Preview Extract

INSTRUCTORโS
SOLUTIONS MANUAL
GAIL ILLICH
PAUL ILLICH
McLennan Community College
Southeast Community College
B USINESS S TATISTICS :
A F IRST C OURSE
EIGHTH EDITION
David M. Levine
Baruch College, City University of New York
Kathryn A. Szabat
La Salle University
David F. Stephan
Two Bridges Instructional Technology
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the
development, research, and testing of the theories and programs to determine their effectiveness. The author and
publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation
contained in this book. The author and publisher shall not be liable in any event for incidental or consequential
damages in connection with, or arising out of, the furnishing, performance, or use of these programs.
Reproduced by Pearson from electronic files supplied by the author.
Copyright ยฉ 2020, 2016, 2013 by Pearson Education, Inc. 221 River Street, Hoboken, NJ 07030. All rights reserved.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any
means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the
publisher. Printed in the United States of America.
ISBN-13: 978-0-13-517974-1
ISBN-10: 0-13-517974-2
Table of Contents
Teaching Tips…………………………………………………………………………………………………………………..1
Chapter 1
Defining and Collecting Data ………………………………………………………………………..29
Chapter 2
Organizing and Visualizing Variables …………………………………………………………….37
Chapter 3
Numerical Descriptive Measures ………………………………………………………………….145
Chapter 4
Basic Probability ………………………………………………………………………………………..187
Chapter 5
Discrete Probability Distributions…………………………………………………………………197
Chapter 6
The Normal Distribution ……………………………………………………………………………..229
Chapter 7
Sampling Distributions ……………………………………………………………………………….263
Chapter 8
Confidence Interval Estimation ……………………………………………………………………289
Chapter 9
Fundamentals of Hypothesis Testing: One-Sample Tests ………………………………..327
Chapter 10
Two-Sample Tests and One-Way ANOVA …………………………………………………..373
Chapter 11 Chi-Square Tests ………………………………………………………………………………………..447
Chapter 12 Simple Linear Regression ……………………………………………………………………………469
Chapter 13 Multiple Regression ……………………………………………………………………………………519
Chapter 14 Business Analytics ……………………………………………………………………………………..557
Chapter 15 Statistical Applications in Quality Management (Online) ………………………………..595
Copyright ยฉ2020 Pearson Education, Inc.
Teaching Tips
Our Starting Point
Over a generation ago, advances in โdata processingโ 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 ASAโs 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 discussed using
statistical software and incorporated โcomputer outputโ as illustrationsโjust the first of many teaching
and curricular innovations in his many years of teaching business statistics. 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. 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
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Teaching Tips
applications to a business statistics faculty audience that included David Levine, an introduction that
would eventually led to the inclusion of Microsoft Excel in this textbook. We also benefit from our many
years teaching undergraduate and graduate business subjects and the diversity of interests and efforts of
our past co-author, Timothy Krehbiel.
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Teaching Tips
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Educational Philosophy
As in prior editions of Business Statistics: A First Course, 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 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 makerโs 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, JMP, and Minitab, with the study of statistics,
without having those instructions dominate the book or distract from the learning of statistical
concepts.
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Teaching Tips
Getting Started: 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 thereโs a lot to cover even before you teach your first
statistical concept.
We created โFirst Things Firstโ 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,
โGetting Startedโ has been developed to be posted online or otherwise distributed before the first class
section.
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 the business education of your students. Make the following points:
โข
This course is not a math course.
โข
State that you will be learning analytical skills for making business decisions.
โข
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.
๏ท
Define the business objective or problem to be solved and then define the variables to be studied.
๏ท
Collect the data from appropriate sources
๏ท
Organize the data
๏ท
Visualize the data by developing charts
๏ท
Analyze the data by using statistical methods to reach conclusions.
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
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organization especially since โbig dataโ, meaning data collected in huge volumes at very fast rates, needs
to be analyzed.
1. Inform the students that there is an Excel Guide, a JMP Guide, and a Minitab Guide at the
end of each chapter. Strongly encourage or require students to read the Excel Guide and/or
the JMP Guide or Minitab Guide at the end of this chapter so that they will be ready to use
Excel and/or JMP or Minitab with this book.
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Chapter 1
You need to continue the discussion of the Define task by establishing the types of variables. Mention the
importance of having an operational definition for each variable. Be sure to discuss the different types
carefully since the ability to distinguish between categorical and numerical variables 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, even if it is just using the table of random numbers to select a random
sample. 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 Think About This essay discusses the important issue of
the use of Web-based surveys.
There is also a section on Data Cleaning that discusses the issues that occur in data collection.
This is followed by a section on data formatting that includes the important concepts of stacking and
unstacking variables and recoding variables. The last section discusses the types of errors that occur in
surveys.
The chapter also introduces three continuing cases — the Managing Ashland MultiComm
Services, CardioGood Fitness, and Clear Mountain State Student Surveys 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 Service, CardioGood Fitness, Clear Mountain State Student Surveys, and Digital
cases are included in this Instructorโs Solutions Manual.).
Make sure that students read the Excel Guide and/or JMP Guide or Minitab Guide at the end of
each chapter. The In-Depth Excel instructions provide step-by-step instructions and live worksheets that
automatically update when data changes. The PHStat add-in instructions provide instructions for using
the PHStat 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.
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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, JMP, Minitab, or Tableau. Show the
summary worksheet and develop tables to help you prepare charts and analyze your data. Begin your
discussion for categorical data with the example on p. 45 concerning the percentage of the time
millennials use different devices for watching television 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. 49. 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 Microsoftยฎ Word and may have already used Excel to
construct charts that they have pasted into Word documents. Now you will be using Excel or JMP or
Minitab or Tableau to construct many different types of charts. Return to the data previously discussed on
what devices millennials use to watch television and illustrate how a bar chart and pie chart can be
constructed. Mention their advantages and disadvantages. A good example is to show the data on
incomplete ATM transactions on p. 60 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 or data that you have collected from your class. You may want to begin with a simple stemand-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.
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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. Also, you may want to discuss
how multidimensional tables allow you to see several variables simultaneously.
If the opportunity is available, we believe that it is worth the time to cover Section 2.9 on Pitfalls in
Organizing and Visualizing Data. 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
the improper display shown in Figure 2.31. Ask students what is โbadโ about this figure. Follow up with a
homework assignment involving Problems 2.69 โ 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 and a separate sample of graduate students.
The Excel Guide and the JMP and Minitab and Tableau Guides for this and the remaining
chapters are organized according to the sections of the chapter. They are quite extensive since they cover
both organizing and visualizing many different graphs. The Excel Guide includes instructions for InDepth Excel, PHStat, and the Analysis ToolPak. Pick and allows you to choose the approaches that you
prefer.
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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 were
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 values 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.
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
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Teaching Tips
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 โ 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. By changing values in the data provided, students can
observe how the mean, median, and standard deviation are affected.
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 and by JMP or Minitab. Once these three characteristics have been discussed,
you are ready to show how they can be computed using Excel or JMP or Minitab.
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 most students have taken, and
the quantile scores that they have received (97th percentile, 48th percentile, 12th percentile, โฆ, 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.
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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 3.9 on page 142 that indicates the shape of the boxplot for four different distributions. Then, use
PHStat or JMP or Minitab or Tableau 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 โ1 to +1. Figure 3.11 on p. 157 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 Followup expands on the discussion of the mutual funds data. The Clear Mountain State Student Survey
provides data collected from a sample of undergraduate students and a separate sample of graduate
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. PHStat can be used to construct a boxplot. Or you can use JMP or Minitab. The Tableau guide
covers the five number summary and the boxplot
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Teaching Tips
Chapter 4
The chapter on probability represents a bridge between the descriptive statistics already covered and the
topics of statistical inference and regression 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 In-Depth Excel or PHStat 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 Bayesโ theorem can be covered. The Think About This concerning email
SPAM is a wonderful way of helping students realize the application of probability to everyday life. In
addition, you may wish to spend a bit of time going over counting rules, especially if the binomial
distribution will be covered in Chapter 5.
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.
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Teaching Tips
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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 or Poisson distributions is a 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 0.0036. 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 (5.4). 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 PHStat, an Excel function, the binomial tables (See the
Online Binomial.pdf tables), JMP, or Minitab.
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 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
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Teaching Tips
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 PHStat, an Excel function the Poisson tables (See the
Online Poisson.pdf tables) or JMP or Minitab.
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.
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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. 234. 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, JMP, and Minitab. 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 PHStat, or various
Excel functions or JMP or Minitab to compute normal probabilities. You can also use the Visual
Explorations in Statistics Normal distribution procedure on p. 239. 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, ๏ญ, or the standard deviation, ๏ณ . The Think About 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 PHStat to generate a normal probability plot,
use Excel functions with Excel charts, or use JMP or Minitab.
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.
Copyright ยฉ2020 Pearson Education, Inc.
16
Teaching Tips
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 find probabilities concerning
the mean, not concerning individual values. It is helpful to display Figure 7.4 on p. 265 to show how the
Central Limit Theorem applies to different shaped populations. A useful classroom or homework exercise
involves using PHStat, Excel, or JMP or Minitab 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, the
Analysis ToolPak, or JMP or Minitab to develop sampling distribution simulations.
Copyright ยฉ2020 Pearson Education, Inc.
Teaching Tips
17
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๏ฐ and n(1 ๏ญ ๏ฐ ) 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 ๏ฐ ๏ฝ 0.5 can be used in the absence of any other estimate.
Since the formulas for the confidence interval estimates and sample sizes discussed in this chapter
are straightforward, using PHStat or In-Depth Excel can remove much of the tedious nature of these
computations or you can use JMP or Minitab.
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
c0nvenience store franchise. This case will appear in the next two chapters, Chapters 9 โ 10. The
CardioGood Fitness, More Descriptive Choices Follow-up, and Clear Mountain State Student Survey
each involve developing confidence interval estimates.
Copyright ยฉ2020 Pearson Education, Inc.
18
Teaching Tips
You can use either Excel functions, the PHStat add-in, or JMP or Minitab to construct confidence
intervals for means and proportions and either Excel functions or the PHStat add-in to determine the
sample size for means and proportions.
Copyright ยฉ2020 Pearson Education, Inc.
Teaching Tips
19
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 the matter) 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 out 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 ๏ก and ๏ข along with the concept of statistical
power.
Set up an example of a sampling distribution such as Figure 9.1 on p. 317, 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 ๏ณ is unknown if you
have numerical data. Emphasize that ๏ณ 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 โIf the p-value is low, H 0 must go.โ and the rules for
rejecting the null hypothesis and indicate that the p-value approach is a natural approach when using
Excel or JMP or Minitab, since the p-value can be determined by using PHStat, Excel functions, the
Analysis Toolpak, or JMP or Minitab.
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 roadmap 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., ๏ญ ๏พ 368,
๏ญ ๏ผ 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.
You can use either Excel functions, the PHStat add-in, or JMP or Minitab to carry out the
hypothesis tests for means and proportions.
Copyright ยฉ2020 Pearson Education, Inc.
20
Teaching Tips
Chapter 10
This chapter discusses tests of hypothesis for the differences between two or more groups. The chapter
begins with t tests for the difference between the means, then covers the Z test for the difference between
two proportions, the F test for the ratio of two variances. and concludes with one-way ANOVA.
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 In-Depth
Excel approach, PHStat, the Analysis Toolpak, or JMP or Minitab 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 Think
About 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 In-Depth
Excel approach, PHStat, the Analysis Toolpak, or JMP or Minitab 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 we might go about determining whether the
results are statistically significant.
The F-test for the 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
Copyright ยฉ2020 Pearson Education, Inc.
Teaching Tips
21
since the statistic is the ratio of two variances. Remind the students that the larger variance is 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 In-Depth Excel approach, PHStat, the Analysis
Toolpak, or JMP or Minitab can be used to determine the test statistic and p-value.
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 InDepth Excel, PHStat, the Analysis Toolpak, or JMP or Minitab. It is also useful to show how to obtain the
critical F value by either referring to Table E.5 or the Excel or JMP or Minitab 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. Leveneโs test can be used to test for
the equality of variances.
Once the Analysis of Variance has been covered, if time permits (which it may not in a onesemester course), 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 In-Depth Excel, PHStat, or JMP or Minitab to compute Tukey-Kramer
multiple comparisons.
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 and on
one-way ANOVA. The Sure Value Convenience Store case now involves a decision between two prices
Copyright ยฉ2020 Pearson Education, Inc.
22
Teaching Tips
for coffee and also between four prices of coffee. The CardioGood Fitness, More Descriptive Choices
Follow-up, and Clear Mountain State Student Survey each involve the determination of differences
between two or more groups on both numerical and categorical variables.
You can use either Excel functions, the PHStat add-in, the Analysis ToolPak, or JMP or Minitab
to carry out the hypothesis tests for the differences between means and variances for the paired t test, and
one-way ANOVA. You can also use Excel functions, the PHStat add-in, or JMP or Minitab to carry out
the hypothesis test for the differences between two proportions.
Copyright ยฉ2020 Pearson Education, Inc.
Teaching Tips
23
Chapter 11
This chapter covers chi-square 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 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 ๏ด 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.
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 case now 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 In-Depth Excel, PHStat, JMP, or Minitab for testing differences between the
proportions and for tests of independence.
Copyright ยฉ2020 Pearson Education, Inc.
24
Teaching Tips
Chapter 12
Regression analysis is probably the most widely used and misused statistical method in business and
economics. In an era of easily available statistical and spreadsheet applications, we believe that the best
approach is one that focuses on the interpretation of regression results obtained from such applications,
the assumptions of regression, how those assumptions can be evaluated, and what can be done if they are
violated. Although we also feel that might be useful for students to work out at least one small example
with the aid of a hand calculator, we believe that there should be minimal focus on hand calculations.
A good way to begin the discussion of regression analysis is to focus on developing a model that
can provide a better prediction of a variable of interest. The Using Statistics example, which forecasts
sales for a clothing store, is useful for this purpose. You can extend the DCOVA approach discussed
earlier by defining the business objective, discussing data collection, and data organization before moving
on to the visualization and analysis in this chapter. Be sure to clearly define the dependent variable and
the independent variable at this point.
Once the two types of variables have been defined, the example should be introduced. Explain the
goal of the analysis and how regression can be useful. Follow this with a scatter plot of the two variables.
Before developing the Least Squares method, review the straight-line formula and note that different
notation is used in statistics for the intercept and the slope than in mathematics. At this point, you need to
develop the concept of how the straight line that best fits the data can be found. One approach involves
plotting several lines on a scatter plot and asking the students how they can determine which line fits the
data better than any other. This usually leads to a criterion that minimizes the differences between the
actual Y value and the value that would be predicted by the regression line. Remind the class that when
you computed the mean in Chapter 3, you found out that the sum of the differences around the mean was
equal to zero. Tell the class that the regression line in two dimensions is similar to the mean in one
dimension, and that the differences between the actual Y value and the value that would be predicted by
the regression line will sum to zero. Students at this point, having covered the variance, will usually tell
you just to square the differences. At this juncture, you might want to substitute the regression equation
for the predicted value, and tell the students that since you are minimizing a quantity, derivatives are used.
We discourage you from doing the actual proof, but mentioning derivatives may help some students
realize that the calculus they may have learned in mathematics courses is actually used to develop the
theory behind the statistical method. The least-squares concepts discussed can be reinforced by using the
Visual Explorations in Statistics Simple Linear Regression procedure on p. 493. This procedure produces
a scatter plot with an unfitted line of regression and a floating control panel of controls with which to
adjust the line. The spinner buttons can be used to change the values of the slope and Y intercept to
Copyright ยฉ2020 Pearson Education, Inc.
Teaching Tips
25
change the line of regression. As these values are changed, the difference from the minimum SSE
changes.
The solution obtained from the Least Squares method allows you to find the slope and Y
intercept. In this text, since the emphasis is on the interpretation of computer output, focus is now on
finding the regression coefficients on the output shown in Figure 12.4 on p. 455. Once this has been done,
carefully review the meaning of these regression coefficients in the problem involved. The coefficients
can now be used to predict the Y value for a given X value. Be sure to discuss the problems that occur if
you try to extrapolate beyond the range of the X variable. Now you can show how to use either the InDepth Excel, the Analysis ToolPak, PHStat, JMP, or Minitab to obtain the regression output.
Tell the students that now you need to determine the usefulness of the regression model by
subdividing the total variation in Y into two component parts, explained variation or regression sum of
squares (SSR) and unexplained variation or error sum of squares (SSE). Once the sum of squares has been
determined and the coefficient of determination r 2 computed, be sure to focus on the interpretation.
Having computed the error sum of squares (SSE), the standard error of the estimate can be computed.
Make the analogy that the standard error of the estimate has the same relationship to the regression line
that the standard deviation had to the arithmetic mean.
The completion of this initial model development phase allows you to begin focusing on the
validity of the model fitted. First, go over the assumptions and emphasize the fact that unless the
assumptions are evaluated, a correct regression analysis has not been carried out. Reiterate the point that
this is one of the things that people are most likely to do incorrectly when they carry out a regression
analysis.
Once the assumptions have been discussed, you are ready to begin evaluating whether they are
true for the model that has been fit. This leads into a discussion of residual analysis. Emphasize that
Excel, JMP, or Minitab can be used to determine the residuals and that in determining whether there is a
pattern in the residuals, you look for gross patterns that are obvious on the plot, not minor patterns that are
not obvious. Be sure to note that the residual plot can also be used to evaluate the assumption of equal
variance along with whether there is a pattern in the residuals over time if the data have been collected in
sequential order. Point out that finding no pattern (i.e., a random pattern) means that the model fit is an
appropriate one. However, it does not mean that other alternative models involving additional variables
should not be considered. Mention also, that a normal probability plot of the residuals can be helpful in
determining the validity of the normality assumption. If time permits, the discussion of the Anscombe
data in Section 12.9 serves as a strong reinforcement of the importance of residual analysis.
Copyright ยฉ2020 Pearson Education, Inc.
26
Teaching Tips
If time is available, you may wish to discuss the Durbin-Watson statistic for autocorrelation. Be
sure to discuss how to find the critical values from the table of the D statistic and the fact that sometimes
the results will be inconclusive.
Once the model fit has been found to be appropriate, inferences in regression can be made. First
cover the t or F test for the slope by referring to the Excel, JMP, or Minitab results. Here, the p-value
approach is usually beneficial. Then, if time permits, you can discuss the confidence interval estimate for
the mean and the prediction interval for the individual value.
The Managing Ashland MultiComm Services case, the Digital case, and the Brynne Packaging
case each involves a simple linear regression analysis of a set of data.
Copyright ยฉ2020 Pearson Education, Inc.

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