Statistics for Managers Using Microsoft Excel 8th Edition Solution Manual
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Table of Contents
Teaching Tips...................................................................................................................................1
Chapter 1 Defining and Collecting Data............................................................................................... 39
Chapter 2 Organizing and Visualizing Variables ................................................................................. 46
Chapter 3 Numerical Descriptive Measures ..................................................................................... ..141
Chapter 4 Basic Probability ................................................................................................................ 183
Chapter 5 Discrete Probability Distributions ...................................................................................... 190
Chapter 6 The Normal Distribution and Other Continuous Distributions .......................................... 215
Chapter 7 Sampling Distributions....................................................................................................... 241
Chapter 8 Confidence Interval Estimation.......................................................................................... 261
Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests.................................................. 292
Chapter 10 Two-Sample Tests............................................................................................................. 337
Chapter 11 Analysis of Variance .......................................................................................................... 415
Chapter 12 Chi-Square and Nonparametric Tests ................................................................................ 441
Chapter 13 Simple Linear Regression .................................................................................................. 482
Chapter 14 Introduction to Multiple Regression .................................................................................. 521
Chapter 15 Multiple Regression Model Building ................................................................................. 584
Chapter 16 Time-Series Forecasting..................................................................................................... 641
Chapter 17 Getting Ready to Analyze Data in the Future .................................................................... 696
Chapter 18 Statistical Applications in Quality Management (Online) ................................................. 748
Chapter 19 Decision Making (Online).................................................................................................. 781
Online Sections .................................................................................................................. 820
Instructional Tips and Solutions for Digital Cases............................................................. 883
The Brynne Packaging Case .............................................................................................. 918
The CardioGood Fitness Case ........................................................................................... 920
Teaching Tips...................................................................................................................................1
Chapter 1 Defining and Collecting Data............................................................................................... 39
Chapter 2 Organizing and Visualizing Variables ................................................................................. 46
Chapter 3 Numerical Descriptive Measures ..................................................................................... ..141
Chapter 4 Basic Probability ................................................................................................................ 183
Chapter 5 Discrete Probability Distributions ...................................................................................... 190
Chapter 6 The Normal Distribution and Other Continuous Distributions .......................................... 215
Chapter 7 Sampling Distributions....................................................................................................... 241
Chapter 8 Confidence Interval Estimation.......................................................................................... 261
Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests.................................................. 292
Chapter 10 Two-Sample Tests............................................................................................................. 337
Chapter 11 Analysis of Variance .......................................................................................................... 415
Chapter 12 Chi-Square and Nonparametric Tests ................................................................................ 441
Chapter 13 Simple Linear Regression .................................................................................................. 482
Chapter 14 Introduction to Multiple Regression .................................................................................. 521
Chapter 15 Multiple Regression Model Building ................................................................................. 584
Chapter 16 Time-Series Forecasting..................................................................................................... 641
Chapter 17 Getting Ready to Analyze Data in the Future .................................................................... 696
Chapter 18 Statistical Applications in Quality Management (Online) ................................................. 748
Chapter 19 Decision Making (Online).................................................................................................. 781
Online Sections .................................................................................................................. 820
Instructional Tips and Solutions for Digital Cases............................................................. 883
The Brynne Packaging Case .............................................................................................. 918
The CardioGood Fitness Case ........................................................................................... 920
Table of Contents
Teaching Tips...................................................................................................................................1
Chapter 1 Defining and Collecting Data............................................................................................... 39
Chapter 2 Organizing and Visualizing Variables ................................................................................. 46
Chapter 3 Numerical Descriptive Measures ..................................................................................... ..141
Chapter 4 Basic Probability ................................................................................................................ 183
Chapter 5 Discrete Probability Distributions ...................................................................................... 190
Chapter 6 The Normal Distribution and Other Continuous Distributions .......................................... 215
Chapter 7 Sampling Distributions....................................................................................................... 241
Chapter 8 Confidence Interval Estimation.......................................................................................... 261
Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests.................................................. 292
Chapter 10 Two-Sample Tests............................................................................................................. 337
Chapter 11 Analysis of Variance .......................................................................................................... 415
Chapter 12 Chi-Square and Nonparametric Tests ................................................................................ 441
Chapter 13 Simple Linear Regression .................................................................................................. 482
Chapter 14 Introduction to Multiple Regression .................................................................................. 521
Chapter 15 Multiple Regression Model Building ................................................................................. 584
Chapter 16 Time-Series Forecasting..................................................................................................... 641
Chapter 17 Getting Ready to Analyze Data in the Future .................................................................... 696
Chapter 18 Statistical Applications in Quality Management (Online) ................................................. 748
Chapter 19 Decision Making (Online).................................................................................................. 781
Online Sections .................................................................................................................. 820
Instructional Tips and Solutions for Digital Cases............................................................. 883
The Brynne Packaging Case .............................................................................................. 918
The CardioGood Fitness Case ........................................................................................... 920
Teaching Tips...................................................................................................................................1
Chapter 1 Defining and Collecting Data............................................................................................... 39
Chapter 2 Organizing and Visualizing Variables ................................................................................. 46
Chapter 3 Numerical Descriptive Measures ..................................................................................... ..141
Chapter 4 Basic Probability ................................................................................................................ 183
Chapter 5 Discrete Probability Distributions ...................................................................................... 190
Chapter 6 The Normal Distribution and Other Continuous Distributions .......................................... 215
Chapter 7 Sampling Distributions....................................................................................................... 241
Chapter 8 Confidence Interval Estimation.......................................................................................... 261
Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests.................................................. 292
Chapter 10 Two-Sample Tests............................................................................................................. 337
Chapter 11 Analysis of Variance .......................................................................................................... 415
Chapter 12 Chi-Square and Nonparametric Tests ................................................................................ 441
Chapter 13 Simple Linear Regression .................................................................................................. 482
Chapter 14 Introduction to Multiple Regression .................................................................................. 521
Chapter 15 Multiple Regression Model Building ................................................................................. 584
Chapter 16 Time-Series Forecasting..................................................................................................... 641
Chapter 17 Getting Ready to Analyze Data in the Future .................................................................... 696
Chapter 18 Statistical Applications in Quality Management (Online) ................................................. 748
Chapter 19 Decision Making (Online).................................................................................................. 781
Online Sections .................................................................................................................. 820
Instructional Tips and Solutions for Digital Cases............................................................. 883
The Brynne Packaging Case .............................................................................................. 918
The CardioGood Fitness Case ........................................................................................... 920
The Choice Is Yours/More Descriptive Choices Follow-up Case .................................... 1043
The Clear Mountain State Student Surveys Case ............................................................. 1130
The Craybill Instrumentation Company Case.................................................................. 1230
The Managing Ashland MultiComm Services Case ......................................................... 1232
The Mountain States Potato Company Case .................................................................... 1287
The Sure Value Convenience Stores Case........................................................................ 1296
The Clear Mountain State Student Surveys Case ............................................................. 1130
The Craybill Instrumentation Company Case.................................................................. 1230
The Managing Ashland MultiComm Services Case ......................................................... 1232
The Mountain States Potato Company Case .................................................................... 1287
The Sure Value Convenience Stores Case........................................................................ 1296
Preface
The first part of the Instructor’s Solutions Manual contains our educational philosophy and teaching tips
for each chapter of the text. Solutions to End-of-Section Problems and Chapter Review Problems in each
chapter follow. Instructional tips and solutions for the digital cases are included next. Answers to the
Brynne Packaging Case, the CardioGood Fitness Case, the Choice Is Yours/More Descriptive Choices
Follow-up Case, the Clear Mountain State Student Surveys Case, the Craybill Instrumentation Company
Case, the Managing Ashland MultiComm Services Case, the Mountain States Potato Company Case and
the Sure Value Convenience Stores Case are included last.
The purpose of this Instructor’s Solutions Manual is to facilitate grading of assignments or exams by
instructors and/or teaching assistants. Screen shots using output from PHStat are integrated throughout.
Most of the problems are solved using PHStat. To present the steps involved in solving a problem, some
intermediate numerical results are presented accurate to only a reasonable number of significant digits.
Hence, instructors are reminded that the final results presented in this manual that are obtained using
PHStat can sometimes be different from those obtained with a hand calculator computed using the
intermediate values due to rounding.
The first part of the Instructor’s Solutions Manual contains our educational philosophy and teaching tips
for each chapter of the text. Solutions to End-of-Section Problems and Chapter Review Problems in each
chapter follow. Instructional tips and solutions for the digital cases are included next. Answers to the
Brynne Packaging Case, the CardioGood Fitness Case, the Choice Is Yours/More Descriptive Choices
Follow-up Case, the Clear Mountain State Student Surveys Case, the Craybill Instrumentation Company
Case, the Managing Ashland MultiComm Services Case, the Mountain States Potato Company Case and
the Sure Value Convenience Stores Case are included last.
The purpose of this Instructor’s Solutions Manual is to facilitate grading of assignments or exams by
instructors and/or teaching assistants. Screen shots using output from PHStat are integrated throughout.
Most of the problems are solved using PHStat. To present the steps involved in solving a problem, some
intermediate numerical results are presented accurate to only a reasonable number of significant digits.
Hence, instructors are reminded that the final results presented in this manual that are obtained using
PHStat can sometimes be different from those obtained with a hand calculator computed using the
intermediate values due to rounding.
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Teaching Tips for
Statistics for Managers using Microsoft® Excel 8th Edition,
Global Edition
Our Starting Point
Over a generation ago, advances in “data processing” led to new business opportunities as first
centralized and then desktop computing proliferated. The Information Age was born. Computer
science became much more than just an adjunct to a mathematics curriculum, and whole new
fields of studies, such as computer information systems, emerged.
More recently, further advances in information technologies have combined with data
analysis techniques to create new opportunities in what is more data science than data processing
or computer science. The world of business statistics has grown larger, bumping into other
disciplines. And, in a reprise of something that occurred a generation ago, new fields of study,
this time with names such as informatics, data analytics, and decision science, have emerged.
This time of change makes what is taught in business statistics and how it is taught all the
more critical. These new fields of study all share statistics as a foundation for further learning.
We are accustomed to thinking about change, as seeking ways to continuously improve the
teaching of business statistics have always guided our efforts. We actively participate in Decision
Sciences Institute (DSI), American Statistical Association (ASA), and Making Statistics More
Effective in Schools and Business (MSMESB) conferences. We use the ASA’s Guidelines for
Assessment and Instruction (GAISE) reports and combine them with our experiences teaching
business statistics to a diverse student body at several large universities.
What to teach and how to teach it are particularly significant questions to ask during a time of
change. As an author team, we bring a unique collection of experiences that we believe helps us
find the proper perspective in balancing the old and the new. Our lead author, David M. Levine,
was the first educator, along with Mark L. Berenson, to create a business statistics textbook that
Statistics for Managers using Microsoft® Excel 8th Edition,
Global Edition
Our Starting Point
Over a generation ago, advances in “data processing” led to new business opportunities as first
centralized and then desktop computing proliferated. The Information Age was born. Computer
science became much more than just an adjunct to a mathematics curriculum, and whole new
fields of studies, such as computer information systems, emerged.
More recently, further advances in information technologies have combined with data
analysis techniques to create new opportunities in what is more data science than data processing
or computer science. The world of business statistics has grown larger, bumping into other
disciplines. And, in a reprise of something that occurred a generation ago, new fields of study,
this time with names such as informatics, data analytics, and decision science, have emerged.
This time of change makes what is taught in business statistics and how it is taught all the
more critical. These new fields of study all share statistics as a foundation for further learning.
We are accustomed to thinking about change, as seeking ways to continuously improve the
teaching of business statistics have always guided our efforts. We actively participate in Decision
Sciences Institute (DSI), American Statistical Association (ASA), and Making Statistics More
Effective in Schools and Business (MSMESB) conferences. We use the ASA’s Guidelines for
Assessment and Instruction (GAISE) reports and combine them with our experiences teaching
business statistics to a diverse student body at several large universities.
What to teach and how to teach it are particularly significant questions to ask during a time of
change. As an author team, we bring a unique collection of experiences that we believe helps us
find the proper perspective in balancing the old and the new. Our lead author, David M. Levine,
was the first educator, along with Mark L. Berenson, to create a business statistics textbook that
Loading page 5...
discussed using statistical software and incorporated “computer output” as illustrations—just the
first of many teaching and curricular innovations in his many years of teaching business statistics.
Our second author, David F. Stephan, developed courses and teaching methods in computer
information systems and digital media during the information revolution, creating, and then
teaching in, one of the first personal computer classrooms in a large school of business along the
way. Early in his career, he introduced spreadsheet applications to a business statistics faculty
audience that included David Levine, an introduction that would eventually led to the first edition
of this textbook. Our newest co-author, Kathryn A. Szabat, has provided statistical advice to
various business and non-business communities. Her background in statistics and operations
research and her experiences interacting with professionals in practice have guided her, as
departmental chair, in developing a new, interdisciplinary academic department, Business
Systems and Analytics, in response to the technology- and data-driven changes in business today.
All three of us benefit from our many years teaching undergraduate business subjects and the
diversity of interests and efforts of our past co-authors, Mark Berenson and Timothy Krehbiel.
Two of us (Stephan and Szabat) also benefit from formal training and background in educational
methods and instructional design.
Educational Philosophy
As in prior editions of Statistics for Managers Using Microsoft Excel, we are guided by these
key learning principles:
1. Help students see the relevance of statistics to their own careers by providing examples
drawn from the functional areas in which they may be specializing. Students need a
frame of reference when learning statistics, especially when statistics is not their major. That
frame of reference for business students should be the functional areas of business, such as
accounting, finance, information systems, management, and marketing. Each statistics topic
first of many teaching and curricular innovations in his many years of teaching business statistics.
Our second author, David F. Stephan, developed courses and teaching methods in computer
information systems and digital media during the information revolution, creating, and then
teaching in, one of the first personal computer classrooms in a large school of business along the
way. Early in his career, he introduced spreadsheet applications to a business statistics faculty
audience that included David Levine, an introduction that would eventually led to the first edition
of this textbook. Our newest co-author, Kathryn A. Szabat, has provided statistical advice to
various business and non-business communities. Her background in statistics and operations
research and her experiences interacting with professionals in practice have guided her, as
departmental chair, in developing a new, interdisciplinary academic department, Business
Systems and Analytics, in response to the technology- and data-driven changes in business today.
All three of us benefit from our many years teaching undergraduate business subjects and the
diversity of interests and efforts of our past co-authors, Mark Berenson and Timothy Krehbiel.
Two of us (Stephan and Szabat) also benefit from formal training and background in educational
methods and instructional design.
Educational Philosophy
As in prior editions of Statistics for Managers Using Microsoft Excel, we are guided by these
key learning principles:
1. Help students see the relevance of statistics to their own careers by providing examples
drawn from the functional areas in which they may be specializing. Students need a
frame of reference when learning statistics, especially when statistics is not their major. That
frame of reference for business students should be the functional areas of business, such as
accounting, finance, information systems, management, and marketing. Each statistics topic
Loading page 6...
needs to be presented in an applied context related to at least one of these functional areas.
The focus in teaching each topic should be on its application in business, the interpretation of
results, the evaluation of the assumptions, and the discussion of what should be done if the
assumptions are violated.
2. Emphasize interpretation of statistical results over mathematical computation.
Introductory business statistics courses should recognize the growing need to interpret
statistical results that computerized processes create. This makes the interpretation of results
more important than knowing how to execute the tedious hand calculations required to
produce them.
3. Give students ample practice in understanding how to apply statistics to business. Both
classroom examples and homework exercises should involve actual or realistic data as much
as possible. Students should work with data sets, both small and large, and be encouraged to
look beyond the statistical analysis of data to the interpretation of results in a managerial
context.
4. Familiarize students with how to use statistical software to assist business decision-
making. Introductory business statistics courses should recognize that programs with
statistical functions are commonly found on a business decision maker’s desktop computer.
Integrating statistical software into all aspects of an introductory statistics course allows the
course to focus on interpretation of results instead of computations (see point 2).
5. Provide clear instructions to students for using statistical applications. Books should
explain clearly how to use programs such as Microsoft Excel with the study of statistics,
without having those instructions dominate the book or distract from the learning of statistical
concepts.
The focus in teaching each topic should be on its application in business, the interpretation of
results, the evaluation of the assumptions, and the discussion of what should be done if the
assumptions are violated.
2. Emphasize interpretation of statistical results over mathematical computation.
Introductory business statistics courses should recognize the growing need to interpret
statistical results that computerized processes create. This makes the interpretation of results
more important than knowing how to execute the tedious hand calculations required to
produce them.
3. Give students ample practice in understanding how to apply statistics to business. Both
classroom examples and homework exercises should involve actual or realistic data as much
as possible. Students should work with data sets, both small and large, and be encouraged to
look beyond the statistical analysis of data to the interpretation of results in a managerial
context.
4. Familiarize students with how to use statistical software to assist business decision-
making. Introductory business statistics courses should recognize that programs with
statistical functions are commonly found on a business decision maker’s desktop computer.
Integrating statistical software into all aspects of an introductory statistics course allows the
course to focus on interpretation of results instead of computations (see point 2).
5. Provide clear instructions to students for using statistical applications. Books should
explain clearly how to use programs such as Microsoft Excel with the study of statistics,
without having those instructions dominate the book or distract from the learning of statistical
concepts.
Loading page 7...
First Things First
In a time of change, you can never know exactly what knowledge and background students bring
into an introductory business statistics classroom. Add that to the need to curb the fear factor
about learning statistics that so many students begin with, and there’s a lot to cover even before
you teach your first statistical concept.
We created “First Things First” to meet this challenge. This unit sets the context for
explaining what statistics is (not what students may think!) while ensuring that all students share
an understanding of the forces that make learning business statistics critically important today.
Especially designed for instructors teaching with course management tools, including those
teaching hybrid or online courses, “First Things First” has been developed to be posted online or
otherwise distributed before the first class section begins and is available from the download page
for this book that is discussed in Appendix Section C.1.
We would argue that the most important class is the first class. First impressions are critically
important. You have the opportunity to set the tone to create a new impression that the course will
be important to their business education. Make the following points:
• This course is not a math course.
• State that you will be learning analytical skills for making business decisions.
• Explain that the focus will be on how statistics can be used in the functional areas of
business.
This book uses a systematic approach for meeting a business objective or solving a business
problem. This approach goes across all the topics in the book and most importantly can be used as
a framework in real world situations when students graduate. The approach has the acronym
DCOVA, which stands for Define, Collect, Organize, Visualize, and Analyze.
• Define the business objective or problem to be solved and then define the variables to be
studied.
• Collect the data from appropriate sources
• Organize the data
In a time of change, you can never know exactly what knowledge and background students bring
into an introductory business statistics classroom. Add that to the need to curb the fear factor
about learning statistics that so many students begin with, and there’s a lot to cover even before
you teach your first statistical concept.
We created “First Things First” to meet this challenge. This unit sets the context for
explaining what statistics is (not what students may think!) while ensuring that all students share
an understanding of the forces that make learning business statistics critically important today.
Especially designed for instructors teaching with course management tools, including those
teaching hybrid or online courses, “First Things First” has been developed to be posted online or
otherwise distributed before the first class section begins and is available from the download page
for this book that is discussed in Appendix Section C.1.
We would argue that the most important class is the first class. First impressions are critically
important. You have the opportunity to set the tone to create a new impression that the course will
be important to their business education. Make the following points:
• This course is not a math course.
• State that you will be learning analytical skills for making business decisions.
• Explain that the focus will be on how statistics can be used in the functional areas of
business.
This book uses a systematic approach for meeting a business objective or solving a business
problem. This approach goes across all the topics in the book and most importantly can be used as
a framework in real world situations when students graduate. The approach has the acronym
DCOVA, which stands for Define, Collect, Organize, Visualize, and Analyze.
• Define the business objective or problem to be solved and then define the variables to be
studied.
• Collect the data from appropriate sources
• Organize the data
Loading page 8...
• Visualize the data by developing charts
• Analyze the data by using statistical methods to reach conclusions.
To this, you can add C for Communicate which is critically important
You can begin by emphasizing the importance of defining your objective or problem. Then,
discuss the importance of operational definitions of variables to be considered and define
variable, data, and statistics.
Just as computers are used not just in the computer course, students need to know that
statistics is used not just in the statistics course. This leads you to a discussion of business
analytics in which data is used to make decisions. Make the point that analytics should be part of
the competitive strategy of every organization especially since “big data” meaning data collected
in huge volumes at very fast rates. needs to be analyzed.
Inform the students that there is an Excel Guide at the end of each chapter. Strongly
encourage or require students to read the Excel Guide at the end of this chapter so that they will
be ready to use Excel with this book.
• Analyze the data by using statistical methods to reach conclusions.
To this, you can add C for Communicate which is critically important
You can begin by emphasizing the importance of defining your objective or problem. Then,
discuss the importance of operational definitions of variables to be considered and define
variable, data, and statistics.
Just as computers are used not just in the computer course, students need to know that
statistics is used not just in the statistics course. This leads you to a discussion of business
analytics in which data is used to make decisions. Make the point that analytics should be part of
the competitive strategy of every organization especially since “big data” meaning data collected
in huge volumes at very fast rates. needs to be analyzed.
Inform the students that there is an Excel Guide at the end of each chapter. Strongly
encourage or require students to read the Excel Guide at the end of this chapter so that they will
be ready to use Excel with this book.
Loading page 9...
Chapter 1
You need to continue the discussion of the Define task by establishing the types of
variables. Be sure to discuss the different types carefully since the ability to distinguish between
categorical and numerical data will be crucial later in the course. Go over examples of each type
of variable and have students provide examples of each type. Then, if you wish, you can cover the
different measurement scales.
Then move on to the C of the DCOVA approach, collecting data. Mention the different
sources of data and make sure to cover the fact that data often needs to be cleaned of errors.
Then, you could spend some time discussing sampling, you may want to take a bit more time and
discuss the types of survey sampling methods and issues involved with survey sampling results.
The Consider This essay discusses the important issue of the use of Web-based surveys.
The chapter also introduces two continuing cases related to Managing Ashland
MultiComm Services and CardioGood Fitness that appear at the end of many chapters. The
Digital cases are introduced in this chapter also. In these cases, students visit Web sites
related to companies and issues raised in the Using Statistics scenarios that start each
chapter. The goal of the Digital cases is for students to develop skills needed to identify
misuses of statistical information. As would be the situation with many real world cases,
in Digital cases, students often need to sift through claims and assorted information in
order to discover the data most relevant to a case task. They will then have to examine
whether the conclusions and claims are supported by the data. (Instructional tips for using
the Managing Ashland MultiComm Services and Digital cases and solutions to the
Managing Ashland MultiComm Services and Digital cases are included in this Instructor’s
Solutions Manual.).
Make sure that students read the Excel Guide at the end of each chapter. Ways of
Working With Excel on pages 7 and 8 explains the different type of Excel instructions.
The Workbook instructions provide step-by-step instructions and live worksheets that
automatically update when data changes. The PHStat2 add-in instructions provide
instructions for using the PHStat2 add-in. Analysis ToolPak instructions provide
instructions for using the Analysis ToolPak, the Excel add-in package that is included
with many versions of Excel.
You need to continue the discussion of the Define task by establishing the types of
variables. Be sure to discuss the different types carefully since the ability to distinguish between
categorical and numerical data will be crucial later in the course. Go over examples of each type
of variable and have students provide examples of each type. Then, if you wish, you can cover the
different measurement scales.
Then move on to the C of the DCOVA approach, collecting data. Mention the different
sources of data and make sure to cover the fact that data often needs to be cleaned of errors.
Then, you could spend some time discussing sampling, you may want to take a bit more time and
discuss the types of survey sampling methods and issues involved with survey sampling results.
The Consider This essay discusses the important issue of the use of Web-based surveys.
The chapter also introduces two continuing cases related to Managing Ashland
MultiComm Services and CardioGood Fitness that appear at the end of many chapters. The
Digital cases are introduced in this chapter also. In these cases, students visit Web sites
related to companies and issues raised in the Using Statistics scenarios that start each
chapter. The goal of the Digital cases is for students to develop skills needed to identify
misuses of statistical information. As would be the situation with many real world cases,
in Digital cases, students often need to sift through claims and assorted information in
order to discover the data most relevant to a case task. They will then have to examine
whether the conclusions and claims are supported by the data. (Instructional tips for using
the Managing Ashland MultiComm Services and Digital cases and solutions to the
Managing Ashland MultiComm Services and Digital cases are included in this Instructor’s
Solutions Manual.).
Make sure that students read the Excel Guide at the end of each chapter. Ways of
Working With Excel on pages 7 and 8 explains the different type of Excel instructions.
The Workbook instructions provide step-by-step instructions and live worksheets that
automatically update when data changes. The PHStat2 add-in instructions provide
instructions for using the PHStat2 add-in. Analysis ToolPak instructions provide
instructions for using the Analysis ToolPak, the Excel add-in package that is included
with many versions of Excel.
Loading page 10...
Chapter 2
This chapter moves on to the organizing and visualizing steps of the DCOVA
framework. If you are going to collect sample data to use in Chapters 2 and 3, you can
illustrate sampling by conducting a survey of students in your class. Ask each student to
collect his or her own personal data concerning the time it takes to get ready to go to class
in the morning or the time it takes to get to school or home from school. First, ask the
students to write down a definition of how they plan to measure this time. Then, collect
the various answers and read them to the class. Then, a single definition could be
provided (such as the time to get ready is the time measured from when you get out of
bed to when you leave your home, recorded to the nearest minute). In the next class,
select a random sample of students and use the data collected (depending on the sample
size) in class when Chapters 2 and 3 are discussed.
Then, move on to the Organize step that involves setting up your data in an Excel
worksheet and develop tables to help you prepare charts and analyze your data. Begin
your discussion for categorical data with the example on p. 34 concerning how people
pay for purchases and other transactions. Show the summary table and then if you wish,
explain that you can sometimes organize the data into a two-way table that has one
variable in the row and another in the column.
Continue with organizing data (but now for numerical data) by referring to the
cost of a restaurant meal on p. 38. Show the simple ordered array and how a frequency
distribution, percentage distribution, or cumulative distribution can summarize the raw
data in a way that is more useful.
Now you are ready to tackle the Visualize step. A good way of starting this part of
the chapter is to display the following quote.
"A picture is worth a thousand words."
Students will almost certainly be familiar with Microsoft® Word and may have already used
Excel to construct charts that they have pasted into Word documents. Now you will be using
Excel to construct many different types of charts. Return to the purchase payment data previously
discussed and illustrate how a bar chart, pie, and doughnut chart can be constructed using Excel.
Mention the advantages and disadvantages of each chart. A good example is to show the data on
This chapter moves on to the organizing and visualizing steps of the DCOVA
framework. If you are going to collect sample data to use in Chapters 2 and 3, you can
illustrate sampling by conducting a survey of students in your class. Ask each student to
collect his or her own personal data concerning the time it takes to get ready to go to class
in the morning or the time it takes to get to school or home from school. First, ask the
students to write down a definition of how they plan to measure this time. Then, collect
the various answers and read them to the class. Then, a single definition could be
provided (such as the time to get ready is the time measured from when you get out of
bed to when you leave your home, recorded to the nearest minute). In the next class,
select a random sample of students and use the data collected (depending on the sample
size) in class when Chapters 2 and 3 are discussed.
Then, move on to the Organize step that involves setting up your data in an Excel
worksheet and develop tables to help you prepare charts and analyze your data. Begin
your discussion for categorical data with the example on p. 34 concerning how people
pay for purchases and other transactions. Show the summary table and then if you wish,
explain that you can sometimes organize the data into a two-way table that has one
variable in the row and another in the column.
Continue with organizing data (but now for numerical data) by referring to the
cost of a restaurant meal on p. 38. Show the simple ordered array and how a frequency
distribution, percentage distribution, or cumulative distribution can summarize the raw
data in a way that is more useful.
Now you are ready to tackle the Visualize step. A good way of starting this part of
the chapter is to display the following quote.
"A picture is worth a thousand words."
Students will almost certainly be familiar with Microsoft® Word and may have already used
Excel to construct charts that they have pasted into Word documents. Now you will be using
Excel to construct many different types of charts. Return to the purchase payment data previously
discussed and illustrate how a bar chart, pie, and doughnut chart can be constructed using Excel.
Mention the advantages and disadvantages of each chart. A good example is to show the data on
Loading page 11...
incomplete ATM transactions on p. 49 and how the Pareto chart enables you to focus on the vital
few categories. If time permits, you can discuss the side-by-side bar chart for a contingency table.
To examine charts for numerical variables you can either use the restaurant data
previously mentioned, the retirement funds data, or data that you have collected from your class.
You may want to begin with a simple stem-and-leaf display that both organizes the data and
shows a bar type chart. Then move on to the histogram and the various polygons, pointing out the
advantages and disadvantages of each.
If time permits, you can discuss the scatter plot and the time-series plot for two numerical
variables. Otherwise, you can wait until you get to regression analysis. If you cover the time
series plot, you might also want to mention sparklines that are discussed in Section 2.6.
Also, if possible, you may want to discuss how multidimensional tables allow you to drill
down to individual cells of the table. You can follow this with further discussion of PivotTables
and Excel slicers that enable you to see panels for each variable being studied.
If the opportunity is available, we believe that it is worth the time to cover Section 2.7 on
Challenges in Organizing and Visualizing Variables. This is a topic that students very much enjoy
since it allows for a great deal of classroom interaction. After discussing the fundamental
principles of good graphs, try to illustrate some of the improper displays shown in Figures 2.26 –
2.28. Ask students what is “bad” about these figures. Follow up with a homework assignment
involving Problems 2.69 – 2.73 (USA Today is a great source).
You will find that the chapter review problems provide large data sets with numerous
variables. Report writing exercises provide the opportunity for students to integrate written and or
oral presentation with the statistics they have learned.
The Managing Ashland MultiComm Services case enables students to examine the use of
statistics in an actual business environment. The Digital case refers to the EndRun Financial
Services and claims that have been made. The CardioGood Fitness case focuses on developing a
customer profile for a market research team. The Choice Is Yours Follow-up expands on the
chapter discussion of the mutual funds data. The Clear Mountain State Student Survey provides
data collected from a sample of undergraduate students.
The Excel Guide for this and the remaining chapters are organized according to the
sections of the chapter. It is quite extensive since it covers both organizing and visualizing many
different graphs. The Excel Guide includes instructions for Workbook, PHStat2, and the Analysis
ToolPak.
few categories. If time permits, you can discuss the side-by-side bar chart for a contingency table.
To examine charts for numerical variables you can either use the restaurant data
previously mentioned, the retirement funds data, or data that you have collected from your class.
You may want to begin with a simple stem-and-leaf display that both organizes the data and
shows a bar type chart. Then move on to the histogram and the various polygons, pointing out the
advantages and disadvantages of each.
If time permits, you can discuss the scatter plot and the time-series plot for two numerical
variables. Otherwise, you can wait until you get to regression analysis. If you cover the time
series plot, you might also want to mention sparklines that are discussed in Section 2.6.
Also, if possible, you may want to discuss how multidimensional tables allow you to drill
down to individual cells of the table. You can follow this with further discussion of PivotTables
and Excel slicers that enable you to see panels for each variable being studied.
If the opportunity is available, we believe that it is worth the time to cover Section 2.7 on
Challenges in Organizing and Visualizing Variables. This is a topic that students very much enjoy
since it allows for a great deal of classroom interaction. After discussing the fundamental
principles of good graphs, try to illustrate some of the improper displays shown in Figures 2.26 –
2.28. Ask students what is “bad” about these figures. Follow up with a homework assignment
involving Problems 2.69 – 2.73 (USA Today is a great source).
You will find that the chapter review problems provide large data sets with numerous
variables. Report writing exercises provide the opportunity for students to integrate written and or
oral presentation with the statistics they have learned.
The Managing Ashland MultiComm Services case enables students to examine the use of
statistics in an actual business environment. The Digital case refers to the EndRun Financial
Services and claims that have been made. The CardioGood Fitness case focuses on developing a
customer profile for a market research team. The Choice Is Yours Follow-up expands on the
chapter discussion of the mutual funds data. The Clear Mountain State Student Survey provides
data collected from a sample of undergraduate students.
The Excel Guide for this and the remaining chapters are organized according to the
sections of the chapter. It is quite extensive since it covers both organizing and visualizing many
different graphs. The Excel Guide includes instructions for Workbook, PHStat2, and the Analysis
ToolPak.
Loading page 12...
Chapter 3
This chapter on descriptive numerical statistical measures represents the initial
presentation of statistical symbols in the text. Students who need to review arithmetic and
algebraic concepts may wish to refer to Appendix A for a quick review or to appropriate texts
(see www.pearson.com) or videos (www.videoaidedinstruction.com). Once again, as with the
tables and charts constructed for numerical data, it is useful to provide an interesting set of data
for classroom discussion. If a sample of students was selected earlier in the semester and data
concerning student time to get ready or commuting time was collected (see Chapters 1 and 2), use
these data in developing the numerous descriptive summary measures in this chapter. (If they
have not been developed, use other data for classroom illustration.)
Discussion of the chapter begins with the property of central tendency. We have found
that almost all students are familiar with the arithmetic mean (which they know as the average)
and most students are familiar with the median. A good way to begin is to compute the mean for
your classroom example. Emphasize the effect of extreme values on the arithmetic mean and
point out that the mean is like the center of a seesaw -- a balance point. Note that you will return
to this concept later when you discuss the variance and the standard deviation. You might want to
introduce summation notation at this point and express the arithmetic mean in formula notation as
in Equation (3.1). (Alternatively, you could wait until you cover the variance and standard
deviation.) A classroom example in which summation notation is reviewed is usually worthwhile.
Remind the students again that Appendix A includes a review of arithmetic and algebra and
summation notation [or refer them to other text sources such as those found at www.pearson.com
or videos (see www. videoaidedinstruction.com)].
The next statistic to compute is the median. Be sure to remind the students that the
median as a measure of position must have all the values ranked in order from lowest to highest.
Be sure to have the students compare the arithmetic mean to the median and explain that this tells
us something about another property of data (skewness). Following the median, the mode can be
briefly discussed. Once again, have the students compare this result to those of the arithmetic
mean and median for your data set. If time permits, you can also discuss the geometric mean
which is heavily used in finance.
The completion of the discussion of central tendency leads to the second characteristic of
data, variability. Mention that all measures of variation have several things in common: (1) they
can never be negative, (2) they will be equal to 0 when all items are the same, (3) they will be
small when there isn't much variation, and (4) they will be large when there is a great deal of
variation.
This chapter on descriptive numerical statistical measures represents the initial
presentation of statistical symbols in the text. Students who need to review arithmetic and
algebraic concepts may wish to refer to Appendix A for a quick review or to appropriate texts
(see www.pearson.com) or videos (www.videoaidedinstruction.com). Once again, as with the
tables and charts constructed for numerical data, it is useful to provide an interesting set of data
for classroom discussion. If a sample of students was selected earlier in the semester and data
concerning student time to get ready or commuting time was collected (see Chapters 1 and 2), use
these data in developing the numerous descriptive summary measures in this chapter. (If they
have not been developed, use other data for classroom illustration.)
Discussion of the chapter begins with the property of central tendency. We have found
that almost all students are familiar with the arithmetic mean (which they know as the average)
and most students are familiar with the median. A good way to begin is to compute the mean for
your classroom example. Emphasize the effect of extreme values on the arithmetic mean and
point out that the mean is like the center of a seesaw -- a balance point. Note that you will return
to this concept later when you discuss the variance and the standard deviation. You might want to
introduce summation notation at this point and express the arithmetic mean in formula notation as
in Equation (3.1). (Alternatively, you could wait until you cover the variance and standard
deviation.) A classroom example in which summation notation is reviewed is usually worthwhile.
Remind the students again that Appendix A includes a review of arithmetic and algebra and
summation notation [or refer them to other text sources such as those found at www.pearson.com
or videos (see www. videoaidedinstruction.com)].
The next statistic to compute is the median. Be sure to remind the students that the
median as a measure of position must have all the values ranked in order from lowest to highest.
Be sure to have the students compare the arithmetic mean to the median and explain that this tells
us something about another property of data (skewness). Following the median, the mode can be
briefly discussed. Once again, have the students compare this result to those of the arithmetic
mean and median for your data set. If time permits, you can also discuss the geometric mean
which is heavily used in finance.
The completion of the discussion of central tendency leads to the second characteristic of
data, variability. Mention that all measures of variation have several things in common: (1) they
can never be negative, (2) they will be equal to 0 when all items are the same, (3) they will be
small when there isn't much variation, and (4) they will be large when there is a great deal of
variation.
Loading page 13...
The first measure of variability to consider is the simplest one, the range. Be sure to point
out that the range only provides information about the extremes, not about the distribution
between the extremes. Point out that the range lacks one important ingredient, the ability to take
into account each data value. Bring up the idea of computing the differences around the mean, but
then return to the fact that as the balance point of the seesaw, these differences add up to zero. At
that point, ask the students what they can do mathematically to remove the negative sign for some
of the values. Most likely, they will answer by telling you to square them (although someone
may realize that the absolute value could be taken). Next, you may want to define the squared
differences as a sum of squares. Now you need to have the students realize that the number of
values being considered affects the magnitude of the sum of squared differences. Therefore, it
makes sense to divide by the number of values and compute a measure called the variance. If a
population is involved, you divide by N, the population size, but if you are using a sample, you
divide by n - 1, to make the sample result a better estimate of the population variance. You can
finish the development of variation by noting that since the variance is in squared units, you need
to take the square root to compute the standard deviation.
Another measure of variation that can be discussed is the coefficient of variation. Be sure
to illustrate the usefulness of this as a measure of relative variation by using an example in which
two data sets have vastly different standard deviations, but also vastly different means. A good
example is one that involves the volatility of stock prices. Point out that the variation of the price
should be considered in the context of the magnitude of the arithmetic mean. The final measure of
variation is the Z score. Point out that this provides a measure of variation in standard deviation
units. You can also say that you will return to Z scores in Chapter 6 when the normal distribution
will be discussed.
You are now ready to move on to the third characteristic of data, shape. Be sure to clearly
define and illustrate both symmetric and skewed distributions by comparing the mean and
median. You may also want to briefly mention the property of kurtosis which is the relative
concentration of values in the center of the distribution as compared to the tails. This statistic is
provided by Excel through an Excel function or the Analysis Toolpak.
Once these three characteristics have been discussed, you are ready to show how they can
be computed using Excel.
Now that these measures are understood, you can further explore data by computing the
quartiles, the interquartile range, the five number summary, and constructing a boxplot. You
begin by determining the quartiles. Reference here can be made to the standardized exams that
students have taken, and the quantile scores that they have received (97th percentile, 48th
out that the range only provides information about the extremes, not about the distribution
between the extremes. Point out that the range lacks one important ingredient, the ability to take
into account each data value. Bring up the idea of computing the differences around the mean, but
then return to the fact that as the balance point of the seesaw, these differences add up to zero. At
that point, ask the students what they can do mathematically to remove the negative sign for some
of the values. Most likely, they will answer by telling you to square them (although someone
may realize that the absolute value could be taken). Next, you may want to define the squared
differences as a sum of squares. Now you need to have the students realize that the number of
values being considered affects the magnitude of the sum of squared differences. Therefore, it
makes sense to divide by the number of values and compute a measure called the variance. If a
population is involved, you divide by N, the population size, but if you are using a sample, you
divide by n - 1, to make the sample result a better estimate of the population variance. You can
finish the development of variation by noting that since the variance is in squared units, you need
to take the square root to compute the standard deviation.
Another measure of variation that can be discussed is the coefficient of variation. Be sure
to illustrate the usefulness of this as a measure of relative variation by using an example in which
two data sets have vastly different standard deviations, but also vastly different means. A good
example is one that involves the volatility of stock prices. Point out that the variation of the price
should be considered in the context of the magnitude of the arithmetic mean. The final measure of
variation is the Z score. Point out that this provides a measure of variation in standard deviation
units. You can also say that you will return to Z scores in Chapter 6 when the normal distribution
will be discussed.
You are now ready to move on to the third characteristic of data, shape. Be sure to clearly
define and illustrate both symmetric and skewed distributions by comparing the mean and
median. You may also want to briefly mention the property of kurtosis which is the relative
concentration of values in the center of the distribution as compared to the tails. This statistic is
provided by Excel through an Excel function or the Analysis Toolpak.
Once these three characteristics have been discussed, you are ready to show how they can
be computed using Excel.
Now that these measures are understood, you can further explore data by computing the
quartiles, the interquartile range, the five number summary, and constructing a boxplot. You
begin by determining the quartiles. Reference here can be made to the standardized exams that
students have taken, and the quantile scores that they have received (97th percentile, 48th
Loading page 14...
percentile, 12th percentile, etc.). Explain that the 1st and 3rd quartiles are merely two special
quantiles -- the 25th and 75th, that unlike the median (the 2nd quartile), are not at the center of the
distribution. Once the quartiles have been computed, the interquartile range can be determined.
Mention that the interquartile range computes the variation in the center of the distribution as
compared to the difference in the extremes computed by the range.
You can then discuss the five-number summary of minimum value, first quartile, median,
third quartile, and maximum value. Then, you construct the boxplot. Present this plot from the
perspective of serving as a tool for determining the location, variability, and symmetry of a
distribution by visual inspection, and as a graphical tool for comparing the distribution of several
groups. It is useful to display Figure 3.6 on page 118 that indicates the shape of the boxplot for
four different distributions. Then, use PHStat2 to construct a boxplot. Note that you can construct
the boxplot for a single group or for multiple groups.
If you desire, you can discuss descriptive measures for a population and introduce the
empirical rule and the Chebyshev rule.
If time permits, and you have covered scatter plots in Chapter 2, you can briefly discuss
the covariance and the coefficient of correlation as a measure of the strength of the association
between two numerical variables. Point out that the coefficient of correlation has the advantage as
compared to the covariance of being on a scale that goes from -1 to +1. Figure 3.9 on p. 127 is
useful in depicting scatter plots for different coefficients of correlation.
Once again, you will find that the chapter review problems provide large data sets with
numerous variables.
The Managing Ashland MultiComm Services case enables students to examine the use of
descriptive statistics in an actual business environment. The Digital case continues the evaluation
of the EndRun Financial Services discussed in the Digital case in Chapter 2. The CardioGood
Fitness case focuses on developing a customer profile for a market research team. More
Descriptive Choices Follow-up expands on the discussion of the mutual funds data. The Clear
Mountain State Student Survey provides data collected from a sample of undergraduate students.
The Excel Guide for the chapter includes instructions on using different Excel functions
to compute various statistics. Alternatively, you can use PHStat or the Analysis ToolPak to
compute a list of statistics. PHStat2 can be used to construct a boxplot.
quantiles -- the 25th and 75th, that unlike the median (the 2nd quartile), are not at the center of the
distribution. Once the quartiles have been computed, the interquartile range can be determined.
Mention that the interquartile range computes the variation in the center of the distribution as
compared to the difference in the extremes computed by the range.
You can then discuss the five-number summary of minimum value, first quartile, median,
third quartile, and maximum value. Then, you construct the boxplot. Present this plot from the
perspective of serving as a tool for determining the location, variability, and symmetry of a
distribution by visual inspection, and as a graphical tool for comparing the distribution of several
groups. It is useful to display Figure 3.6 on page 118 that indicates the shape of the boxplot for
four different distributions. Then, use PHStat2 to construct a boxplot. Note that you can construct
the boxplot for a single group or for multiple groups.
If you desire, you can discuss descriptive measures for a population and introduce the
empirical rule and the Chebyshev rule.
If time permits, and you have covered scatter plots in Chapter 2, you can briefly discuss
the covariance and the coefficient of correlation as a measure of the strength of the association
between two numerical variables. Point out that the coefficient of correlation has the advantage as
compared to the covariance of being on a scale that goes from -1 to +1. Figure 3.9 on p. 127 is
useful in depicting scatter plots for different coefficients of correlation.
Once again, you will find that the chapter review problems provide large data sets with
numerous variables.
The Managing Ashland MultiComm Services case enables students to examine the use of
descriptive statistics in an actual business environment. The Digital case continues the evaluation
of the EndRun Financial Services discussed in the Digital case in Chapter 2. The CardioGood
Fitness case focuses on developing a customer profile for a market research team. More
Descriptive Choices Follow-up expands on the discussion of the mutual funds data. The Clear
Mountain State Student Survey provides data collected from a sample of undergraduate students.
The Excel Guide for the chapter includes instructions on using different Excel functions
to compute various statistics. Alternatively, you can use PHStat or the Analysis ToolPak to
compute a list of statistics. PHStat2 can be used to construct a boxplot.
Loading page 15...
Chapter 4
The chapter on probability represents a bridge between the descriptive statistics already
covered and the topics of statistical inference, regression, time series, and business analytics to be
covered in subsequent chapters. In many traditional statistics courses, often a great deal of time is
spent on probability topics that are of little direct applicability in basic statistics. The approach in
this text is to cover only those topics that are of direct applicability in the remainder of the text.
You need to begin with a relatively concise discussion of some probability rules.
Essentially, students really just need to know that (1) no probability can be negative, (2) no
probability can be more than 1, and (3) the sum of the probabilities of a set of mutually exclusive
events adds to 1.0. Students often understand the subject best if it is taught intuitively with a
minimum of formulas, with an example that relates to a business application shown as a two-way
contingency table (see the Using Statistics example). If desired, you can use the Excel Workbook
instructions or PHStat2 to compute probabilities from the contingency table.
Once these basic elements of probability have been discussed, if there is time and you
desire, conditional probability and Bayes’ theorem (an online topic) can be covered. The
Consider This concerning email SPAM is a wonderful way of helping students realize the
application of probability to everyday life. Be aware that in a one-semester course where time is
particularly limited, these topics may be of marginal importance. The Digital case in this chapter
extends the evaluation of the EndRun Financial Services to consider claims made about various
probabilities. The CardioGood Fitness, More Descriptive Choices Follow-up, and Clear Mountain
State Student Survey each involve developing contingency tables to be able to compute and
interpret conditional and marginal probabilities.
The chapter on probability represents a bridge between the descriptive statistics already
covered and the topics of statistical inference, regression, time series, and business analytics to be
covered in subsequent chapters. In many traditional statistics courses, often a great deal of time is
spent on probability topics that are of little direct applicability in basic statistics. The approach in
this text is to cover only those topics that are of direct applicability in the remainder of the text.
You need to begin with a relatively concise discussion of some probability rules.
Essentially, students really just need to know that (1) no probability can be negative, (2) no
probability can be more than 1, and (3) the sum of the probabilities of a set of mutually exclusive
events adds to 1.0. Students often understand the subject best if it is taught intuitively with a
minimum of formulas, with an example that relates to a business application shown as a two-way
contingency table (see the Using Statistics example). If desired, you can use the Excel Workbook
instructions or PHStat2 to compute probabilities from the contingency table.
Once these basic elements of probability have been discussed, if there is time and you
desire, conditional probability and Bayes’ theorem (an online topic) can be covered. The
Consider This concerning email SPAM is a wonderful way of helping students realize the
application of probability to everyday life. Be aware that in a one-semester course where time is
particularly limited, these topics may be of marginal importance. The Digital case in this chapter
extends the evaluation of the EndRun Financial Services to consider claims made about various
probabilities. The CardioGood Fitness, More Descriptive Choices Follow-up, and Clear Mountain
State Student Survey each involve developing contingency tables to be able to compute and
interpret conditional and marginal probabilities.
Loading page 16...
Chapter 5
Now that the basic principles of probability have been discussed, the probability
distribution is developed and the expected value and variance (and standard deviation) are
computed and interpreted. Given that a probability distribution has been defined, you can now
discuss some specific distributions. Although every introductory course undoubtedly covers the
normal distribution to be discussed in Chapter 6, the decision about whether to cover the
binomial, Poisson, or hypergeometric distributions is matter of personal choice and depends on
whether the course is part of a two-course sequence.
If the binomial distribution is covered, an interesting way of developing the binomial
formula is to follow the Using Statistics example that involves an accounting information system.
Note, in this example, the value for p is 0.10. (It is best not to use an example with p = 0.50 since
this represents a special case). The discussion proceeds by asking how you could get three tagged
order forms in a sample of 4. Usually a response will be elicited that provides three items of
interest out of four selections in a particular order such as Tagged Tagged Not Tagged Tagged.
Ask the class, what would be the probability of getting Tagged on the first selection? When
someone responds 0.1, ask them how they found that answer and what would be the probability
of getting Tagged on the second selection. When they answer 0.1 again, you will be able to make
the point that in saying 0.1 again, they are assuming that the probability of Tagged stays constant
from trial to trial. When you get to the third selection and the students respond 0.9, point out that
this is a second assumption of the binomial distribution -- that only two outcomes are possible --
in this case Tagged and Not Tagged, and the sum of the probabilities of Tagged and Not Tagged
must add to 1.0. Now you can compute the probability of three out of four in this order by
multiplying (0.1)(0.1)(0.9)(0.1) to get 0.0009. Ask the class if this is the answer to the original
question. Point out that this is just one way of getting three Tagged out of four selections in a
specific order, and, that there are four ways to get three Tagged out of four selections. This leads
to the development of the binomial formula Equation (5.5). You might want to do another
example at this point that calls for adding several probabilities such as three or more Tagged, less
than three Tagged, etc. Complete the discussion of the binomial distribution with the computation
of the mean and standard deviation of the distribution. Be sure to point out that for samples
greater than five, computations can become unwieldy and the student should use PHStat2, an
Excel function, or the binomial tables (See the Online Binomial.pdf tables).
Once the binomial distribution has been covered, if time permits, other discrete
probability distributions can be presented. If you cover the Poisson distribution, point out the
distinction between the binomial and Poisson distributions. Note that the Poisson is based on an
Now that the basic principles of probability have been discussed, the probability
distribution is developed and the expected value and variance (and standard deviation) are
computed and interpreted. Given that a probability distribution has been defined, you can now
discuss some specific distributions. Although every introductory course undoubtedly covers the
normal distribution to be discussed in Chapter 6, the decision about whether to cover the
binomial, Poisson, or hypergeometric distributions is matter of personal choice and depends on
whether the course is part of a two-course sequence.
If the binomial distribution is covered, an interesting way of developing the binomial
formula is to follow the Using Statistics example that involves an accounting information system.
Note, in this example, the value for p is 0.10. (It is best not to use an example with p = 0.50 since
this represents a special case). The discussion proceeds by asking how you could get three tagged
order forms in a sample of 4. Usually a response will be elicited that provides three items of
interest out of four selections in a particular order such as Tagged Tagged Not Tagged Tagged.
Ask the class, what would be the probability of getting Tagged on the first selection? When
someone responds 0.1, ask them how they found that answer and what would be the probability
of getting Tagged on the second selection. When they answer 0.1 again, you will be able to make
the point that in saying 0.1 again, they are assuming that the probability of Tagged stays constant
from trial to trial. When you get to the third selection and the students respond 0.9, point out that
this is a second assumption of the binomial distribution -- that only two outcomes are possible --
in this case Tagged and Not Tagged, and the sum of the probabilities of Tagged and Not Tagged
must add to 1.0. Now you can compute the probability of three out of four in this order by
multiplying (0.1)(0.1)(0.9)(0.1) to get 0.0009. Ask the class if this is the answer to the original
question. Point out that this is just one way of getting three Tagged out of four selections in a
specific order, and, that there are four ways to get three Tagged out of four selections. This leads
to the development of the binomial formula Equation (5.5). You might want to do another
example at this point that calls for adding several probabilities such as three or more Tagged, less
than three Tagged, etc. Complete the discussion of the binomial distribution with the computation
of the mean and standard deviation of the distribution. Be sure to point out that for samples
greater than five, computations can become unwieldy and the student should use PHStat2, an
Excel function, or the binomial tables (See the Online Binomial.pdf tables).
Once the binomial distribution has been covered, if time permits, other discrete
probability distributions can be presented. If you cover the Poisson distribution, point out the
distinction between the binomial and Poisson distributions. Note that the Poisson is based on an
Loading page 17...
area of opportunity in which you are counting occurrences within an area such as time or space.
Contrast this with the binomial distribution in which each value is classified as of interest or not
of interest. Point out the equations for the mean and standard deviation of the Poisson distribution
and indicate that the mean is equal to the variance. Since the computation of probabilities from
these discrete probability distributions can become tedious for other than small sample sizes, it is
important to discuss PHStat2, an Excel function or the Poisson tables (See the Online
Poisson.pdf tables).
If you so desire, you can discuss the covariance of a probability distribution (online
Section 5.4), which is of particular importance to students majoring in finance. It is referred to in
various finance courses including those on portfolio management and corporate finance. Use the
example in the text to illustrate the covariance. If desired, continue with coverage of portfolio
expected return and portfolio risk. Note that the PHStat2 Covariance and Portfolio Management
menu selection allows you to readily compute the pertinent statistics. It also allows you to
demonstrate changes in either the probabilities or the returns and their effect on the results. If you
are using Workbook, you can start with the Portfolio.xls workbook and show how various Excel
functions can be used to compute the desired statistics.
The hypergeometric distribution (online Section 5.5) can be developed for the situation in
which one is sampling without replacement. Once again, use PHStat2 or an Excel function.
The Managing Ashland MultiComm Services case for this chapter relates to the binomial
distribution. The Digital case involves the expected value and standard deviation of a probability
distribution and applications of the covariance in finance.
Contrast this with the binomial distribution in which each value is classified as of interest or not
of interest. Point out the equations for the mean and standard deviation of the Poisson distribution
and indicate that the mean is equal to the variance. Since the computation of probabilities from
these discrete probability distributions can become tedious for other than small sample sizes, it is
important to discuss PHStat2, an Excel function or the Poisson tables (See the Online
Poisson.pdf tables).
If you so desire, you can discuss the covariance of a probability distribution (online
Section 5.4), which is of particular importance to students majoring in finance. It is referred to in
various finance courses including those on portfolio management and corporate finance. Use the
example in the text to illustrate the covariance. If desired, continue with coverage of portfolio
expected return and portfolio risk. Note that the PHStat2 Covariance and Portfolio Management
menu selection allows you to readily compute the pertinent statistics. It also allows you to
demonstrate changes in either the probabilities or the returns and their effect on the results. If you
are using Workbook, you can start with the Portfolio.xls workbook and show how various Excel
functions can be used to compute the desired statistics.
The hypergeometric distribution (online Section 5.5) can be developed for the situation in
which one is sampling without replacement. Once again, use PHStat2 or an Excel function.
The Managing Ashland MultiComm Services case for this chapter relates to the binomial
distribution. The Digital case involves the expected value and standard deviation of a probability
distribution and applications of the covariance in finance.
Loading page 18...
Chapter 6
Now that probability and probability distributions have been discussed in Chapters 4 and
5, you are ready to introduce the normal distribution. We recommend that you begin by
mentioning some reasons that the normal distribution is so important and discuss several of its
properties. We would also recommend that you do not show Equation (6.1) in class as it will just
intimidate some students. You might begin by focusing on the fact that any normal distribution is
defined by its mean and standard deviation and display Figure 6.3 on p. 193. Then, an example
can be introduced and you can explain that if you subtracted the mean from a particular value,
and divided by the standard deviation, the difference between the value and the mean would be
expressed as a standardized normal or Z score that was discussed in Chapter 3. Next, use Table
E.2, the cumulative normal distribution, to find probabilities under the normal curve. In the text,
the cumulative normal distribution is used since this table is consistent with results provided by
Excel. Make sure that all the students can find the appropriate area under the normal curve in
their cumulative normal distribution tables. If anyone cannot, show them how to find the correct
value. Be sure to remind the class that since the total area under the curve adds to 1.0, the word
area is synonymous with the word probability. Once this has been accomplished, a good approach
is to work through a series of examples with the class, having a different student explain how to
find each answer. The example that will undoubtedly cause the most difficulty will be finding the
values corresponding to known probabilities. Slowly go over the fact that in this type of example,
the probability is known and the Z value needs to be determined, which is the opposite of what
the student has done in previous examples. Also point out that in cases in which the unknown X
value is below the mean, the negative sign must be assigned to the Z value. Once the normal
distribution has been covered, you can use PHStat2, or various Excel functions to compute
normal probabilities. You can also use the Visual Explorations in Statistics Normal distribution
procedure on p. 199. This will be useful if you intend to use examples that explore the effect on
the probabilities obtained by changing the X value, the population mean,
, or the standard
deviation,
. The Consider This essay provides a historical perspective of the application of the
normal distribution.
If you have sufficient time in the course, the normal probability plot can be discussed. Be
sure to note that all the data values need to be ranked in order from lowest to highest and that
each value needs to be converted to a normal score. Again, you can either use PHStat2 to
generate a normal probability plot or use Excel functions and charts.
If time permits, you may want to cover the uniform distribution and refer to the table of
random numbers as an example of this distribution. If you plan to cover the exponential
Now that probability and probability distributions have been discussed in Chapters 4 and
5, you are ready to introduce the normal distribution. We recommend that you begin by
mentioning some reasons that the normal distribution is so important and discuss several of its
properties. We would also recommend that you do not show Equation (6.1) in class as it will just
intimidate some students. You might begin by focusing on the fact that any normal distribution is
defined by its mean and standard deviation and display Figure 6.3 on p. 193. Then, an example
can be introduced and you can explain that if you subtracted the mean from a particular value,
and divided by the standard deviation, the difference between the value and the mean would be
expressed as a standardized normal or Z score that was discussed in Chapter 3. Next, use Table
E.2, the cumulative normal distribution, to find probabilities under the normal curve. In the text,
the cumulative normal distribution is used since this table is consistent with results provided by
Excel. Make sure that all the students can find the appropriate area under the normal curve in
their cumulative normal distribution tables. If anyone cannot, show them how to find the correct
value. Be sure to remind the class that since the total area under the curve adds to 1.0, the word
area is synonymous with the word probability. Once this has been accomplished, a good approach
is to work through a series of examples with the class, having a different student explain how to
find each answer. The example that will undoubtedly cause the most difficulty will be finding the
values corresponding to known probabilities. Slowly go over the fact that in this type of example,
the probability is known and the Z value needs to be determined, which is the opposite of what
the student has done in previous examples. Also point out that in cases in which the unknown X
value is below the mean, the negative sign must be assigned to the Z value. Once the normal
distribution has been covered, you can use PHStat2, or various Excel functions to compute
normal probabilities. You can also use the Visual Explorations in Statistics Normal distribution
procedure on p. 199. This will be useful if you intend to use examples that explore the effect on
the probabilities obtained by changing the X value, the population mean,
, or the standard
deviation,
. The Consider This essay provides a historical perspective of the application of the
normal distribution.
If you have sufficient time in the course, the normal probability plot can be discussed. Be
sure to note that all the data values need to be ranked in order from lowest to highest and that
each value needs to be converted to a normal score. Again, you can either use PHStat2 to
generate a normal probability plot or use Excel functions and charts.
If time permits, you may want to cover the uniform distribution and refer to the table of
random numbers as an example of this distribution. If you plan to cover the exponential
Loading page 19...
distribution (which is an online topic), it is useful to discuss applications of this distribution in
queuing (waiting line) theory. In addition, be sure to point out that Equation (6.10) provides the
probability of an arrival in less than or equal to a given amount of time. Be sure to mention that
you can use PHStat2 or an Excel function to compute exponential probabilities.
The Managing Ashland MultiComm Services case for this chapter relates to the normal
distribution. The Digital case involves the normal distribution and the normal probability plot.
The CardioGood Fitness, More Descriptive Choices Follow-up, and Clear Mountain State
Student Survey each involve developing normal probability plots.
You can use either Excel functions or the PHStat add-in to compute normal and
exponential probabilities and to construct normal probability plots.
queuing (waiting line) theory. In addition, be sure to point out that Equation (6.10) provides the
probability of an arrival in less than or equal to a given amount of time. Be sure to mention that
you can use PHStat2 or an Excel function to compute exponential probabilities.
The Managing Ashland MultiComm Services case for this chapter relates to the normal
distribution. The Digital case involves the normal distribution and the normal probability plot.
The CardioGood Fitness, More Descriptive Choices Follow-up, and Clear Mountain State
Student Survey each involve developing normal probability plots.
You can use either Excel functions or the PHStat add-in to compute normal and
exponential probabilities and to construct normal probability plots.
Loading page 20...
Chapter 7
The coverage of the normal distribution in Chapter 6 flows into a discussion of sampling
distributions. Point out the fact that the concept of the sampling distribution of a statistic is
important for statistical inference. Make sure that students realize that problems in this section
will compute probabilities concerning the mean, not concerning individual values. It is helpful to
display Figure 7.4 on p. 224 to show how the Central Limit Theorem applies to different shaped
populations. A useful classroom or homework exercise involves using PHStat2 or Excel to form
sampling distributions. This reinforces the concept of the Central Limit Theorem.
The Managing Ashland MultiComm Services case for this chapter relates to the sampling
distribution of the mean. The Digital case also involves the sampling distribution of the mean.
You might want to have students experiment with using the Visual Explorations add-in
workbook to explore sampling distributions. You can also use either Excel functions, the PHStat
add-in, or the Analysis ToolPak to develop sampling distribution simulations.
The coverage of the normal distribution in Chapter 6 flows into a discussion of sampling
distributions. Point out the fact that the concept of the sampling distribution of a statistic is
important for statistical inference. Make sure that students realize that problems in this section
will compute probabilities concerning the mean, not concerning individual values. It is helpful to
display Figure 7.4 on p. 224 to show how the Central Limit Theorem applies to different shaped
populations. A useful classroom or homework exercise involves using PHStat2 or Excel to form
sampling distributions. This reinforces the concept of the Central Limit Theorem.
The Managing Ashland MultiComm Services case for this chapter relates to the sampling
distribution of the mean. The Digital case also involves the sampling distribution of the mean.
You might want to have students experiment with using the Visual Explorations add-in
workbook to explore sampling distributions. You can also use either Excel functions, the PHStat
add-in, or the Analysis ToolPak to develop sampling distribution simulations.
Loading page 21...
Chapter 8
You should begin this chapter by reviewing the concept of the sampling distribution
covered in Chapter 7. It is important that the students realize that (1) an interval estimate provides
a range of values for the estimate of the population parameter, (2) you can never be sure that the
interval developed does include the population parameter, and (3) the proportion of intervals that
include the population parameter within the interval is equal to the confidence level.
Note that the Using Statistics example for this chapter, which refers to the Ricknel Home
Centers is actually a case study that relates to every part of the chapter. This scenario is a good
candidate for use as the classroom example demonstrating an application of statistics in
accounting. It also enables you to use the DCOVA approach of Define, Collect, Organize,
Visualize, and Analyze in the context of statistical inference.
When introducing the t distribution for the confidence interval estimate of the population
mean, be sure to point out the differences between the t and normal distributions, the assumption
of normality, and the robustness of the procedure. It is useful to display Table E.3 in class to
illustrate how to find the critical t value. When developing the confidence interval for the
proportion, remind the students that the normal distribution may be used here as an
approximation to the binomial distribution as long as the assumption of normality is valid [when
n
and n(1 -
) are at least 5].
Having covered confidence intervals, you can move on to sample size determination by
turning the initial question of estimation around, and focusing on the sample size needed for a
desired confidence level and width of the interval. In discussing sample size determination for the
mean, be sure to focus on the need for an estimate of the standard deviation. When discussing
sample size determination for the proportion, be sure to focus on the need for an estimate of the
population proportion and the fact that a value of
= 0.5 can be used in the absence of any other
estimate. If time permits, you may wish to discuss the effect of the finite population (this is an
Online Topic) on the width of the confidence interval and the sample size needed. Point out that
the correction factor should always be used when dealing with a finite population, but will have
only a small effect when the sample size is a small proportion of the population size.
Due to the existence of a large number of accounting majors in many business schools,
we have included an online section on applications of estimation in auditing. Two applications
are included, the estimation of the total, and difference estimation. In estimating the total, point
out that estimating the total is similar to estimating the mean, except that you are multiplying both
the mean and the width of the confidence interval by the population size. When discussing
difference estimation, be sure that the students realize that all differences of zero must be
You should begin this chapter by reviewing the concept of the sampling distribution
covered in Chapter 7. It is important that the students realize that (1) an interval estimate provides
a range of values for the estimate of the population parameter, (2) you can never be sure that the
interval developed does include the population parameter, and (3) the proportion of intervals that
include the population parameter within the interval is equal to the confidence level.
Note that the Using Statistics example for this chapter, which refers to the Ricknel Home
Centers is actually a case study that relates to every part of the chapter. This scenario is a good
candidate for use as the classroom example demonstrating an application of statistics in
accounting. It also enables you to use the DCOVA approach of Define, Collect, Organize,
Visualize, and Analyze in the context of statistical inference.
When introducing the t distribution for the confidence interval estimate of the population
mean, be sure to point out the differences between the t and normal distributions, the assumption
of normality, and the robustness of the procedure. It is useful to display Table E.3 in class to
illustrate how to find the critical t value. When developing the confidence interval for the
proportion, remind the students that the normal distribution may be used here as an
approximation to the binomial distribution as long as the assumption of normality is valid [when
n
and n(1 -
) are at least 5].
Having covered confidence intervals, you can move on to sample size determination by
turning the initial question of estimation around, and focusing on the sample size needed for a
desired confidence level and width of the interval. In discussing sample size determination for the
mean, be sure to focus on the need for an estimate of the standard deviation. When discussing
sample size determination for the proportion, be sure to focus on the need for an estimate of the
population proportion and the fact that a value of
= 0.5 can be used in the absence of any other
estimate. If time permits, you may wish to discuss the effect of the finite population (this is an
Online Topic) on the width of the confidence interval and the sample size needed. Point out that
the correction factor should always be used when dealing with a finite population, but will have
only a small effect when the sample size is a small proportion of the population size.
Due to the existence of a large number of accounting majors in many business schools,
we have included an online section on applications of estimation in auditing. Two applications
are included, the estimation of the total, and difference estimation. In estimating the total, point
out that estimating the total is similar to estimating the mean, except that you are multiplying both
the mean and the width of the confidence interval by the population size. When discussing
difference estimation, be sure that the students realize that all differences of zero must be
Loading page 22...
accounted for in computing the mean difference and the standard deviation of the difference when
using Equations (8.8) and (8.9).
Since the formulas for the confidence interval estimates and sample sizes discussed in
this chapter are straightforward, using PHStat2 or Workbook can remove much of the tedious
nature of these computations.
The Managing Ashland MultiComm Services case for this chapter involves developing
various confidence intervals and interpreting the results in a marketing context. The Digital case
also relates to confidence interval estimation. This chapter marks the first appearance of the Sure
Value Convenience Store case which places the student in the role of someone working in the
corporate office of a nationwide convenience store franchise. This case will appear in the next
three chapters, Chapters 9 – 12, and also in Chapter 15.The CardioGood Fitness, More
Descriptive Choices Follow-up, and Clear Mountain State Student Survey each involve
developing confidence interval estimates.
You can use either Excel functions or the PHStat add-in to construct confidence intervals
for means and proportions and to determine the sample size for means and proportions.
using Equations (8.8) and (8.9).
Since the formulas for the confidence interval estimates and sample sizes discussed in
this chapter are straightforward, using PHStat2 or Workbook can remove much of the tedious
nature of these computations.
The Managing Ashland MultiComm Services case for this chapter involves developing
various confidence intervals and interpreting the results in a marketing context. The Digital case
also relates to confidence interval estimation. This chapter marks the first appearance of the Sure
Value Convenience Store case which places the student in the role of someone working in the
corporate office of a nationwide convenience store franchise. This case will appear in the next
three chapters, Chapters 9 – 12, and also in Chapter 15.The CardioGood Fitness, More
Descriptive Choices Follow-up, and Clear Mountain State Student Survey each involve
developing confidence interval estimates.
You can use either Excel functions or the PHStat add-in to construct confidence intervals
for means and proportions and to determine the sample size for means and proportions.
Loading page 23...
Chapter 9
A good way to begin the chapter is to focus on the reasons that hypothesis testing is used.
We believe that it is important for students to understand the logic of hypothesis testing before
they delve into the details of computing test statistics and making decisions. If you begin with the
Using Statistics example concerning the filling of cereal boxes, slowly develop the rationale for
the null and alternative hypotheses. Ask the students what conclusion they would reach if a
sample revealed a mean of 200 grams (They will all say that something is wrong) and if a sample
revealed a mean of 367.99 grams (Almost all will say that the difference between the sample
result and what the mean is supposed to be is so small that it must be due to chance). Be sure to
make the point that hypothesis testing allows you to take away the decision from a person's
subjective judgment, and enables you to make a decision while at the same time quantifying the
risks of different types of incorrect decisions. Be sure to go over the meaning of the Type I and
Type II errors, and their associated probabilities
and
along with the concept of statistical
power (more extensive coverage of the power of a test is included in Section 9.6 which is an
Online Topic).
Set up an example of a sampling distribution such as Figure 9.1 on p. 273, and show the
regions of rejection and nonrejection. Explain that the sampling distribution and the test statistic
involved will change depending on the characteristic being tested. Focus on the situation where
is unknown if you have numerical data. Emphasize that
is virtually never known. It is also
useful at this point to introduce the concept of the p-value approach as an alternative to the
classical hypothesis testing approach. Define the p-value and use the phrase given in the text “If
the p-value is low, Ho must go.” and the rules for rejecting the null hypothesis and indicate that
the p-value approach is a natural approach when using Excel, since the p-value can be determined
by using PHStat, Excel functions, or the Analysis Toolpak.
Once the initial example of hypothesis testing has been developed, you need to focus on
the differences between the tests used in various situations. The Chapter 9 summary table is
useful for this since it presents a road map for determining which test is used in which
circumstance. Be sure to point out that one-tail tests are used when the alternative hypothesis
involved is directional (e.g.,
> 368,
< 0.20). Examine the effect on the results of changing the
hypothesized mean or proportion.
The Managing Ashland MultiComm Services case, Digital case, and the Sure Value
Convenience Store case each involves the use of the one-sample test of hypothesis for the mean.
A good way to begin the chapter is to focus on the reasons that hypothesis testing is used.
We believe that it is important for students to understand the logic of hypothesis testing before
they delve into the details of computing test statistics and making decisions. If you begin with the
Using Statistics example concerning the filling of cereal boxes, slowly develop the rationale for
the null and alternative hypotheses. Ask the students what conclusion they would reach if a
sample revealed a mean of 200 grams (They will all say that something is wrong) and if a sample
revealed a mean of 367.99 grams (Almost all will say that the difference between the sample
result and what the mean is supposed to be is so small that it must be due to chance). Be sure to
make the point that hypothesis testing allows you to take away the decision from a person's
subjective judgment, and enables you to make a decision while at the same time quantifying the
risks of different types of incorrect decisions. Be sure to go over the meaning of the Type I and
Type II errors, and their associated probabilities
and
along with the concept of statistical
power (more extensive coverage of the power of a test is included in Section 9.6 which is an
Online Topic).
Set up an example of a sampling distribution such as Figure 9.1 on p. 273, and show the
regions of rejection and nonrejection. Explain that the sampling distribution and the test statistic
involved will change depending on the characteristic being tested. Focus on the situation where
is unknown if you have numerical data. Emphasize that
is virtually never known. It is also
useful at this point to introduce the concept of the p-value approach as an alternative to the
classical hypothesis testing approach. Define the p-value and use the phrase given in the text “If
the p-value is low, Ho must go.” and the rules for rejecting the null hypothesis and indicate that
the p-value approach is a natural approach when using Excel, since the p-value can be determined
by using PHStat, Excel functions, or the Analysis Toolpak.
Once the initial example of hypothesis testing has been developed, you need to focus on
the differences between the tests used in various situations. The Chapter 9 summary table is
useful for this since it presents a road map for determining which test is used in which
circumstance. Be sure to point out that one-tail tests are used when the alternative hypothesis
involved is directional (e.g.,
> 368,
< 0.20). Examine the effect on the results of changing the
hypothesized mean or proportion.
The Managing Ashland MultiComm Services case, Digital case, and the Sure Value
Convenience Store case each involves the use of the one-sample test of hypothesis for the mean.
Loading page 24...
You can use either Excel functions or the PHStat add-in to carry out the hypothesis tests
for means and proportions.
for means and proportions.
Loading page 25...
Chapter 10
This chapter discusses tests of hypothesis for the differences between two groups. The
chapter begins with t tests for the difference between the means, then covers the Z test for the
difference between two proportions, and concludes with the F test for the ratio of two variances.
The first test of hypothesis covered is usually the test for the difference between the
means of two groups for independent samples. Point out that the test statistic involves pooling of
the sample variances from the two groups and assumes that the population variances are the same
for the two groups. Students should be familiar with the t distribution, assuming that the
confidence interval estimate for the mean has been previously covered, Point out that a stem-and-
leaf display, a boxplot, or a normal probability plot can be used to evaluate the validity of the
assumptions of the t test for a given set of data. This allows you to once again use the DCOVA
approach of Define, Collect, Organize, Visualize, and Analyze to meet a business objective.
Once the t test has been discussed, you can use the Excel worksheets provided with the
Workbook approach, PHStat2, or the Analysis Toolpak to determine the test statistic and p-value.
Mention that if the variances are not equal, a separate variance t test can be conducted. The
Consider This essay is a wonderful example of how the two-sample t test was used to solve a
business problem that a student had after she graduated and had taken the introductory statistics
course.
At this point, having covered the test for the difference between the means of two
independent groups, if you have time in your course, you can discuss a test that examines
differences in the means of two paired or matched groups. The key difference is that the focus in
this test is on differences between the values in the two groups since the data have been collected
from matched pairs or repeated measurements on the same individuals or items. Once the paired t
test has been discussed, the Workbook approach, PHStat2, or the Data Analysis tool can be used
to determine the test statistic and p-value.
You can continue the coverage of differences between two groups by testing for the
difference between two proportions. Be sure to review the difference between numerical and
categorical data emphasizing the categorical variable used here classifies each observation as of
interest or not of interest. Make sure that the students realize that the test for the difference
between two proportions follows the normal distribution. A good classroom example involves
asking the students if they enjoy shopping for clothing and then classifying the yes and no
responses by gender. Since there will often be a difference between males and females, you can
then ask the class how to go about determining whether the results are statistically significant.
This chapter discusses tests of hypothesis for the differences between two groups. The
chapter begins with t tests for the difference between the means, then covers the Z test for the
difference between two proportions, and concludes with the F test for the ratio of two variances.
The first test of hypothesis covered is usually the test for the difference between the
means of two groups for independent samples. Point out that the test statistic involves pooling of
the sample variances from the two groups and assumes that the population variances are the same
for the two groups. Students should be familiar with the t distribution, assuming that the
confidence interval estimate for the mean has been previously covered, Point out that a stem-and-
leaf display, a boxplot, or a normal probability plot can be used to evaluate the validity of the
assumptions of the t test for a given set of data. This allows you to once again use the DCOVA
approach of Define, Collect, Organize, Visualize, and Analyze to meet a business objective.
Once the t test has been discussed, you can use the Excel worksheets provided with the
Workbook approach, PHStat2, or the Analysis Toolpak to determine the test statistic and p-value.
Mention that if the variances are not equal, a separate variance t test can be conducted. The
Consider This essay is a wonderful example of how the two-sample t test was used to solve a
business problem that a student had after she graduated and had taken the introductory statistics
course.
At this point, having covered the test for the difference between the means of two
independent groups, if you have time in your course, you can discuss a test that examines
differences in the means of two paired or matched groups. The key difference is that the focus in
this test is on differences between the values in the two groups since the data have been collected
from matched pairs or repeated measurements on the same individuals or items. Once the paired t
test has been discussed, the Workbook approach, PHStat2, or the Data Analysis tool can be used
to determine the test statistic and p-value.
You can continue the coverage of differences between two groups by testing for the
difference between two proportions. Be sure to review the difference between numerical and
categorical data emphasizing the categorical variable used here classifies each observation as of
interest or not of interest. Make sure that the students realize that the test for the difference
between two proportions follows the normal distribution. A good classroom example involves
asking the students if they enjoy shopping for clothing and then classifying the yes and no
responses by gender. Since there will often be a difference between males and females, you can
then ask the class how to go about determining whether the results are statistically significant.
Loading page 26...
The F-test for the difference between two variances can be covered next. Be sure to
carefully explain that this distribution, unlike the normal and t distributions, is not symmetric and
cannot have a negative value since the statistic is the ratio of two variances. Remind the students
that the larger variance is placed in the numerator. Be sure to mention that a boxplot of the two
groups and normal probability plots can be used to determine the validity of the assumptions of
the F test. This is particularly important here since this test is sensitive to non-normality in the
two populations. The Workbook approach, PHStat2, or the Analysis Toolpak can be used to
determine the test statistic and p-value.
The online section on effect size is particularly appropriate when you have big data with
very large sample sizes.
Be aware that the Managing Ashland MultiComm Services case since it contains both
independent sample and matched sample aspects, involves all the sections of the chapter except
the test for the difference between two proportions. The Digital case is based on two independent
samples. Thus, only the sections on the t test for independent samples and the F test for the
difference between two variances are involved. The Sure Value Convenience Store case now
involves a decision between two prices for coffee. The CardioGood Fitness, More Descriptive
Choices Follow-up, and Clear Mountain State Student Survey each involve the determination of
differences between two groups on both numerical and categorical variables.
You can use either Excel functions, the PHStat add-in, or the Analysis ToolPak to carry
out the hypothesis tests for the differences between means and variances and for the paired t test.
You can also use Excel functions or the PHStat add-in to carry out the hypothesis test for the
differences between two proportions.
carefully explain that this distribution, unlike the normal and t distributions, is not symmetric and
cannot have a negative value since the statistic is the ratio of two variances. Remind the students
that the larger variance is placed in the numerator. Be sure to mention that a boxplot of the two
groups and normal probability plots can be used to determine the validity of the assumptions of
the F test. This is particularly important here since this test is sensitive to non-normality in the
two populations. The Workbook approach, PHStat2, or the Analysis Toolpak can be used to
determine the test statistic and p-value.
The online section on effect size is particularly appropriate when you have big data with
very large sample sizes.
Be aware that the Managing Ashland MultiComm Services case since it contains both
independent sample and matched sample aspects, involves all the sections of the chapter except
the test for the difference between two proportions. The Digital case is based on two independent
samples. Thus, only the sections on the t test for independent samples and the F test for the
difference between two variances are involved. The Sure Value Convenience Store case now
involves a decision between two prices for coffee. The CardioGood Fitness, More Descriptive
Choices Follow-up, and Clear Mountain State Student Survey each involve the determination of
differences between two groups on both numerical and categorical variables.
You can use either Excel functions, the PHStat add-in, or the Analysis ToolPak to carry
out the hypothesis tests for the differences between means and variances and for the paired t test.
You can also use Excel functions or the PHStat add-in to carry out the hypothesis test for the
differences between two proportions.
Loading page 27...
Chapter 11
If the one-way ANOVA F test for the difference between c means is to be covered in
your course, a good way to start is to go back to the sum of squares concept that was originally
covered when the variance and standard deviation were introduced in Section 3.2. Explain that in
the one-way Analysis of Variance, the sum of squared differences around the overall mean can be
divided into two other sums of squares that add up to the total sum of squares. One of these
measures differences among the means of the groups and thus is called sum of squares among
groups (SSA), while the other measures the differences within the groups and is called the sum of
squares within the groups (SSW). Be sure to remind the students that, since the variance is a sum
of squares divided by degrees of freedom, a variance among the groups and a variance within the
groups can be computed by dividing each sum of squares by the corresponding degrees of
freedom. Make the point that the terminology used in the Analysis of Variance for variance is
Mean Square, so the variances computed are called MSA, MSW, and MST. This will lead to the
development of the F statistic as the ratio of two variances. A useful approach at this point when
all formulas are defined, is to set up the ANOVA summary table. Try to minimize the focus on
the computations by reminding students that the Analysis of Variance computations can be done
using Workbook, PHStat2, or the Analysis Toolpak. It is also useful to show how to obtain the
critical F value by either referring to Table E.5 or the Excel results. Be sure to mention the
assumptions of the Analysis of Variance and that the boxplot and normal probability plot can be
used to evaluate the validity of these assumptions for a given set of data. Levene’s test can be
used to test for the equality of variances. Workbook or PHStat2 can be used to compute the
results for this test.
Once the Analysis of Variance has been covered, if time permits, you will want to
determine which means are different. Although many approaches are available, this text uses the
Tukey-Kramer procedure that involves the Studentized range statistic shown in Table E.7. Be
sure that students compare each paired difference between the means to the critical range. Note
that you can use Workbook or PHStat2 to compute Tukey-Kramer multiple comparisons.
The factorial design model in Section 11.2 provides coverage of the two-way analysis of
variance with equal number of observations for each combination of factor A and factor B. The
approach taken in the text is primarily conceptual since, due to the complexity of the
computations, the Analysis ToolPak, or PHStat2 should be used to perform the computations.
You should develop the concept of partitioning the total sum of squares (SST) into factor A
variation (SSA), factor B variation (SSB), interaction (SSAB) and random variation (SSE). Then
move on to the development of the ANOVA table displayed in Table 11.6 on p. 367. Perhaps the
If the one-way ANOVA F test for the difference between c means is to be covered in
your course, a good way to start is to go back to the sum of squares concept that was originally
covered when the variance and standard deviation were introduced in Section 3.2. Explain that in
the one-way Analysis of Variance, the sum of squared differences around the overall mean can be
divided into two other sums of squares that add up to the total sum of squares. One of these
measures differences among the means of the groups and thus is called sum of squares among
groups (SSA), while the other measures the differences within the groups and is called the sum of
squares within the groups (SSW). Be sure to remind the students that, since the variance is a sum
of squares divided by degrees of freedom, a variance among the groups and a variance within the
groups can be computed by dividing each sum of squares by the corresponding degrees of
freedom. Make the point that the terminology used in the Analysis of Variance for variance is
Mean Square, so the variances computed are called MSA, MSW, and MST. This will lead to the
development of the F statistic as the ratio of two variances. A useful approach at this point when
all formulas are defined, is to set up the ANOVA summary table. Try to minimize the focus on
the computations by reminding students that the Analysis of Variance computations can be done
using Workbook, PHStat2, or the Analysis Toolpak. It is also useful to show how to obtain the
critical F value by either referring to Table E.5 or the Excel results. Be sure to mention the
assumptions of the Analysis of Variance and that the boxplot and normal probability plot can be
used to evaluate the validity of these assumptions for a given set of data. Levene’s test can be
used to test for the equality of variances. Workbook or PHStat2 can be used to compute the
results for this test.
Once the Analysis of Variance has been covered, if time permits, you will want to
determine which means are different. Although many approaches are available, this text uses the
Tukey-Kramer procedure that involves the Studentized range statistic shown in Table E.7. Be
sure that students compare each paired difference between the means to the critical range. Note
that you can use Workbook or PHStat2 to compute Tukey-Kramer multiple comparisons.
The factorial design model in Section 11.2 provides coverage of the two-way analysis of
variance with equal number of observations for each combination of factor A and factor B. The
approach taken in the text is primarily conceptual since, due to the complexity of the
computations, the Analysis ToolPak, or PHStat2 should be used to perform the computations.
You should develop the concept of partitioning the total sum of squares (SST) into factor A
variation (SSA), factor B variation (SSB), interaction (SSAB) and random variation (SSE). Then
move on to the development of the ANOVA table displayed in Table 11.6 on p. 367. Perhaps the
Loading page 28...
most difficult concept to teach in the factorial design model is that of interaction. We believe that
the display of an interaction graph such as the one shown in Figure 11.13 on p. 371 is helpful. In
addition, showing an example such as Example 11.2 on page 371 is particularly important, so that
students observe the lack of parallel lines when significant interaction is present. Be sure to
emphasize that the interaction effect is always tested prior to the main effects of A and B, since
the interpretation of effects A and B will be affected by whether the interaction is significant.
The randomized block model which is an online topic is an extension of the paired t test
in Chapter 10. Slowly go over the partitioning of the total sum of squares (SST) into Among
Group variation (SSA), Among Block variation (SSBL), and Random variation (SSE). Discuss the
ANOVA table and be sure students realize that Excel can be used to perform the computations.
Finish this topic with a brief discussion of the relative efficiency of using the randomized block
model and the use of the Tukey procedure for multiple comparisons. The online Section 11.4
briefly discusses the difference between the F tests involved when there are fixed and random
effects.
The Managing Ashland MultiComm Services case for this chapter involves the one way
ANOVA and the two-factor factorial design. The Digital case uses the One Way ANOVA. The
Sure Value Convenience Store case now involves a decision among four prices for coffee. The
CardioGood Fitness, More Descriptive Choices Follow-up, and Clear Mountain State Student
Survey each involves using the one-way ANOVA to determine whether differences in numerical
variables exist among three or more groups
In this chapter, using Workbook is more complicated than in other chapters, so you may
want to focus on using the Analysis ToolPak or PHStat2.
the display of an interaction graph such as the one shown in Figure 11.13 on p. 371 is helpful. In
addition, showing an example such as Example 11.2 on page 371 is particularly important, so that
students observe the lack of parallel lines when significant interaction is present. Be sure to
emphasize that the interaction effect is always tested prior to the main effects of A and B, since
the interpretation of effects A and B will be affected by whether the interaction is significant.
The randomized block model which is an online topic is an extension of the paired t test
in Chapter 10. Slowly go over the partitioning of the total sum of squares (SST) into Among
Group variation (SSA), Among Block variation (SSBL), and Random variation (SSE). Discuss the
ANOVA table and be sure students realize that Excel can be used to perform the computations.
Finish this topic with a brief discussion of the relative efficiency of using the randomized block
model and the use of the Tukey procedure for multiple comparisons. The online Section 11.4
briefly discusses the difference between the F tests involved when there are fixed and random
effects.
The Managing Ashland MultiComm Services case for this chapter involves the one way
ANOVA and the two-factor factorial design. The Digital case uses the One Way ANOVA. The
Sure Value Convenience Store case now involves a decision among four prices for coffee. The
CardioGood Fitness, More Descriptive Choices Follow-up, and Clear Mountain State Student
Survey each involves using the one-way ANOVA to determine whether differences in numerical
variables exist among three or more groups
In this chapter, using Workbook is more complicated than in other chapters, so you may
want to focus on using the Analysis ToolPak or PHStat2.
Loading page 29...
Chapter 12
This chapter covers chi-square tests and nonparametric tests. The Using Statistics
example concerning hotels relates to the first three sections of the chapter.
If you covered the Z test for the difference between two proportions in Chapter 10, you
can return to the example you used there and point out that the chi-square test can be used as an
alternative. A good classroom example involves asking the students if they enjoy shopping for
clothing (or revisiting Chapter 10’s example) and then classifying the yes and no responses by
gender. Since there will often be a difference between males and females, you can then ask the
class how they might go about determining whether the results are statistically significant. The
expected frequencies are computed by finding the mean proportion of items of interest (enjoying
shopping) and items not of interest (not enjoying shopping) and multiplying by the sample sizes
of males and females respectively. This leads to the computation of the test statistic. Once again
as with the case of the normal, t, and F distribution, be sure to set up a picture of the chi-square
distribution with its regions of rejection and non-rejection and critical values. In addition, go over
the assumptions of the chi square test including the requirement for an expected frequency of at
least five in each cell of the 2 × 2 contingency table.
Now you are ready to extend the chi-square test to more than two groups. Be sure to
discuss the fact that with more than two groups, the number of degrees of freedom will change
and the requirements for minimum cell expected frequencies will be somewhat less restrictive. If
you have time, you can develop the Marascuilo procedure to determine which groups differ.
The discussion of the chi-square test concludes with the test of independence in the r by c
table. Be sure to go over the interpretation of the null and alternative hypotheses and how they
differ from the situation in which there are only two rows.
If you will be covering the Wilcoxon rank sum test, begin by noting that if the normality
assumption was seriously violated, this test would be a good alternative to the t test for the
difference between the means of two independent samples. Be sure to discuss the need to rank all
the data values without regard to group. Review the fact that the statistic T1 refers to the sum of
the ranks for the group with the smaller sample size. If small samples are involved, be sure to
point out that the null hypothesis is rejected if the test statistic T1 is less than or equal to the lower
critical value or greater than or equal to the upper critical value. In addition, explain when the
normal approximation can be used. Point out that Workbook or PHStat2 can be used for the
Wilcoxon rank sum test.
This chapter covers chi-square tests and nonparametric tests. The Using Statistics
example concerning hotels relates to the first three sections of the chapter.
If you covered the Z test for the difference between two proportions in Chapter 10, you
can return to the example you used there and point out that the chi-square test can be used as an
alternative. A good classroom example involves asking the students if they enjoy shopping for
clothing (or revisiting Chapter 10’s example) and then classifying the yes and no responses by
gender. Since there will often be a difference between males and females, you can then ask the
class how they might go about determining whether the results are statistically significant. The
expected frequencies are computed by finding the mean proportion of items of interest (enjoying
shopping) and items not of interest (not enjoying shopping) and multiplying by the sample sizes
of males and females respectively. This leads to the computation of the test statistic. Once again
as with the case of the normal, t, and F distribution, be sure to set up a picture of the chi-square
distribution with its regions of rejection and non-rejection and critical values. In addition, go over
the assumptions of the chi square test including the requirement for an expected frequency of at
least five in each cell of the 2 × 2 contingency table.
Now you are ready to extend the chi-square test to more than two groups. Be sure to
discuss the fact that with more than two groups, the number of degrees of freedom will change
and the requirements for minimum cell expected frequencies will be somewhat less restrictive. If
you have time, you can develop the Marascuilo procedure to determine which groups differ.
The discussion of the chi-square test concludes with the test of independence in the r by c
table. Be sure to go over the interpretation of the null and alternative hypotheses and how they
differ from the situation in which there are only two rows.
If you will be covering the Wilcoxon rank sum test, begin by noting that if the normality
assumption was seriously violated, this test would be a good alternative to the t test for the
difference between the means of two independent samples. Be sure to discuss the need to rank all
the data values without regard to group. Review the fact that the statistic T1 refers to the sum of
the ranks for the group with the smaller sample size. If small samples are involved, be sure to
point out that the null hypothesis is rejected if the test statistic T1 is less than or equal to the lower
critical value or greater than or equal to the upper critical value. In addition, explain when the
normal approximation can be used. Point out that Workbook or PHStat2 can be used for the
Wilcoxon rank sum test.
Loading page 30...
If the Kruskal-Wallis rank test is to be covered, you can explain that if the assumption of
normality has been seriously violated, the Kruskal-Wallis rank test may be a better test procedure
than the one-way ANOVA. Once again, be sure to discuss the need to rank all the data values
without regard to group. Go over how to find the critical values of the chi-square statistic using
Table E.4. As was the case with the Wilcoxon rank sum test, Workbook or PHStat2 can be used
for the Kruskal-Wallis rank test.
If you wish, you can briefly discuss the McNemar test which is an online topic. Explain
that just like you used the paired-t test when you had related samples of numerical data, you use
the McNemar test instead of the chi-square test when you have related samples of categorical
data. Make sure to state that for two samples of related categorical data, the McNemar test is
more powerful than the chi-square test.
You can then move on, if you wish, to the one sample test for the variance which is an
online topic. Remind the students that if they are doing a two-tail test, they also need to find the
lower critical value in the lower tail of the chi-square distribution.
The Managing Ashland MultiComm Services case extends the survey discussed in
Chapter 8 to analyze data from contingency tables. The Digital case also involves analyzing
various contingency tables. The Sure Value Convenience Store case and the CardioGood Fitness
cases involve using the Kruskal-Wallis test instead of the one-way ANOVA, The More
Descriptive Choices Follow-up and Clear Mountain State Student Survey cases involve both
contingency tables and nonparametric tests.
You can use Workbook or PHStat2.for testing differences between the proportions, tests
of independence, and also for the Wilcoxon rank sum test and the Kruskal-Wallis test.
normality has been seriously violated, the Kruskal-Wallis rank test may be a better test procedure
than the one-way ANOVA. Once again, be sure to discuss the need to rank all the data values
without regard to group. Go over how to find the critical values of the chi-square statistic using
Table E.4. As was the case with the Wilcoxon rank sum test, Workbook or PHStat2 can be used
for the Kruskal-Wallis rank test.
If you wish, you can briefly discuss the McNemar test which is an online topic. Explain
that just like you used the paired-t test when you had related samples of numerical data, you use
the McNemar test instead of the chi-square test when you have related samples of categorical
data. Make sure to state that for two samples of related categorical data, the McNemar test is
more powerful than the chi-square test.
You can then move on, if you wish, to the one sample test for the variance which is an
online topic. Remind the students that if they are doing a two-tail test, they also need to find the
lower critical value in the lower tail of the chi-square distribution.
The Managing Ashland MultiComm Services case extends the survey discussed in
Chapter 8 to analyze data from contingency tables. The Digital case also involves analyzing
various contingency tables. The Sure Value Convenience Store case and the CardioGood Fitness
cases involve using the Kruskal-Wallis test instead of the one-way ANOVA, The More
Descriptive Choices Follow-up and Clear Mountain State Student Survey cases involve both
contingency tables and nonparametric tests.
You can use Workbook or PHStat2.for testing differences between the proportions, tests
of independence, and also for the Wilcoxon rank sum test and the Kruskal-Wallis test.
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