hearts in a deck of 52 cards King of Hearts P(A and B) = 1/52 1 king of hearts in a deck of 52 cards

Lin66360_ch05_132-174.indd 145 1/10/17 7:41 PM

Formulas Formulas that are used for the first time are boxed and numbered for reference. In addi- tion, a formula card is bound into the back of the text that lists all the key formulas.

A SURVEY OF PROBABILITY CONCEPTS 147

16. Two coins are tossed. If A is the event “two heads” and B is the event “two tails,” are A and B mutually exclusive? Are they complements?

17. The probabilities of the events A and B are .20 and .30, respectively. The probability that both A and B occur is .15. What is the probability of either A or B occurring?

18. Let P(X) = .55 and P(Y) = .35. Assume the probability that they both occur is .20. What is the probability of either X or Y occurring?

19. Suppose the two events A and B are mutually exclusive. What is the probability of their joint occurrence?

20. A student is taking two courses, history and math. The probability the student will pass the history course is .60, and the probability of passing the math course is .70. The probability of passing both is .50. What is the probability of passing at least one?

21. The aquarium at Sea Critters Depot contains 140 fish. Eighty of these fish are green swordtails (44 female and 36 male) and 60 are orange swordtails (36 female and 24 males). A fish is randomly captured from the aquarium:

a. What is the probability the selected fish is a green swordtail? b. What is the probability the selected fish is male? c. What is the probability the selected fish is a male green swordtail? d. What is the probability the selected fish is either a male or a green swordtail?

22. A National Park Service survey of visitors to the Rocky Mountain region revealed that 50% visit Yellowstone Park, 40% visit the Tetons, and 35% visit both.

a. What is the probability a vacationer will visit at least one of these attractions? b. What is the probability .35 called? c. Are the events mutually exclusive? Explain.

RULES OF MULTIPLICATION TO CALCULATE PROBABILITY In this section, we discuss the rules for computing the likelihood that two events both happen, or their joint probability. For example, 16% of the 2016 tax returns were pre- pared by H&R Block and 75% of those returns showed a refund. What is the likelihood a person’s tax form was prepared by H&R Block and the person received a refund? Venn diagrams illustrate this as the intersection of two events. To find the likelihood of two events happening, we use the rules of multiplication. There are two rules of multipli- cation: the special rule and the general rule.

Special Rule of Multiplication The special rule of multiplication requires that two events A and B are independent. Two events are independent if the occurrence of one event does not alter the probabil- ity of the occurrence of the other event.

LO5-4 Calculate probabilities using the rules of multiplication.

INDEPENDENCE The occurrence of one event has no effect on the probability of the occurrence of another event.

One way to think about independence is to assume that events A and B occur at differ- ent times. For example, when event B occurs after event A occurs, does A have any effect on the likelihood that event B occurs? If the answer is no, then A and B are independent events. To illustrate independence, suppose two coins are tossed. The outcome of a coin toss (head or tail) is unaffected by the outcome of any other prior coin toss (head or tail).

For two independent events A and B, the probability that A and B will both occur is found by multiplying the two probabilities. This is the special rule of multiplication and is written symbolically as:

SPECIAL RULE OF MULTIPLICATION P(A and B) = P(A)P(B) [5–5]

Lin66360_ch05_132-174.indd 147 1/10/17 7:41 PM

Exercises Exercises are included after sec- tions within the chapter and at the end of the chapter. Section exercises cover the material stud- ied 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.

DESCRIBING DATA: NUMERICAL MEASURES 79

INTERPRETATION AND USES OF THE STANDARD DEVIATION The standard deviation is commonly used as a measure to compare the spread in two or more sets of observations. For example, the standard deviation of the biweekly amounts invested in the Dupree Paint Company profit-sharing plan is computed to be $7.51. Suppose these employees are located in Georgia. If the standard deviation for a group of employees in Texas is $10.47, and the means are about the same, it indicates that the amounts invested by the Georgia employees are not dispersed as much as those in Texas (because $7.51 < $10.47). Since the amounts invested by the Georgia employees are clustered more closely about the mean, the mean for the Georgia em- ployees is a more reliable measure than the mean for the Texas group.

Chebyshev’s Theorem We have stressed that a small standard deviation for a set of values indicates that these values are located close to the mean. Conversely, a large standard deviation reveals that the observations are widely scattered about the mean. The Russian mathematician P. L. Chebyshev (1821–1894) developed a theorem that allows us to determine the minimum proportion of the values that lie within a specified number of standard deviations of the mean. For example, according to Chebyshev’s theorem, at least three out of every four, or 75%, of the values must lie between the mean plus two standard deviations and the mean minus two standard deviations. This relationship applies regardless of the shape of the distribution. Further, at least eight of nine values, or 88.9%, will lie between plus three standard deviations and minus three standard deviations of the mean. At least 24 of 25 values, or 96%, will lie between plus and minus five standard deviations of the mean.

Chebyshev’s theorem states:

LO3-5 Explain and apply Chebyshev’s theorem and the Empirical Rule.

STATISTICS IN ACTION

Most colleges report the “average class size.” This information can be mislead- ing because average class size can be found in several ways. If we find the number of students in each class at a particular university, the result is the mean number of students per class. If we compile a list of the class sizes for each student and find the mean class size, we might find the mean to be quite different. One school found the mean number of students in each of its 747 classes to be 40. But when

(continued)

CHEBYSHEV’S THEOREM For any set of observations (sample or population), the proportion of the values that lie within k standard deviations of the mean is at least 1 – 1/k2, where k is any value greater than 1.

For Exercises 47–52, do the following:

a. Compute the sample variance. b. Determine the sample standard deviation.

47. Consider these values a sample: 7, 2, 6, 2, and 3. 48. The following five values are a sample: 11, 6, 10, 6, and 7. 49. Dave’s Automatic Door, referred to in Exercise 37, installs automatic garage

door openers. Based on a sample, following are the times, in minutes, required to install 10 door openers: 28, 32, 24, 46, 44, 40, 54, 38, 32, and 42.

50. The sample of eight companies in the aerospace industry, referred to in Exer- cise 38, was surveyed as to their return on investment last year. The results are 10.6, 12.6, 14.8, 18.2, 12.0, 14.8, 12.2, and 15.6.

51. The Houston, Texas, Motel Owner Association conducted a survey regarding weekday motel rates in the area. Listed below is the room rate for business-class guests for a sample of 10 motels.

$101 $97 $103 $110 $78 $87 $101 $80 $106 $88

52. A consumer watchdog organization is concerned about credit card debt. A survey of 10 young adults with credit card debt of more than $2,000 showed they paid an average of just over $100 per month against their balances. Listed below are the amounts each young adult paid last month.

$110 $126 $103 $93 $99 $113 $87 $101 $109 $100

E X E R C I S E S

Lin66360_ch03_051-093.indd 79 1/6/17 4:51 AM

Computer Output The text includes many software examples, using Excel, MegaStat®, and Minitab. The software results are illustrated in the chapters. Instructions for a particular software example are in Appendix C.

64 CHAPTER 3

E X A M P L E

Table 2–4 on page 26 shows the profit on the sales of 180 vehicles at Applewood Auto Group. Determine the mean and the median selling price.

S O L U T I O N

The mean, median, and modal amounts of profit are reported in the following output (highlighted in the screen shot). (Reminder: The instructions to create the output appear in the Software Commands in Appendix C.) There are 180 vehicles in the study, so using a calculator would be tedious and prone to error.

Software Solution We can use a statistical software package to find many measures of location.

a. What is the arithmetic mean of the Alaska unemployment rates? b. Find the median and the mode for the unemployment rates. c. Compute the arithmetic mean and median for just the winter (Dec–Mar) months.

Is it much different? 22. Big Orange Trucking is designing an information system for use in “in-cab”

communications. It must summarize data from eight sites throughout a region to describe typical conditions. Compute an appropriate measure of central location for the variables wind direction, temperature, and pavement.

City Wind Direction Temperature Pavement

Anniston, AL West 89 Dry Atlanta, GA Northwest 86 Wet Augusta, GA Southwest 92 Wet Birmingham, AL South 91 Dry Jackson, MS Southwest 92 Dry Meridian, MS South 92 Trace Monroe, LA Southwest 93 Wet Tuscaloosa, AL Southwest 93 Trace

Lin66360_ch03_051-093.indd 64 1/6/17 4:51 AM

HOW DOES THIS TEXT REINFORCE STUDENT LEARNING?

x

BY CHAPTER

Chapter Summary Each chapter contains a brief summary of the chapter material, including vocab- ulary, definitions, and critical formulas.

202 CHAPTER 6

the number of transmission services, muffler replacements, and oil changes per day at Avellino’s Auto Shop. They follow Poisson distributions with means of 0.7, 2.0, and 6.0, respectively.

In summary, the Poisson distribution is a family of discrete distributions. All that is needed to construct a Poisson probability distribution is the mean number of defects, errors, or other random variable, designated as μ.

From actuary tables, Washington Insurance Company determined the likelihood that a man age 25 will die within the next year is .0002. If Washington Insurance sells 4,000 policies to 25-year-old men this year, what is the probability they will pay on exactly one policy?

S E L F - R E V I E W 6–6

31. In a Poisson distribution μ = 0.4. a. What is the probability that x = 0? b. What is the probability that x > 0?

32. In a Poisson distribution μ = 4. a. What is the probability that x = 2? b. What is the probability that x ≤ 2? c. What is the probability that x > 2?

33. Ms. Bergen is a loan officer at Coast Bank and Trust. From her years of experience, she estimates that the probability is .025 that an applicant will not be able to repay his or her installment loan. Last month she made 40 loans.

a. What is the probability that three loans will be defaulted? b. What is the probability that at least three loans will be defaulted?

34. Automobiles arrive at the Elkhart exit of the Indiana Toll Road at the rate of two per minute. The distribution of arrivals approximates a Poisson distribution.

a. What is the probability that no automobiles arrive in a particular minute? b. What is the probability that at least one automobile arrives during a particular

minute? 35. It is estimated that 0.5% of the callers to the Customer Service department of Dell

Inc. will receive a busy signal. What is the probability that of today’s 1,200 callers at least 5 received a busy signal?

36. In the past, schools in Los Angeles County have closed an average of 3 days each year for weather emergencies. What is the probability that schools in Los Angeles County will close for 4 days next year?

E X E R C I S E S

C H A P T E R S U M M A R Y

I. A random variable is a numerical value determined by the outcome of an experiment. II. A probability distribution is a listing of all possible outcomes of an experiment and the

probability associated with each outcome. A. A discrete probability distribution can assume only certain values. The main features are:

1. The sum of the probabilities is 1.00. 2. The probability of a particular outcome is between 0.00 and 1.00. 3. The outcomes are mutually exclusive.

B. A continuous distribution can assume an infinite number of values within a specific range. III. The mean and variance of a probability distribution are computed as follows.

A. The mean is equal to:

μ = Σ[xP(x)] (6–1) B. The variance is equal to:

σ2 = Σ[(x − μ)2P(x)] (6–2)

Lin66360_ch06_175-208.indd 202 1/14/17 7:02 AM

Pronunciation Key This section 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 en- hance course communications.

168 CHAPTER 5

P R O N U N C I A T I O N K E Y

SYMBOL MEANING PRONUNCIATION

P(A) Probability of A P of A

P(∼A) Probability of not A P of not A P(A and B) Probability of A and B P of A and B

P(A or B) Probability of A or B P of A or B

P(A | B) Probability of A given B has happened P of A given B

nPr Permutation of n items selected r at a time Pnr

nCr Combination of n items selected r at a time Cnr

C H A P T E R E X E R C I S E S

47. The marketing research department at Pepsico plans to survey teenagers about a newly developed soft drink. Each will be asked to compare it with his or her favorite soft drink. a. What is the experiment? b. What is one possible event?

48. The number of times a particular event occurred in the past is divided by the number of occurrences. What is this approach to probability called?

49. The probability that the cause and the cure for all cancers will be discovered before the year 2020 is .20. What viewpoint of probability does this statement illustrate?

50. Berdine’s Chicken Factory has several stores in the Hilton Head, South Carolina, area. When interviewing applicants for server positions, the owner would like to in- clude information on the amount of tip a server can expect to earn per check (or bill). A study of 500 recent checks indicated the server earned the following amounts in tips per 8-hour shift.

Amount of Tip Number

$0 up to $ 20 200 20 up to 50 100 50 up to 100 75 100 up to 200 75 200 or more 50

Total 500

a. What is the probability of a tip of $200 or more? b. Are the categories “$0 up to $20,” “$20 up to $50,” and so on considered mutually

exclusive? c. If the probabilities associated with each outcome were totaled, what would that total be? d. What is the probability of a tip of up to $50? e. What is the probability of a tip of less than $200?

51. Winning all three “Triple Crown” races is considered the greatest feat of a pedigree racehorse. After a successful Kentucky Derby, Corn on the Cob is a heavy favorite at 2 to 1 odds to win the Preakness Stakes. a. If he is a 2 to 1 favorite to win the Belmont Stakes as well, what is his probability of

winning the Triple Crown? b. What do his chances for the Preakness Stakes have to be in order for him to be

“even money” to earn the Triple Crown? 52. The first card selected from a standard 52-card deck is a king.

a. If it is returned to the deck, what is the probability that a king will be drawn on the second selection?

b. If the king is not replaced, what is the probability that a king will be drawn on the second selection?

Lin66360_ch05_132-174.indd 168 1/10/17 7:41 PM

Chapter Exercises 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 are in Appendix D at the end of the text. Many exercises are noted with a data file icon in the margin. For these exercises, there are data files in Excel format located on the text’s website, www.mhhe.com/Lind17e. These files help students use statistical software to solve the exercises.

348 CHAPTER 10

The major characteristics of the t distribution are: 1. It is a continuous distribution. 2. It is mound-shaped and symmetrical. 3. It is flatter, or more spread out, than the standard normal distribution. 4. There is a family of t distributions, depending on the number of degrees of freedom.

V. There are two types of errors that can occur in a test of hypothesis. A. A Type I error occurs when a true null hypothesis is rejected.

1. The probability of making a Type I error is equal to the level of significance. 2. This probability is designated by the Greek letter α.

B. A Type II error occurs when a false null hypothesis is not rejected. 1. The probability of making a Type II error is designated by the Greek letter β. 2. The likelihood of a Type II error must be calculated comparing the hypothesized

distribution to an alternate distribution based on sample results.

P R O N U N C I A T I O N K E Y

SYMBOL MEANING PRONUNCIATION

H0 Null hypothesis H sub zero

H1 Alternate hypothesis H sub one

α/2 Two-tailed significance level Alpha divided by 2 xc Limit of the sample mean x bar sub c

μ0 Assumed population mean mu sub zero

C H A P T E R E X E R C I S E S

25. According to the local union president, the mean gross income of plumbers in the Salt Lake City area follows the normal probability distribution with a mean of $45,000 and a standard deviation of $3,000. A recent investigative reporter for KYAK TV found, for a sample of 120 plumbers, the mean gross income was $45,500. At the .10 significance level, is it reasonable to conclude that the mean income is not equal to $45,000? Deter- mine the p-value.

26. Rutter Nursery Company packages its pine bark mulch in 50-pound bags. From a long history, the production department reports that the distribution of the bag weights follows the normal distribution and the standard deviation of the packaging process is 3 pounds per bag. At the end of each day, Jeff Rutter, the production manager, weighs 10 bags and computes the mean weight of the sample. Below are the weights of 10 bags from today’s production.

45.6 47.7 47.6 46.3 46.2 47.4 49.2 55.8 47.5 48.5

a. Can Mr. Rutter conclude that the mean weight of the bags is less than 50 pounds? Use the .01 significance level.

b. In a brief report, tell why Mr. Rutter can use the z distribution as the test statistic. c. Compute the p-value.

27. A new weight-watching company, Weight Reducers International, advertises that those who join will lose an average of 10 pounds after the first two weeks. The standard devi- ation is 2.8 pounds. A random sample of 50 people who joined the weight reduction program revealed a mean loss of 9 pounds. At the .05 level of significance, can we conclude that those joining Weight Reducers will lose less than 10 pounds? Determine the p-value.

28. Dole Pineapple Inc. is concerned that the 16-ounce can of sliced pineapple is being overfilled. Assume the standard deviation of the process is .03 ounce. The quality-con- trol department took a random sample of 50 cans and found that the arithmetic mean weight was 16.05 ounces. At the 5% level of significance, can we conclude that the mean weight is greater than 16 ounces? Determine the p-value.

Lin66360_ch10_318-352.indd 348 1/16/17 9:53 PM

Data Analytics The goal of the Data Analytics sec- tions is to develop analytical skills. The exercises present a real world context with supporting data. The data sets are printed in Appendix A and available to download from the text’s website www.mhhe.com/Lind17e. Statistical software is required to analyze the data and respond to the exercises. Each data set is used to explore questions and dis- cover findings that relate to a real world context. For each business context, a story is uncovered as students progress from chapters one to seventeen.

244 CHAPTER 7

68. In establishing warranties on HDTVs, the manufacturer wants to set the limits so that few will need repair at the manufacturer’s expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV, the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only 10% of the HDTVs need repairs at the manufacturer’s expense?

69. DeKorte Tele-Marketing Inc. is considering purchasing a machine that randomly selects and automatically dials telephone numbers. DeKorte Tele-Marketing makes most of its calls during the evening, so calls to business phones are wasted. The manufacturer of the machine claims that its programming reduces the calling to business phones to 15% of all calls. To test this claim, the director of purchasing at DeKorte programmed the machine to select a sample of 150 phone numbers. What is the likelihood that more than 30 of the phone numbers selected are those of businesses, assuming the manu- facturer’s claim is correct?

70. A carbon monoxide detector in the Wheelock household activates once every 200 days on average. Assume this activation follows the exponential distribution. What is the probability that: a. There will be an alarm within the next 60 days? b. At least 400 days will pass before the next alarm? c. It will be between 150 and 250 days until the next warning? d. Find the median time until the next activation.

71. “Boot time” (the time between the appearance of the Bios screen to the first file that is loaded in Windows) on Eric Mouser’s personal computer follows an exponential distribu- tion with a mean of 27 seconds. What is the probability his “boot” will require: a. Less than 15 seconds? b. More than 60 seconds? c. Between 30 and 45 seconds? d. What is the point below which only 10% of the boots occur?

72. The time between visits to a U.S. emergency room for a member of the general popula- tion follows an exponential distribution with a mean of 2.5 years. What proportion of the population: a. Will visit an emergency room within the next 6 months? b. Will not visit the ER over the next 6 years? c. Will visit an ER next year, but not this year? d. Find the first and third quartiles of this distribution.

73. The times between failures on a personal computer follow an exponential distribution with a mean of 300,000 hours. What is the probability of: a. A failure in less than 100,000 hours? b. No failure in the next 500,000 hours? c. The next failure occurring between 200,000 and 350,000 hours? d. What are the mean and standard deviation of the time between failures?

D A T A A N A L Y T I C S

(The data for these exercises are available at the text website: www.mhhe.com/lind17e.)

74. Refer to the North Valley Real Estate data, which report information on homes sold during the last year. a. The mean selling price (in $ thousands) of the homes was computed earlier to be $357.0,

with a standard deviation of $160.7. Use the normal distribution to estimate the percent- age of homes selling for more than $500.000. Compare this to the actual results. Is price normally distributed? Try another test. If price is normally distributed, how many homes should have a price greater than the mean? Compare this to the actual number of homes. Construct a frequency distribution of price. What do you observe?

b. The mean days on the market is 30 with a standard deviation of 10 days. Use the normal distribution to estimate the number of homes on the market more than 24 days. Compare this to the actual results. Try another test. If days on the market is normally distributed, how many homes should be on the market more than the mean number of days? Compare this to the actual number of homes. Does the normal

Lin66360_ch07_209-249.indd 244 1/14/17 8:29 AM

Software Commands Software examples using Excel, Mega- Stat®, and Minitab are included through- out the text. The explanations of the computer input commands are placed at the end of the text in Appendix C.

780

11–2. The Minitab commands for the two-sample t-test on page 368 are:

a. Put the amount absorbed by the Store brand in C1 and the amount absorbed by the Name brand paper towel in C2.

b. From the toolbar, select Stat, Basic Statistics, and then 2-Sample, and click OK.

c. In the next dialog box, select Samples in different col- umns, select C1 Store for the First column and C2 Name of the Second, click the box next to Assume equal variances, and click OK.

11–3. The Excel commands for the paired t-test on page 373 are: a. Enter the data into columns B and C (or any other two col-

umns) in the spreadsheet, with the variable names in the first row.

b. Select the Data tab on the top menu. Then, on the far right, select Data Analysis. Select t-Test: Paired Two Sample for Means, and then click OK.

c. In the dialog box, indicate that the range of Variable 1 is from B1 to B11 and Variable 2 from C1 to C11, the Hypothesized Mean Difference is 0, click Labels, Alpha is .05, and the Output Range is E1. Click OK.

CHAPTER 12 12–1. The Excel commands for the test of variances on page 391 are: a. Enter the data for U.S. 25 in column A and for I-75 in col-

umn B. Label the two columns. b. Select the Data tab on the top menu. Then, on the far right,

select Data Analysis. Select F-Test: Two-Sample for Variances, then click OK.

c. The range of the first variable is A1:A8, and B1:B9 for the second. Click on Labels, enter 0.05 for Alpha, select D1 for the Output Range, and click OK.

12–2. The Excel commands for the one-way ANOVA on page 400 are: a. Key in data into four columns labeled Northern, WTA, Po-

cono, and Branson. b. Select the Data tab on the top menu. Then, on the far right,

select Data Analysis. Select ANOVA: Single Factor, then click OK.

c. In the subsequent dialog box, make the input range A1:D8, click on Grouped by Columns, click on Labels in first row, the Alpha text box is 0.05, and finally select Output Range as F1 and click OK.

c. In the dialog box, indicate that the range of Variable 1 is from A1 to A6 and Variable 2 from B1 to B7, the Hypothe- sized Mean Difference is 0, click Labels, Alpha is 0.05, and the Output Range is D1. Click OK.

Lin66360_appc_774-784.indd 780 1/20/17 10:28 AM

xi

Answers to Self-Review The worked-out solutions to the Self-Reviews are pro- vided at the end of the text in Appendix E.

11

16–7 a. Rank

x y x y d d 2

805 23 5.5 1 4.5 20.25 777 62 3.0 9 −6.0 36.00 820 60 8.5 8 0.5 0.25 682 40 1.0 4 −3.0 9.00 777 70 3.0 10 −7.0 49.00 810 28 7.0 2 5.0 25.00 805 30 5.5 3 2.5 6.25 840 42 10.0 5 5.0 25.00 777 55 3.0 7 −4.0 16.00 820 51 8.5 6 2.5 6.25

0 193.00

rs = 1 − 6(193)

10(99) = −.170

b. H0: ρ = 0; H1: ρ ≠ 0. Reject H0 if t < −2.306 or t > 2.306.

t = −.170√ 10 − 2

1 − (−0.170)2 = −0.488

H0 is not rejected. We have not shown a relationship between the two tests.

CHAPTER 17 17–1 1.

Country Amount Index (Based=US) China 822.7 932.8 Japan 110.7 125.5 United States 88.2 100.0 India 86.5 98.1 Russia 71.5 81.1

China Produced 832.8% more steel than the US

2. a.

Year Average Hourly Earnings Index (1995 = Base) 1995 11.65 100.0 2000 14.02 120.3 2005 16.13 138.5 2013 19.97 171.4 2016 21.37 183.4

2016 Average wage Increased 83.4% from 1995

b.

Year Average Hourly Earnings Index (1995 – 2000 = Base) 1995 11.65 90.8 2000 14.02 109.2 2005 16.13 125.7 2013 19.97 155.6 2016 21.37 166.5

2016 Average wage Increased 86.5% from the average of 1995, 2000

17–2 1. a. P1 = ($85/$75)(100) = 113.3 P2 = ($45/$40)(100) = 112.5 P = (113.3 + 112.5)/2 = 112.9 b. P = ($130/$115)(100) = 113.0

c. P = $85(500) + $45(1,200) $75(500) + $40(1,200)

(100)

= $96,500 85,500

(100) = 112.9

d. P = $85(520) + $45(1,300) $75(520) + $40(1,300)

(100)

= $102,700

$91,000 (100) = 112.9

e. P = √(112.9) (112.9) = 112.9

17–3 a. P = $4(9,000) + $5(200) + $8(5,000) $3(10,000) + $1(600) + $10(3,000)

(100)

= $77,000 60,600

(100) = 127.1

b. The value of sales went up 27.1% from 2001 to 2017

17–4 a. For 2011

Item Weight

Cotton ($0.25/$0.20)(100)(.10) = 12.50 Autos (1,200/1,000)(100)(.30) = 36.00 Money turnover (90/80)(100)(.60) = 67.50 Total 116.00

For 2016

Item Weight

Cotton ($0.50/$0.20)(100)(.10) = 25.00 Autos (900/1,000)(100)(.30) = 27.00 Money turnover (75/80)(100)(.60) = 56.25 Total 108.25

b. Business activity increased 16% from 2004 to 2009. It increased 8.25% from 2004 to 2014.

17–5 In terms of the base period, Jon’s salary was $14,637 in 2000 and $17,944 in 2016. This indicates that take-home pay in- creased at a faster rate than the rate of prices paid for food, transportation, etc.

17–6 $0.42, round by ($1.00/238.132)(100). The purchasing power has declined by $0.58.

17–7 Year IPI PPI

2007 111.07 92.9 2008 107.12 100.2 2009 94.80 95.3 2010 100.00 100.0 2011 102.93 107.8 2012 105.80 110.1 2013 107.83 110.5 2014 110.98 111.5 2015 111.32 105.8

The Industrial Production index (IPI) increased 11.32% from 2010 to 2015. The Producer Price Index (PPI) increases 5.8%.

CHAPTER 18 18–1

Year Number Produced Moving Average

2011 2 2012 6 4 2013 4 5 2014 5 4 2015 3 6 2016 10

Lin66360_appe_01-13.indd 11 1/11/17 8:22 AM

BY SECTION

Section Reviews After selected groups of chapters (1–4, 5–7, 8 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 chap- ters and problems for review.

126 A REVIEW OF CHAPTERS 1–4

D A T A A N A L Y T I C S

44. Refer to the North Valley real estate data recorded on homes sold during the last year. Prepare a report on the selling prices of the homes based on the answers to the following questions. a. Compute the minimum, maximum, median, and the first and the third quartiles of

price. Create a box plot. Comment on the distribution of home prices. b. Develop a scatter diagram with price on the vertical axis and the size of the home on

the horizontal. Is there a relationship between these variables? Is the relationship direct or indirect?

c. For homes without a pool, develop a scatter diagram with price on the vertical axis and the size of the home on the horizontal. Do the same for homes with a pool. How do the relationships between price and size for homes without a pool and homes with a pool compare?

45. Refer to the Baseball 2016 data that report information on the 30 Major League Baseball teams for the 2016 season. a. In the data set, the year opened, is the first year of operation for that stadium. For

each team, use this variable to create a new variable, stadium age, by subtracting the value of the variable, year opened, from the current year. Develop a box plot with the new variable, age. Are there any outliers? If so, which of the stadiums are outliers?

b. Using the variable, salary, create a box plot. Are there any outliers? Compute the quartiles using formula (4–1). Write a brief summary of your analysis.

c. Draw a scatter diagram with the variable, wins, on the vertical axis and salary on the horizontal axis. What are your conclusions?

d. Using the variable, wins, draw a dot plot. What can you conclude from this plot? 46. Refer to the Lincolnville School District bus data.

a. Referring to the maintenance cost variable, develop a box plot. What are the mini- mum, first quartile, median, third quartile, and maximum values? Are there any outliers?

b. Using the median maintenance cost, develop a contingency table with bus manufac- turer as one variable and whether the maintenance cost was above or below the median as the other variable. What are your conclusions?

A REVIEW OF CHAPTERS 1–4 This section is a review of the major concepts and terms introduced in Chapters 1–4. Chapter 1 began by describing the meaning and purpose of statistics. Next we described the different types of variables and the four levels of measurement. Chapter 2 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 3 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, variance, and standard deviation. Chapter 4 included several graphing techniques such as dot plots, box plots, and scatter diagrams. We also discussed the coefficient of skew- ness, 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 of variation calculated, and the information presented in graphical form.

Lin66360_ch04_094-131.indd 126 1/10/17 7:41 PM

Cases The review also includes continuing cases and several small cases that let students make decisions using tools and techniques from a variety of chapters.

5. Refer to the following diagram.

0 40 80 120 160 200

* *

a. What is the graph called? b. What are the median, and first and third quartile values? c. Is the distribution positively skewed? Tell how you know. d. Are there any outliers? If yes, estimate these values. e. Can you determine the number of observations in the study?

A REVIEW OF CHAPTERS 1–4 129

C A S E S

A. Century National Bank The following case will appear in subsequent review sec- tions. Assume that you work in the Planning Department of the Century National Bank and report to Ms. Lamberg. You will need to do some data analysis and prepare a short writ- ten 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 custom- ers. What is the balance of a typical customer? How many other bank services do the checking ac- count customers use? Do the customers use the ATM ser- vice 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 sam- ple 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 (automatic teller machine) transac- tions in the last month; (2) the number of other bank ser- vices (a savings account, a certificate of deposit, etc.) the customer uses; (3) whether the customer has a debit card (this is a bank service in which charges are made directly to the customer’s account); and (4) whether or not interest is paid on the checking account. The sample includes cus- tomers from the branches in Cincinnati, Ohio; Atlanta, Georgia; Louisville, Kentucky; and Erie, Pennsylvania.

1. Develop a graph or table that portrays the checking balances. What is the balance of a typical customer? Do many customers have more than $2,000 in their accounts? Does it appear that there is a difference in the distribution of the accounts among the four branches? Around what value do the account bal- ances tend to cluster?

2. Determine the mean and median of the checking ac- count balances. Compare the mean and the 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.

3. Determine the range and the standard deviation of the checking account balances. What do 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 es- sentially the same job but at different pay. To investi- gate, 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 summarizing the situation.

Yearly Salary ($000) Women Men

Less than 30 2 0 30 up to 40 3 1 40 up to 50 17 4 50 up to 60 17 24 60 up to 70 8 21 70 up to 80 3 7 80 or more 0 3

To kick off the project, Mr. Cory St. Julian held a meeting with his staff and you were invited. At this meeting, it was suggested that you calculate several measures of

Lin66360_ch04_094-131.indd 129 1/10/17 7:41 PM

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.

130 A REVIEW OF CHAPTERS 1–4

location, create charts or draw graphs such as a cumula- tive frequency distribution, and determine the quartiles for both men and women. Develop the charts and write the report summarizing the yearly salaries of employees at Wildcat Plumbing Supply. Does it appear that there are pay differences based on gender?

C. Kimble Products: Is There a Difference In the Commissions?

At the January national sales meeting, the CEO of Kimble Products was questioned extensively regarding the com- pany policy for paying commissions to its sales represen- tatives. The company sells sporting goods to two major

markets. There are 40 sales representatives who call di- rectly on large-volume customers, such as the athletic de- partments at major colleges and universities and professional sports franchises. There are 30 sales repre- sentatives who represent the company to retail stores lo- cated in shopping malls and large discounters such as Kmart and Target. Upon his return to corporate headquarters, the CEO asked the sales manager for a report comparing the com- missions earned last year by the two parts of the sales team. The information is reported below. Write a brief re- port. Would you conclude that there is a difference? Be sure to include information in the report on both the cen- tral tendency and dispersion of the two groups.

Commissions Earned by Sales Representatives Calling on Large Retailers ($)

1,116 681 1,294 12 754 1,206 1,448 870 944 1,255 1,213 1,291 719 934 1,313 1,083 899 850 886 1,556 886 1,315 1,858 1,262 1,338 1,066 807 1,244 758 918

Commissions Earned by Sales Representatives Calling on Athletic Departments ($)

354 87 1,676 1,187 69 3,202 680 39 1,683 1,106 883 3,140 299 2,197 175 159 1,105 434 615 149 1,168 278 579 7 357 252 1,602 2,321 4 392 416 427 1,738 526 13 1,604 249 557 635 527

P R A C T I C E T E S T

There is a practice test at the end of each review section. The tests are in two parts. The first part contains several objec- tive 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 1. The science of collecting, organizing, presenting, analyzing, and interpreting data to assist in

making effective decisions is called . 1. 2. Methods of organizing, summarizing, and presenting data in an informative way are

called . 2. 3. The entire set of individuals or objects of interest or the measurements obtained from all

individuals or objects of interest are called the . 3. 4. List the two types of variables. 4. 5. The number of bedrooms in a house is an example of a . (discrete variable,

continuous variable, qualitative variable—pick one) 5. 6. The jersey numbers of Major League Baseball players are an example of what level of

measurement? 6. 7. The classification of students by eye color is an example of what level of measurement? 7. 8. The sum of the differences between each value and the mean is always equal to what value? 8. 9. A set of data contained 70 observations. How many classes would the 2k method suggest to

construct a frequency distribution? 9. 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,

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 1. The Russell 2000 index of stock prices increased by the following amounts over the last 3 years.

18% 4% 2%

What is the geometric mean increase for the 3 years?

Lin66360_ch04_094-131.indd 130 1/10/17 7:41 PM

Required=Results

®

McGraw-Hill Connect® Learn Without Limits Connect is a teaching and learning platform that is proven to deliver better results for students and instructors.

Connect empowers students by continually adapting to deliver precisely what they need, when they need it, and how they need it, so your class time is more engaging and effective.

Mobile

Connect Insight® Connect Insight is Connect’s new one-of-a- kind visual analytics dashboard—now available for both instructors and students—that provides at-a-glance information regarding student performance, which is immediately actionable. By presenting assignment, assessment, and topical performance results together with a time metric that is easily visible for aggregate or individual results, Connect Insight gives the user the ability to take a just-in-time approach to teaching and learning, which was never before available. Connect Insight presents data that empowers students and helps instructors improve class performance in a way that is efficient and effective.

73% of instructors who use Connect require it; instructor satisfaction increases by 28%

when Connect is required.

Students can view their results for any

Connect course.

Analytics

Connect’s new, intuitive mobile interface gives students and instructors flexible and convenient, anytime–anywhere access to all components of the Connect platform.

©Getty Images/iStockphoto

Using Connect improves retention rates by 19.8%, passing rates by 12.7%, and exam scores by 9.1%.

SmartBook® Proven to help students improve grades and study more efficiently, SmartBook contains the same content within the print book, but actively tailors that content to the needs of the individual. SmartBook’s adaptive technology provides precise, personalized instruction on what the student should do next, guiding the student to master and remember key concepts, targeting gaps in knowledge and offering customized feedback, and driving the student toward comprehension and retention of the subject matter. Available on tablets, SmartBook puts learning at the student’s fingertips—anywhere, anytime.

Adaptive

Over 8 billion questions have been answered, making McGraw-Hill

Education products more intelligent, reliable, and precise.

THE ADAPTIVE READING EXPERIENCE DESIGNED TO TRANSFORM THE WAY STUDENTS READ

More students earn A’s and B’s when they use McGraw-Hill Education Adaptive products.

www.mheducation.com

INSTRUCTOR LIBRARY The Connect® Business Statistics Instructor Library is your repository for additional resources to improve student engagement in and out of class. You can select and use any asset that enhances your lecture, including:

• Solutions Manual The Solutions Manual, carefully revised by the authors, contains solutions to all basic, inter- mediate, and challenge problems found at the end of each chapter.

• Test Bank The Test Bank, revised by Wendy Bailey of Troy University, contains hundreds of true/false, multiple choice and short-answer/discussions, updated based on the revisions of the authors. The level of difficulty varies, as indicated by the easy, medium, and difficult labels.

• Powerpoint Presentations Prepared by Stephanie Campbell of Mineral Area College, the presentations con- tain exhibits, tables, key points, and summaries in a visually stimulating collection of slides.

• Excel Templates There are templates for various end of chapter problems that have been set as Excel spreadsheets—all denoted by an icon. Students can easily download, save the files and use the data to solve end of chapter problems.

MEGASTAT® FOR MICROSOFT EXCEL® MegaStat® by J. B. Orris of Butler University is a full-featured Excel statistical analysis add-in that is available on the MegaStat website at www.mhhe.com/megastat (for purchase). MegaStat works with recent versions of Microsoft Excel® (Windows and Mac OS X). See the website for details on supported versions.

Once installed, MegaStat will always be available on the Excel add-ins ribbon with no expiration date or data limita- tions. MegaStat performs statistical analyses within an Excel workbook. When a MegaStat menu item is selected, a dialog box pops up for data selection and options. Since MegaStat is an easy-to-use extension of Excel, students can focus on learning statistics without being distracted by the software. Ease-of-use features include Auto Expand for quick data selection and Auto Label detect.

MegaStat does most calculations found in introductory statistics textbooks, such as computing descriptive statistics, creating frequency distributions, and computing probabilities as well as hypothesis testing, ANOVA, chi-square analysis, and regression analysis (simple and multiple). MegaStat output is carefully formatted and appended to an output worksheet.

Video tutorials are included that provide a walkthrough using MegaStat for typical business statistics topics. A con- text-sensitive help system is built into MegaStat and a User’s Guide is included in PDF format.

MINITAB®/SPSS®/JMP® Minitab® Version 17, SPSS® Student Version 18.0, and JMP® Student Edition Version 8 are software products that are available to help students solve the exercises with data files. Each software product can be packaged with any McGraw-Hill business statistics text.

ADDITIONAL RESOURCES

xiv

xv

ACKNOWLEDGMENTS

Stefan Ruediger Arizona State University Anthony Clark St. Louis Community College Umair Khalil West Virginia University Leonie Stone SUNY Geneseo

Golnaz Taghvatalab Central Michigan University John Yarber Northeast Mississippi Community College John Beyers University of Maryland

Mohammad Kazemi University of North Carolina Charlotte Anna Terzyan Loyola Marymount University Lee O. Cannell El Paso Community College

This edition of Statistical Techniques in Business and Economics is the product of many people: students, colleagues, reviewers, and the staff at McGraw-Hill Education. We thank them all. We wish to express our sincere gratitude to the reviewers:

Their suggestions and thorough reviews of the previous edition and the manuscript of this edi- tion make this a better text.

Special thanks go to a number of people. Shelly Moore, College of Western Idaho, and John Arcaro, Lakeland Community College, accuracy checked the Connect exercises. Ed Pappanastos, Troy University, built new data sets and revised Smartbook. Rene Ordonez, Southern Oregon University, built the Connect guided examples. Wendy Bailey, Tory University, prepared the test bank. Stephanie Campbell, Mineral Area College, prepared the Powerpoint decks. Vickie Fry, Westmoreland County Community College, provided countless hours of digital accuracy checking and support.

We also wish to thank the staff at McGraw-Hill. This includes Dolly Womack, Senior Brand Man- ager; Michele Janicek, Product Developer Coordinator; Camille Corum and Ryan McAndrews, Product Developers; Harvey Yep and Bruce Gin, Content Project Managers; and others we do not know per- sonally, but who have made valuable contributions.

xvi CONTENTS

xvi

ENHANCEMENTS TO STATISTICAL TECHNIQUES IN BUSINESS & ECONOMICS, 17E

MAJOR CHANGES MADE TO INDIVIDUAL CHAPTERS:

CHAPTER 1 What Is Statistics? • Revised Self-Review 1-2.

• New Section describing Business Analytics and its integration with the text.

• Updated exercises 2, 3, 17, and 19.

• New Data Analytics section with new data and questions.

CHAPTER 2 Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation • Revised chapter introduction.

• Added more explanation about cumulative relative frequency distributions.

• Updated exercises 47 and 48 using real data.

• New Data Analytics section with new data and questions.

CHAPTER 3 Describing Data: Numerical Measures • Updated Self-Review 3-2.

• Updated Exercises 16, 18, 73, 77, and 82.

• New Data Analytics section with new data and questions.

CHAPTER 4 Describing Data: Displaying and Exploring Data • Updated exercise 22 with 2016 New York Yankee player

salaries.

• New Data Analytics section with new data and questions.

CHAPTER 5 A Survey of Probability Concepts • Revised the Example/Solution in the section on Bayes

Theorem.

• Updated exercises 45 and 58 using real data.

• New Data Analytics section with new data and questions.

CHAPTER 6 Discrete Probability Distributions • Expanded discussion of random variables.

• Revised the Example/Solution in the section on Poisson distribution.

• Updated exercises 18, 58, and 68.

• New Data Analytics section with new data and questions.

CHAPTER 7 Continuous Probability Distributions • Revised Self-Review 7-1.

• Revised the Example/Solutions using Uber as the context.

• Updated exercises 19, 22, 28, 36, 47, and 64.

• New Data Analytics section with new data and questions.

CHAPTER 8 Sampling Methods and the Central Limit Theorem • New Data Analytics section with new data and questions.

CHAPTER 9 Estimation and Confidence Intervals • New Self-Review 9-3 problem description.

• Updated exercises 5, 6, 12, 14, 23, 24, 33, 41, 43, and 61.

• New Data Analytics section with new data and questions.

CHAPTER 10 One-Sample Tests of Hypothesis • Revised the Example/Solutions using an airport, cell phone

parking lot as the context.

• Revised the section on Type II error to include an additional example.

• New Type II error exercises, 23 and 24.

• Updated exercises 19, 31, 32, and 43.

• New Data Analytics section with new data and questions.

CHAPTER 11 Two-Sample Tests of Hypothesis • Updated exercises 5, 9, 12, 26, 27, 30, 32, 34, 40, 42,

and 46.

• New Data Analytics section with new data and questions.

CHAPTER 12 Analysis of Variance • Revised Self-Reviews 12-1 and 12-3.

• Updated exercises 10, 21, 24, 33, 38, 42, and 44.

• New Data Analytics section with new data and questions.

CHAPTER 13 Correlation and Linear Regression • Added new conceptual formula, to relate the standard error

to the regression ANOVA table.

• Updated exercises 36, 41, 42, 43, and 57.

• New Data Analytics section with new data and questions.

CHAPTER 14 Multiple Regression Analysis • Updated exercises 19, 21, 23, 24, and 25.

• New Data Analytics section with new data and questions.

CHAPTER 15 Nonparametric Methods: Nominal Level Hypothesis Tests • Updated the context of Manelli Perfume Company Example/

Solution.

• Revised the “Hypothesis Test of Unequal Expected Frequen- cies” Example/Solution.

• Updated exercises 3, 31, 42, 46, and 61.

• New Data Analytics section with new data and questions.

xvii

CHAPTER 16 Nonparametric Methods: Analysis of Ordinal Data • Revised the “Sign Test” Example/Solution.

• Revised the “Testing a Hypothesis About a Median” Example/ Solution.

• Revised the “Wilcoxon Rank-Sum Test for Independent Popu- lations” Example/Solution.

• Revised Self-Reviews 16-3 and 16-6.

• Updated exercise 25.

• New Data Analytics section with new data and questions.

CHAPTER 17 Index Numbers • Revised Self-Reviews 17-1, 17-2, 17-3, 17-4, 17-5, 17-6, 17-7.

• Updated dates, illustrations, and examples.

• New Data Analytics section with new data and questions.

CHAPTER 18 Time Series and Forecasting • Updated dates, illustrations, and examples.

• New Data Analytics section with new data and questions.

CHAPTER 19 Statistical Process Control and Quality Management • Updated 2016 Malcolm Baldridge National Quality Award

winners.

• Updated exercises 13, 22, and 25.

xix

B R I E F C O N T E N T S

1 What is Statistics? 1 2 Describing Data: Frequency Tables, Frequency Distributions,

and Graphic Presentation 18

3 Describing Data: Numerical Measures 51 4 Describing Data: Displaying and Exploring Data 94 Review Section

5 A Survey of Probability Concepts 132 6 Discrete Probability Distributions 175 7 Continuous Probability Distributions 209 Review Section 8 Sampling Methods and the Central Limit Theorem 250 9 Estimation and Confidence Intervals 282 Review Section 10 One-Sample Tests of Hypothesis 318 11 Two-Sample Tests of Hypothesis 353 12 Analysis of Variance 386 Review Section 13 Correlation and Linear Regression 436 14 Multiple Regression Analysis 488 Review Section 15 Nonparametric Methods:

Nominal Level Hypothesis Tests 545

16 Nonparametric Methods: Analysis of Ordinal Data 582 Review Section

17 Index Numbers 621 18 Time Series and Forecasting 653 Review Section 19 Statistical Process Control and Quality Management 697 20 An Introduction to Decision Theory 728

Appendixes: Data Sets, Tables, Software Commands, Answers 745

Glossary 847

Index 851

xx

C O N T E N T S

1 What is Statistics? 1 Introduction 2

Why Study Statistics? 2

What is Meant by Statistics? 3

Types of Statistics 4

Descriptive Statistics 4 Inferential Statistics 5

Types of Variables 6

Levels of Measurement 7

Nominal-Level Data 7 Ordinal-Level Data 8 Interval-Level Data 9 Ratio-Level Data 10

EXERCISES 11

Ethics and Statistics 12

Basic Business Analytics 12

Chapter Summary 13

Chapter Exercises 14

Data Analytics 17

2 Describing Data: FREQUENCY TABLES, FREQUENCY

DISTRIBUTIONS, AND GRAPHIC PRESENTATION 18 Introduction 19

Constructing Frequency Tables 19

Relative Class Frequencies 20

Graphic Presentation of Qualitative Data 21

EXERCISES 25

Constructing Frequency Distributions 26

Relative Frequency Distribution 30

EXERCISES 31

Graphic Presentation of a Distribution 32

Histogram 32 Frequency Polygon 35

EXERCISES 37

Cumulative Distributions 38

EXERCISES 41

Chapter Summary 42

Chapter Exercises 43

Data Analytics 49

3 Describing Data: NUMERICAL MEASURES 51

Introduction 52

Measures of Location 52

The Population Mean 53 The Sample Mean 54 Properties of the Arithmetic Mean 55

EXERCISES 56

The Median 57 The Mode 59

EXERCISES 61

The Relative Positions of the Mean, Median, and Mode 62

EXERCISES 63

Software Solution 64

The Weighted Mean 65

EXERCISES 66

The Geometric Mean 66

EXERCISES 68

Why Study Dispersion? 69

Range 70 Variance 71

EXERCISES 73

Population Variance 74 Population Standard Deviation 76

EXERCISES 76

Sample Variance and Standard Deviation 77 Software Solution 78

EXERCISES 79

Interpretation and Uses of the Standard Deviation 79

Chebyshev’s Theorem 79 The Empirical Rule 80

A Note from the Authors vi

CONTENTS xxi

EXERCISES 81

The Mean and Standard Deviation of Grouped Data 82

Arithmetic Mean of Grouped Data 82 Standard Deviation of Grouped Data 83

EXERCISES 85

Ethics and Reporting Results 86

Chapter Summary 86

Pronunciation Key 88

Chapter Exercises 88

Data Analytics 92

4 Describing Data: DISPLAYING AND EXPLORING DATA 94

Introduction 95

Dot Plots 95

Stem-and-Leaf Displays 96

EXERCISES 101

Measures of Position 103

Quartiles, Deciles, and Percentiles 103

EXERCISES 106

Box Plots 107

EXERCISES 109

Skewness 110

EXERCISES 113

Describing the Relationship between Two Variables 114

Contingency Tables 116

EXERCISES 118

Chapter Summary 119

Pronunciation Key 120

Chapter Exercises 120

Data Analytics 126

Problems 127

Cases 129

Practice Test 130

5 A Survey of Probability Concepts 132 Introduction 133

What is a Probability? 134

Approaches to Assigning Probabilities 136

Classical Probability 136 Empirical Probability 137 Subjective Probability 139

EXERCISES 140

Rules of Addition for Computing Probabilities 141

Special Rule of Addition 141 Complement Rule 143 The General Rule of Addition 144

EXERCISES 146

Rules of Multiplication to Calculate Probability 147

Special Rule of Multiplication 147 General Rule of Multiplication 148

Contingency Tables 150

Tree Diagrams 153

EXERCISES 155

Bayes’ Theorem 157

EXERCISES 161

Principles of Counting 161

The Multiplication Formula 161 The Permutation Formula 163 The Combination Formula 164

EXERCISES 166

Chapter Summary 167

Pronunciation Key 168

Chapter Exercises 168

Data Analytics 173

6 Discrete Probability Distributions 175 Introduction 176

What is a Probability Distribution? 176

Random Variables 178

Discrete Random Variable 179 Continuous Random Variable 179

The Mean, Variance, and Standard Deviation of a Discrete Probability Distribution 180

Mean 180 Variance and Standard Deviation 180

EXERCISES 182

Binomial Probability Distribution 184

How Is a Binomial Probability Computed? 185 Binomial Probability Tables 187

EXERCISES 190

Cumulative Binomial Probability Distributions 191

EXERCISES 193

Hypergeometric Probability Distribution 193

xxii CONTENTS

EXERCISES 197

Poisson Probability Distribution 197

EXERCISES 202

Chapter Summary 202

Chapter Exercises 203

Data Analytics 208

7 Continuous Probability Distributions 209 Introduction 210

The Family of Uniform Probability Distributions 210

EXERCISES 213

The Family of Normal Probability Distributions 214

The Standard Normal Probability Distribution 217

Applications of the Standard Normal Distribution 218 The Empirical Rule 218

EXERCISES 220

Finding Areas under the Normal Curve 221

EXERCISES 224

EXERCISES 226

EXERCISES 229

The Normal Approximation to the Binomial 229

Continuity Correction Factor 230 How to Apply the Correction Factor 232

EXERCISES 233

The Family of Exponential Distributions 234

EXERCISES 238

Chapter Summary 239

Chapter Exercises 240

Data Analytics 244

Problems 246

Cases 247

Practice Test 248

8 Sampling Methods and the Central Limit Theorem 250 Introduction 251

Sampling Methods 251

Reasons to Sample 251 Simple Random Sampling 252 Systematic Random Sampling 255 Stratified Random Sampling 255 Cluster Sampling 256

EXERCISES 257

Sampling “Error” 259

Sampling Distribution of the Sample Mean 261

EXERCISES 264

The Central Limit Theorem 265

EXERCISES 271

Using the Sampling Distribution of the Sample Mean 273

EXERCISES 275

Chapter Summary 275

Pronunciation Key 276

Chapter Exercises 276

Data Analytics 281

9 Estimation and Confidence Intervals 282 Introduction 283

Point Estimate for a Population Mean 283

Confidence Intervals for a Population Mean 284

Population Standard Deviation, Known σ 284 A Computer Simulation 289

EXERCISES 291

Population Standard Deviation, σ Unknown 292 EXERCISES 299

A Confidence Interval for a Population Proportion 300

EXERCISES 303

Choosing an Appropriate Sample Size 303

Sample Size to Estimate a Population Mean 304 Sample Size to Estimate a Population Proportion 305

EXERCISES 307

Finite-Population Correction Factor 307

EXERCISES 309

Chapter Summary 310

Chapter Exercises 311

Data Analytics 315

Problems 316

Cases 317

Practice Test 317

10 One-Sample Tests of Hypothesis 318 Introduction 319

What is Hypothesis Testing? 319

CONTENTS xxiii

Six-Step Procedure for Testing a Hypothesis 320

Step 1: State the Null Hypothesis (H0) and the Alternate Hypothesis (H1) 320 Step 2: Select a Level of Significance 321 Step 3: Select the Test Statistic 323 Step 4: Formulate the Decision Rule 323 Step 5: Make a Decision 324 Step 6: Interpret the Result 324

One-Tailed and Two-Tailed Hypothesis Tests 325

Hypothesis Testing for a Population Mean: Known Population Standard Deviation 327

A Two-Tailed Test 327 A One-Tailed Test 330

p-Value in Hypothesis Testing 331

EXERCISES 333

Hypothesis Testing for a Population Mean: Population Standard Deviation Unknown 334

EXERCISES 339

A Statistical Software Solution 340

EXERCISES 342

Type II Error 343

EXERCISES 346

Chapter Summary 347

Pronunciation Key 348

Chapter Exercises 348

Data Analytics 352

11 Two-Sample Tests of Hypothesis 353 Introduction 354

Two-Sample Tests of Hypothesis: Independent Samples 354

EXERCISES 359

Comparing Population Means with Unknown Population Standard Deviations 360

Two-Sample Pooled Test 360

EXERCISES 364

Unequal Population Standard Deviations 366

EXERCISES 369

Two-Sample Tests of Hypothesis: Dependent Samples 370

Comparing Dependent and Independent Samples 373

EXERCISES 375

Chapter Summary 377

Pronunciation Key 378

Chapter Exercises 378

Data Analytics 385

12 Analysis of Variance 386 Introduction 387

Comparing Two Population Variances 387

The F Distribution 387 Testing a Hypothesis of Equal Population Variances 388

EXERCISES 391

ANOVA: Analysis of Variance 392

ANOVA Assumptions 392 The ANOVA Test 394

EXERCISES 401

Inferences about Pairs of Treatment Means 402

EXERCISES 404

Two-Way Analysis of Variance 406

EXERCISES 411

Two-Way ANOVA with Interaction 412

Interaction Plots 412 Testing for Interaction 413 Hypothesis Tests for Interaction 415

EXERCISES 417

Chapter Summary 418

Pronunciation Key 420

Chapter Exercises 420

Data Analytics 429

Problems 431

Cases 433

Practice Test 434

13 Correlation and Linear Regression 436 Introduction 437

What is Correlation Analysis? 437

The Correlation Coefficient 440

EXERCISES 445

Testing the Significance of the Correlation Coefficient 447

EXERCISES 450

Regression Analysis 451

Least Squares Principle 451 Drawing the Regression Line 454

EXERCISES 457

Testing the Significance of the Slope 459

xxiv CONTENTS

EXERCISES 461

Evaluating a Regression Equation’s Ability to Predict 462

The Standard Error of Estimate 462 The Coefficient of Determination 463

EXERCISES 464

Relationships among the Correlation Coefficient, the Coefficient of Determination, and the Standard Error of Estimate 464

EXERCISES 466

Interval Estimates of Prediction 467

Assumptions Underlying Linear Regression 467 Constructing Confidence and Prediction Intervals 468

EXERCISES 471

Transforming Data 471

EXERCISES 474

Chapter Summary 475

Pronunciation Key 477

Chapter Exercises 477

Data Analytics 487

14 Multiple Regression Analysis 488 Introduction 489

Multiple Regression Analysis 489

EXERCISES 493

Evaluating a Multiple Regression Equation 495

The ANOVA Table 495 Multiple Standard Error of Estimate 496 Coefficient of Multiple Determination 497 Adjusted Coefficient of Determination 498

EXERCISES 499

Inferences in Multiple Linear Regression 499

Global Test: Testing the Multiple Regression Model 500 Evaluating Individual Regression Coefficients 502

EXERCISES 505

Evaluating the Assumptions of Multiple Regression 506

Linear Relationship 507 Variation in Residuals Same for Large and Small ŷ Values 508 Distribution of Residuals 509 Multicollinearity 509 Independent Observations 511

Qualitative Independent Variables 512

Regression Models with Interaction 515

Stepwise Regression 517

EXERCISES 519

Review of Multiple Regression 521

Chapter Summary 527

Pronunciation Key 528

Chapter Exercises 529

Data Analytics 539

Problems 541

Cases 542

Practice Test 543

15 Nonparametric Methods: NOMINAL LEVEL HYPOTHESIS TESTS 545

Introduction 546

Test a Hypothesis of a Population Proportion 546

EXERCISES 549

Two-Sample Tests about Proportions 550

EXERCISES 554

Goodness-of-Fit Tests: Comparing Observed and Expected Frequency Distributions 555

Hypothesis Test of Equal Expected Frequencies 555

EXERCISES 560

Hypothesis Test of Unequal Expected Frequencies 562

Limitations of Chi-Square 563

EXERCISES 565

Testing the Hypothesis That a Distribution is Normal 566

EXERCISES 569

Contingency Table Analysis 570

EXERCISES 573

Chapter Summary 574

Pronunciation Key 575

Chapter Exercises 576

Data Analytics 581

16 Nonparametric Methods: ANALYSIS OF ORDINAL DATA 582

Introduction 583

The Sign Test 583

CONTENTS xxv

EXERCISES 587

Using the Normal Approximation to the Binomial 588

EXERCISES 590

Testing a Hypothesis About a Median 590

EXERCISES 592

Wilcoxon Signed-Rank Test for Dependent Populations 592

EXERCISES 596

Wilcoxon Rank-Sum Test for Independent Populations 597

EXERCISES 601

Kruskal-Wallis Test: Analysis of Variance by Ranks 601

EXERCISES 605

Rank-Order Correlation 607

Testing the Significance of rs 609

EXERCISES 610

Chapter Summary 612

Pronunciation Key 613

Chapter Exercises 613

Data Analytics 616

Problems 618

Cases 619

Practice Test 619

17 Index Numbers 621 Introduction 622

Simple Index Numbers 622

Why Convert Data to Indexes? 625 Construction of Index Numbers 625

EXERCISES 627

Unweighted Indexes 628

Simple Average of the Price Indexes 628 Simple Aggregate Index 629

Weighted Indexes 629

Laspeyres Price Index 629 Paasche Price Index 631 Fisher’s Ideal Index 632

EXERCISES 633

Value Index 634

EXERCISES 635

Special-Purpose Indexes 636

Consumer Price Index 637 Producer Price Index 638 Dow Jones Industrial Average (DJIA) 638

EXERCISES 640

Consumer Price Index 640

Special Uses of the Consumer Price Index 641 Shifting the Base 644

EXERCISES 646

Chapter Summary 647

Chapter Exercises 648

Data Analytics 652

18 Time Series and Forecasting 653 Introduction 654

Components of a Time Series 654

Secular Trend 654 Cyclical Variation 655 Seasonal Variation 656 Irregular Variation 656

A Moving Average 657

Weighted Moving Average 660

EXERCISES 663

Linear Trend 663

Least Squares Method 665

EXERCISES 667

Nonlinear Trends 668

EXERCISES 669

Seasonal Variation 670

Determining a Seasonal Index 671

EXERCISES 676

Deseasonalizing Data 677

Using Deseasonalized Data to Forecast 678

EXERCISES 680

The Durbin-Watson Statistic 680

EXERCISES 686

Chapter Summary 686

Chapter Exercises 686

Data Analytics 693

Problems 695

Practice Test 696

19 Statistical Process Control and Quality Management 697 Introduction 698

A Brief History of Quality Control 698

Six Sigma 700

xxvi CONTENTS

Sources of Variation 701

Diagnostic Charts 702

Pareto Charts 702 Fishbone Diagrams 704

EXERCISES 705

Purpose and Types of Quality Control Charts 705

Control Charts for Variables 706 Range Charts 709

In-Control and Out-of-Control Situations 711

EXERCISES 712

Attribute Control Charts 713

p-Charts 713 c-Bar Charts 716

EXERCISES 718

Acceptance Sampling 719

EXERCISES 722

Chapter Summary 722

Pronunciation Key 723

Chapter Exercises 724

20 An Introduction to Decision Theory 728 Introduction 729

Elements of a Decision 729

Decision Making Under Conditions of Uncertainty 730

Payoff Table 730 Expected Payoff 731

EXERCISES 732

Opportunity Loss 733

EXERCISES 734

Expected Opportunity Loss 734

EXERCISES 735

Maximin, Maximax, and Minimax Regret Strategies 735

Value of Perfect Information 736

Sensitivity Analysis 737

EXERCISES 738

Decision Trees 739

Chapter Summary 740

Chapter Exercises 741

APPENDIXES 745

Appendix A: Data Sets 746

Appendix B: Tables 756

Appendix C: Software Commands 774

Appendix D: Answers to Odd-Numbered Chapter Exercises 785

Review Exercises 829

Solutions to Practice Tests 831

Appendix E: Answers to Self-Review 834

Glossary 847

Index 851

What is Statistics? 1

BEST BUY sells Fitbit wearable technology products that track a person’s physical activity and sleep quality. The Fitbit technology collects daily information on a person’s number of steps so that a person can track calories consumed. The information can be synced with a cell phone and displayed with a Fitbit app. Assume you know the daily number of Fitbit Flex 2 units sold last month at the Best Buy store in Collegeville, Pennsylvania. Describe a situation where the number of units sold is considered a sample. Illustrate a second situation where the number of units sold is considered a population. (See Exercise 11 and LO1-3.)

LEARNING OBJECTIVES When you have completed this chapter, you will be able to:

LO1-1 Explain why knowledge of statistics is important.

LO1-2 Define statistics and provide an example of how statistics is applied.

LO1-3 Differentiate between descriptive and inferential statistics.

LO1-4 Classify variables as qualitative or quantitative, and discrete or continuous.

LO1-5 Distinguish between nominal, ordinal, interval, and ratio levels of measurement.

LO1-6 List the values associated with the practice of statistics.

© Kelvin Wong/Shutterstock.com

2 CHAPTER 1

INTRODUCTION Suppose you work for a large company and your supervisor asks you to decide if a new version of a smartphone should be produced and sold. You start by thinking about the product’s innovations and new features. Then, you stop and realize the consequences of the decision. The product will need to make a profit so the pricing and the costs of production and distribution are all very important. The decision to introduce the product is based on many alternatives. So how will you know? Where do you start?

Without a long experience in the industry, beginning to develop an intelligence that will make you an expert is essential. You select three other people to work with and meet with them. The conversation focuses on what you need to know and what information and data you need. In your meeting, many questions are asked. How many competitors are already in the market? How are smartphones priced? What design features do com- petitors’ products have? What features does the market require? What do customers want in a smartphone? What do customers like about the existing products? The answers will be based on business intelligence consisting of data and information collected through customer surveys, engineering analysis, and market research. In the end, your presentation to support your decision regarding the introduction of a new smartphone is based on the statistics that you use to summarize and organize your data, the statistics that you use to compare the new product to existing products, and the statistics to esti- mate future sales, costs, and revenues. The statistics will be the focus of the conversa- tion that you will have with your supervisor about this very important decision.

As a decision maker, you will need to acquire and analyze data to support your decisions. The purpose of this text is to develop your knowledge of basic statistical techniques and methods and how to apply them to develop the business and personal intelligence that will help you make decisions.

WHY STUDY STATISTICS? If you look through your university catalogue, you will find that statistics is required for many college programs. As you investigate a future career in accounting, economics,

human resources, finance, business analytics, or other business area, you also will discover that statistics is required as part of these college pro- grams. So why is statistics a requirement in so many disciplines?

A major driver of the requirement for statistics knowledge is the tech- nologies available for capturing data. Examples include the technology that Google uses to track how Internet users access websites. As people use Google to search the Internet, Google records every search and then uses these data to sort and prioritize the results for future Internet searches. One recent estimate indicates that Google processes 20,000 terabytes of information per day. Big-box retailers like Target, Walmart, Kroger, and others scan every purchase and use the data to manage the distribution of products, to make decisions about marketing and sales, and to track daily and even hourly sales. Police departments collect and use data to provide city residents with maps that communicate informa- tion about crimes committed and their location. Every organization is col- lecting and using data to develop knowledge and intelligence that will help people make informed decisions, and to track the implementation of their decisions. The graphic to the left shows the amount of data gener- ated every minute (www.domo.com). A good working knowledge of sta- tistics is useful for summarizing and organizing data to provide information that is useful and supportive of decision making. Statistics is used to make valid comparisons and to predict the outcomes of decisions.

In summary, there are at least three reasons for studying statistics: (1) data are collected everywhere and require statistical knowledge to

LO1-1 Explain why knowledge of statistics is important.

© Gregor Schuster/Getty Images RF

WHAT IS STATISTICS? 3

make the information useful, (2) statistical techniques are used to make professional and personal decisions, and (3) no matter what your career, you will need a knowl- edge of statistics to understand the world and to be conversant in your career. An understanding of statistics and statistical method will help you make more effective personal and professional decisions.

WHAT IS MEANT BY STATISTICS? This question can be rephrased in two, subtly different ways: what are statistics and what is statistics? To answer the first question, a statistic is a number used to communi- cate a piece of information. Examples of statistics are:

• The inflation rate is 2%. • Your grade point average is 3.5. • The price of a new Tesla Model S sedan is $79,570.