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2e
Essentials of
Business Statistics
SANJIV JAGGIA
California Polytechnic
State University
ALISON KELLY
Suffolk University

ESSENTIALS OF BUSINESS STATISTICS: COMMUNICATING WITH NUMBERS, SECOND EDITION
Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2020 by McGraw-Hill
Education. All rights reserved. Printed in the United States of America. Previous editions © 2014. No part of this
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or other electronic storage or transmission, or broadcast for distance learning.
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All credits appearing on page or at the end of the book are considered to be an extension of the copyright page.
Library of Congress Cataloging-in-Publication Data
Names: Jaggia, Sanjiv, 1960- author. | Hawke, Alison Kelly, author.
Title: Essentials of business statistics : communicating with numbers/Sanjiv Jaggia,
California Polytechnic State University, Alison Kelly, Suffolk University.
Description: Second Edition. | Dubuque : McGraw-Hill Education, [2018] |
Revised edition of the authors’ Essentials of business statistics, c2014.
Identifiers: LCCN 2018023099 | ISBN 9781260239515 (alk. paper)
Subjects: LCSH: Commercial statistics.
Classification: LCC HF1017 .J343 2018 | DDC 519.5-dc23
LC record available at https://lccn.loc.gov/2018023099
The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website
does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education
does not guarantee the accuracy of the information presented at these sites.
mheducation.com/highered

v
Dedicated to Chandrika, Minori,
John, Megan, and Matthew

vi
ABOUT THE AUTHORS
Sanjiv Jaggia
Sanjiv Jaggia is the associate dean of graduate programs
and a professor of economics and finance at California
Polytechnic State University in San Luis Obispo, California.
After earning a Ph.D. from Indiana University, Bloomington,
in 1990, Dr. Jaggia spent 17 years at Suffolk University,
Boston. In 2003, he became a Chartered Financial
Analyst (CFA®
). Dr. Jaggia’s research interests include
empirical finance, statistics, and econometrics. He has
published extensively in research journals, including the
Journal of Empirical Finance, Review of Economics and
Statistics, Journal of Business and Economic Statistics, Journal of Applied Economet-
rics, and Journal of Econometrics. Dr. Jaggia’s ability to communicate in the classroom
has been acknowledged by several teaching awards. In 2007, he traded one coast for
the other and now lives in San Luis Obispo, California, with his wife and daughter. In his
spare time, he enjoys cooking, hiking, and listening to a wide range of music.
Alison Kelly
Alison Kelly is a professor of economics at Suffolk
University in Boston, Massachusetts. She received her
B.A. degree from the College of the Holy Cross in
Worcester, Massachusetts; her M.A. degree from the
University of Southern California in Los Angeles; and her
Ph.D. from Boston College in Chestnut Hill, Massachusetts.
Dr. Kelly has published in journals such as the American
Journal of Agricultural Economics, Journal of Macro-
economics, Review of Income and Wealth, Applied
Financial Economics, and Contemporary Economic
Policy. She is a Chartered Financial Analyst (CFA®
) and teaches review courses in quan-
titative methods to candidates preparing to take the CFA exam. Dr. Kelly has also
served as a consultant for a number of companies; her most recent work focused on
how large financial institutions satisfy requirements mandated by the Dodd-Frank Act.
She resides in Hamilton, Massachusetts, with her husband, daughter, and son.
Courtesy of Sanjiv Jaggia
Courtesy of Alison Kelly

WALKTHROUGH E S S E N T I A L S O F B usiness S tatistics vii
A Unique Emphasis on
Makes Business Statistics Relevant
to Students
We wrote Essentials of Business Statistics: Communicating with Numbers because we
saw a need for a contemporary, core statistics text that sparked student interest and
bridged the gap between how statistics is taught and how practitioners think about and
apply statistical methods. Throughout the text, the emphasis is on communicating with
numbers rather than on number crunching. In every chapter, students are exposed to
statistical information conveyed in written form. By incorporating the perspective of
practitioners, it has been our goal to make the subject matter more relevant and the pre-
sentation of material more straightforward for students. Although the text is application-
oriented and practical, it is also mathematically sound and uses notation that is generally
accepted for the topic being covered.
From our years of experience in the classroom, we have found that an effective way
to make statistics interesting is to use timely applications. For these reasons, examples
in Essentials of Business Statistics come from all walks of life, including business, eco-
nomics, sports, health, housing, the environment, polling, and psychology. By carefully
matching examples with statistical methods, students learn to appreciate the relevance of
statistics in our world today, and perhaps, end up learning statistics without realizing they
are doing so.
This is probably the best book I have seen in terms of explaining concepts.
Brad McDonald, Northern Illinois University
The book is well written, more readable and interesting than most
stats texts, and effective in explaining concepts. The examples and
cases are particularly good and effective teaching tools.
Andrew Koch, James Madison University
Clarity and brevity are the most important things I look for—this text
has both in abundance.
Michael Gordinier, Washington University, St. Louis

viii E S S E N T I A L S O F B usiness S tatistics WALKTHROUGH
Continuing Key Features
The second edition of Essentials of Business Statistics reinforces and expands six core
features that were well-received in the first edition.
Integrated Introductory Cases. Each chapter begins with an interesting and relevant
introductory case. The case is threaded throughout the chapter, and once the relevant sta-
tistical tools have been covered, a synopsis—a short summary of findings—is provided.
The introductory case often serves as the basis of several examples in other chapters.
Writing with Statistics. Interpreting results and conveying information effectively is
critical to effective decision making in virtually every field of employment. Students are
taught how to take the data, apply it, and convey the information in a meaningful way.
Unique Coverage of Regression Analysis. Relevant and extensive coverage of
regression without repetition is an important hallmark of this text.
Written as Taught. Topics are presented the way they are taught in class, beginning
with the intuition and explanation and concluding with the application.
Integration of Microsoft Excel®. Students are taught to develop an understanding of
the concepts and how to derive the calculation; then Excel is used as a tool to perform
the cumbersome calculations. In addition, guidelines for using Minitab, SPSS, JMP, and
now R are provided in chapter appendices.
Connect®. Connect is an online system that gives students the tools they need to be
successful in the course. Through guided examples and LearnSmart adaptive study tools,
students receive guidance and practice to help them master the topics.
I really like the case studies and the emphasis on writing. We are making a big effort
to incorporate more business writing in our core courses, so that meshes well.
Elizabeth Haran, Salem State University
For a statistical analyst, your analytical skill is only as good as your communication
skill. Writing with statistics reinforces the importance of communication and
provides students with concrete examples to follow.
Jun Liu, Georgia Southern University

WALKTHROUGH E S S E N T I A L S O F B usiness S tatistics ix
Features New to the Second Edition
The second edition of Essentials of Business Statistics features a number of improve-
ments suggested by many reviewers and users of the first edition. The following are the
major changes.
We focus on the p-Value Approach. We have found that students often get confused
with the mechanics of implementing a hypothesis test using both the p-value approach and
the critical value approach. While the critical value approach is attractive when a computer
is unavailable and all calculations must be done by hand, most researchers and practitioners
favor the p-value approach since virtually every statistical software package reports p-values.
Our decision to focus on the p-value approach was further supported by recommendations
set forth by the Guidelines for Assessment and Instruction in Statistics Education (GAISE)
College Report 2016 published by the American Statistical Association (http://www.amstat.
org/asa/files/pdfs/GAISE/GaiseCollege_Full.pdf). The GAISE Report recommends that
‘students should be able to interpret and draw conclusions from standard output from sta-
tistical software’ (page 11) and that instructors should consider shifting away from the use
of tables (page 23). Finally, we surveyed users of Essentials of Business Statistics, and they
unanimously supported our decision to focus on the p-value approach. For those instructors
interested in covering the critical value approach, it is discussed in the appendix to Chapter 9.
We added dozens of applied exercises with varying levels of difficulty. Many of
these exercises include new data sets that encourage the use of the computer; however,
just as many exercises retain the flexibility of traditional solving by hand.
We streamlined the Excel instructions. We feel that this modification provides a more
seamless reinforcement for the relevant topic. For those instructors who prefer to omit the
Excel parts so that they can use a different software, these sections can be easily skipped.
We completely revised Chapter 13 (More on Regression Analysis). Recognizing
the importance of regression analysis in applied work, we have made major enhance-
ments to Chapter 13. The chapter now contains the following sections: Dummy Vari-
ables, Interaction with Dummy Variables, Nonlinear Relationships, Trend Forecasting
Models, and Forecasting with Trend and Seasonality.
In addition to the Minitab, SPSS, and JMP instructions that appear in chapter
appendices, we now include instructions for R. The main reason for this addition
is that R is an easy-to-use and wildly popular software that merges the convenience of
statistical packages with the power of coding.
We reviewed every Connect exercise. Since both of us use Connect in our classes,
we have attempted to make the technology component seamless with the text itself. In
addition to reviewing every Connect exercise, we have added more conceptual exercises,
evaluated rounding rules, and revised tolerance levels. The positive feedback from users
of the first edition has been well worth the effort. We have also reviewed every Learn-
Smart probe. Instructors who teach in an online or hybrid environment will especially
appreciate our Connect product.
Here are other noteworthy changes:
∙ For the sake of simplicity and consistency, we have streamlined or rewritten many
Learning Outcomes.
∙ In Chapter 1 (Statistics and Data), we introduce structured data, unstructured data,
and big data; we have also revised the section on online data sources.
∙ In Chapter 4 (Introduction to Probability), we examine marijuana legalization in the
United States in the Writing with Statistics example.
∙ In Chapter 6 (Continuous Probability Distributions), we cover the normal distribution
in one section, rather than two sections.
∙ In Chapter 7 (Sampling and Sampling Distributions), we added a discussion of the
Trump election coupled with social-desirability bias.
∙ We have moved the section on “Model Assumptions and Common Violations” from
Chapter 13 (More on Regression Analysis) to Chapter 12 (Basics of Regression Analysis).

x E S S E N T I A L S O F B usiness S tatistics WALKTHROUGH
Students Learn Through Real-World
Cases and Business Examples . . .
Integrated Introductory Cases
Each chapter opens with a real-life case study that forms the basis for several exam-
ples within the chapter. The questions included in the examples create a roadmap for
mastering the most important learning outcomes within the chapter. A synopsis of
each chapter’s introductory case is presented when the last of these examples has
been discussed. Instructors of distance learners may find these introductory cases partic-
ularly useful.
Revised Pages
61
jag39519_ch03_060-103 61 06/13/18 07:43 PM
Introductory Case
Investment Decision
Jacqueline Brennan works as a financial advisor at a large investment firm. She meets with
an inexperienced investor who has some questions regarding two approaches to mutual
fund investing: growth investing versus value investing. The investor has heard that growth
funds invest in companies whose stock prices are expected to grow at a faster rate, relative to
the overall stock market, and value funds invest in companies whose stock prices are below
their true worth. The investor has also heard that the main component of investment return is
through capital appreciation in growth funds and through dividend income in value funds. The
investor shows Jacqueline the annual return data for Vanguard’s Growth Index mutual fund
(henceforth, Growth) and Vanguard’s Value Index mutual fund (henceforth, Value). Table 3.1
shows the annual return data for these two mutual funds for the years 2007–2016.
Year Growth Value Year Growth Value
2007 12.56 0.09 2012 16.89 15.00
2008 −38.32 −35.97 2013 32.16 32.85
2009 36.29 19.58 2014 13.47 13.05
2010 16.96 14.28 2015 3.17 −1.03
2011 1.71 1.00 2016 5.99 16.75
TABLE 3.1 Returns (in percent) for the Growth and the Value Funds
Source: finance.yahoo.com, data retrieved February 17, 2017.
In addition to clarifying the style differences in growth investing versus value investing, Jacqueline
will use the above sample information to
1. Calculate and interpret the typical return for these two mutual funds.
2. Calculate and interpret the investment risk for these two mutual funds.
3. Determine which mutual fund provides the greater return relative to risk.
A synopsis of this case is provided at the end of Section 3.4.
Growth_Value
©Mark Bowden/Getty Images
Revised Pages
ChAPTeR 3 numerical Descriptive Measures B u S I n e S S S TAT I S T I C S 83
jag39519_ch03_060-103 83 06/13/18 07:43 PM
EXAMPLE 3.14
Calculate and interpret the Sharpe ratios for the Growth and the Value mutual
funds given that the return on a 1-year T-bill is 2%.
SOLUTION: Since the return on a 1-year T-bill is 2%, ¯
Rf = 2. Plugging in the values
of the relevant means and standard deviations into the Sharpe ratio yields
Sharpe ratio for the Growth mutual fund:
¯
xI − ¯
Rf
______
sI
=
10.09 − 2
________
20.45
= 0.40.
Sharpe ratio for the Value mutual fund:
¯
xI − ¯
Rf
______
sI
=
7.56 − 2
_______
18.46
= 0.30.
We had earlier shown that the Growth mutual fund had a higher return, which is
good, along with a higher variance, which is bad. We can use the Sharpe ratio to
make a valid comparison between the funds. The Growth mutual fund provides
a higher Sharpe ratio than the Value mutual fund (0.40 > 0.30); therefore, the
Growth mutual fund offered more reward per unit of risk compared to the Value
mutual fund.
S Y N O P S I S O F I N T R O D U C T O R Y C A S E
Growth and value are two fundamental styles in stock and mutual
fund investing. Proponents of growth investing believe that com-
panies that are growing faster than their peers are trendsetters
and will be able to maintain their superior growth. By investing in
the stocks of these companies, they expect their investment to
grow at a rate faster than the overall stock market. By comparison,
value investors focus on the stocks of companies that are trading
at a discount relative to the overall market or a specific sector.
Investors of value stocks believe that these stocks are under-
valued and that their price will increase once their true value is
recognized by other investors. The debate between growth and
value investing is age-old, and which style dominates depends on
the sample period used for the analysis.
An analysis of annual return data for Vanguard’s Growth Index mutual fund (Growth) and Vanguard’s Value
Index mutual fund (Value) for the years 2007 through 2016 provides important information for an investor trying
to determine whether to invest in a growth mutual fund, a value mutual fund, or both types of mutual funds. Over
this period, the mean return for the Growth fund of 10.09% is greater than the mean return for the Value fund
of 7.56%. While the mean return typically represents the reward of investing, it does not incorporate the risk of
investing.
Standard deviation tends to be the most common measure of risk with financial data. Since the standard devia-
tion for the Growth fund (20.45%) is greater than the standard deviation for the Value fund (18.46%), the Growth
fund is likelier to have returns farther above and below its mean. Finally, given a risk-free rate of 2%, the Sharpe ratio
for the Growth fund is 0.40 compared to that for the Value fund of 0.30, indicating that the Growth fund provides
more reward per unit of risk. Assuming that the behavior of these returns will continue, the investor will favor invest-
ing in Growth over Value. A commonly used disclaimer, however, states that past performance is no guarantee of
future results. Since the two styles often complement each other, it might be advisable for the investor to add diver-
sity to his portfolio by using them together.
©Ingram Publishing/Getty Images
In all of these chapters, the opening case leads directly into the application questions that
students will have regarding the material. Having a strong and related case will certainly provide
more benefit to the student, as context leads to improved learning.
Alan Chow, University of South Alabama
This is an excellent approach. The student gradually gets the idea that he can look at a problem—
one which might be fairly complex—and break it down into root components. He learns that a
little bit of math could go a long way, and even more math is even more beneficial to evaluating
the problem.
Dane Peterson, Missouri State University

WALKTHROUGH E S S E N T I A L S O F B usiness S tatistics xi
and Build Skills to Communicate
Results
These technical writing
examples provide a very
useful example of how to
make statistics work and
turn it into a report that will
be useful to an organization.
I will strive to have my
students learn from these
examples.
Bruce P. Christensen,
Weber State University
This is an excellent
approach. . . . The ability
to translate numerical
information into words that
others can understand is
critical.
Scott Bailey, Troy University
Writing with statistics shows
that statistics is more than
number crunching.
Greg Cameron,
Brigham Young University
Excellent. Students need to
become better writers.
Bob Nauss, University of
Missouri, St. Louis
Writing with Statistics
One of our most important innovations is the inclusion of a sample report
within every chapter (except Chapter 1). Our intent is to show students how
to convey statistical information in written form to those who may not know
detailed statistical methods. For example, such a report may be needed as
input for managerial decision making in sales, marketing, or company plan-
ning. Several similar writing exercises are provided at the end of each chap-
ter. Each chapter also includes a synopsis that addresses questions raised from
the introductory case. This serves as a shorter writing sample for students.
Instructors of large sections may find these reports useful for incorporating
writing into their statistics courses.
First Pages
209
jag39519_ch06_182-217 209 05/25/18 02:33 PM
W R I T I N G W I T H S TAT I S T I C S
Professor Lang is a professor of economics at Salem State university. She has been
teaching a course in Principles of economics for over 25 years. Professor Lang has
never graded on a curve since she believes that relative grading may unduly penalize
(benefit) a good (poor) student in an unusually strong (weak) class. She always uses an
absolute scale for making grades, as shown in the two left columns of table 6.5.
Absolute Grading Relative Grading
Grade Score Grade Probability
A 92 and above A 0.10
B 78 up to 92 B 0.35
C 64 up to 78 C 0.40
D 58 up to 64 D 0.10
F Below 58 F 0.05
TABLE 6.5 Grading Scales with Absolute Grading versus Relative Grading
A colleague of Professor Lang’s has convinced her to move to relative grading, since it cor-
rects for unanticipated problems. Professor Lang decides to experiment with grading based
on the relative scale as shown in the two right columns of table 6.5. using this relative grading
scheme, the top 10% of students will get A’s, the next 35% B’s, and so on. Based on her years
of teaching experience, Professor Lang believes that the scores in her course follow a normal
distribution with a mean of 78.6 and a standard deviation of 12.4.
Professor Lang wants to use the above information to
1. Calculate probabilities based on the absolute scale. Compare these probabilities to the
relative scale.
2. Calculate the range of scores for various grades based on the relative scale. Compare
these ranges to the absolute scale.
3. Determine which grading scale makes it harder to get higher grades.
©image Source, all rights reserved.
Sample
Report—
Absolute
Grading
versus
Relative
Grading
Many teachers would confess that grading is one of the most difficult tasks of their profession.
two common grading systems used in higher education are relative and absolute. Relative
grading systems are norm-referenced or curve-based, in which a grade is based on the stu-
dent’s relative position in class. Absolute grading systems, on the other hand, are criterion-
referenced, in which a grade is related to the student’s absolute performance in class. in short,
with absolute grading, the student’s score is compared to a predetermined scale, whereas with
relative grading, the score is compared to the scores of other students in the class.
Let X represent a grade in Professor Lang’s class, which is normally distributed with a mean
of 78.6 and a standard deviation of 12.4. this information is used to derive the grade probabili-
ties based on the absolute scale. For instance, the probability of receiving an A is derived as
P(X ≥ 92) = P(Z ≥ 1.08) = 0.14. Other probabilities, derived similarly, are presented in table 6.A.
Grade
Probability Based on
Absolute Scale
Relative Scale
A 0.14 0.10
B 0.38 0.35
C 0.36 0.40
D 0.07 0.10
F 0.05 0.05
TABLE 6.A Probabilities Based on Absolute Scale and Relative Scale
First Pages
209
jag39519_ch06_182-217 209 05/25/18 02:33 PM
W R I T I N G W I T H S TAT I S T I C S
Professor Lang is a professor of economics at Salem State university. She has been
teaching a course in Principles of economics for over 25 years. Professor Lang has
never graded on a curve since she believes that relative grading may unduly penalize
(benefit) a good (poor) student in an unusually strong (weak) class. She always uses an
absolute scale for making grades, as shown in the two left columns of table 6.5.
Absolute Grading Relative Grading
Grade Score Grade Probability
A 92 and above A 0.10
B 78 up to 92 B 0.35
C 64 up to 78 C 0.40
D 58 up to 64 D 0.10
F Below 58 F 0.05
TABLE 6.5 Grading Scales with Absolute Grading versus Relative Grading
A colleague of Professor Lang’s has convinced her to move to relative grading, since it cor-
rects for unanticipated problems. Professor Lang decides to experiment with grading based
on the relative scale as shown in the two right columns of table 6.5. using this relative grading
scheme, the top 10% of students will get A’s, the next 35% B’s, and so on. Based on her years
of teaching experience, Professor Lang believes that the scores in her course follow a normal
distribution with a mean of 78.6 and a standard deviation of 12.4.
Professor Lang wants to use the above information to
1. Calculate probabilities based on the absolute scale. Compare these probabilities to the
relative scale.
2. Calculate the range of scores for various grades based on the relative scale. Compare
these ranges to the absolute scale.
3. Determine which grading scale makes it harder to get higher grades.
©image Source, all rights reserved.
Sample
Report—
Absolute
Grading
versus
Relative
Grading
Many teachers would confess that grading is one of the most difficult tasks of their profession.
two common grading systems used in higher education are relative and absolute. Relative
grading systems are norm-referenced or curve-based, in which a grade is based on the stu-
dent’s relative position in class. Absolute grading systems, on the other hand, are criterion-
referenced, in which a grade is related to the student’s absolute performance in class. in short,
with absolute grading, the student’s score is compared to a predetermined scale, whereas with
relative grading, the score is compared to the scores of other students in the class.
Let X represent a grade in Professor Lang’s class, which is normally distributed with a mean
of 78.6 and a standard deviation of 12.4. this information is used to derive the grade probabili-
ties based on the absolute scale. For instance, the probability of receiving an A is derived as
P(X ≥ 92) = P(Z ≥ 1.08) = 0.14. Other probabilities, derived similarly, are presented in table 6.A.
Grade
Absolute Scale
Relative Scale
A 0.14 0.10
B 0.38 0.35
C 0.36 0.40
D 0.07 0.10
F 0.05 0.05
TABLE 6.A Probabilities Based on Absolute Scale and Relative Scale

xii E S S E N T I A L S O F B usiness S tatistics WALKTHROUGH
Unique Coverage and
Presentation . . .
Unique Coverage of Regression Analysis
We combine simple and multiple regression in one chapter, which we believe is a
seamless grouping and eliminates needless repetition. This grouping allows more
coverage of regression analysis than the vast majority of Essentials texts. This focus
reflects the topic’s growing use in practice. However, for those instructors who prefer
to cover only simple regression, doing so is still an option.
By comparing this
chapter with other
books, I think that
this is one of the best
explanations about
regression I have seen.
Cecilia Maldonado,
Georgia Southwestern
State University
This is easy for students
to follow and I do get
the feeling . . . the
sections are spoken
language.
Zhen Zhu, University of
Central Oklahoma
The authors have put forth a novel and innovative way to present
regression which in and of itself should make instructors take a long and
hard look at this book. Students should find this book very readable and
a good companion for their course.
Harvey A. Singer, George Mason University
Written as Taught
We introduce topics just the way we teach them; that is, the relevant tools follow the
opening application. Our roadmap for solving problems is
1. Start with intuition
2. Introduce mathematical rigor, and
3. Produce computer output that confirms results.
We use worked examples throughout the text to illustrate how to apply concepts to
solve real-world problems.

WALKTHROUGH E S S E N T I A L S O F B usiness S tatistics xiii
that Make the Content More
Effective
Integration of Microsoft Excel®
We prefer that students first focus on and absorb the statistical material before replicating
their results with a computer. Solving each application manually provides students with
a deeper understanding of the relevant concept. However, we recognize that, primarily
due to cumbersome calculations or the need for statistical tables, embedding computer
output is necessary. Microsoft Excel is the primary software package used in this text.
We chose Excel over other statistical packages based on reviewer feedback and the fact
that students benefit from the added spreadsheet experience. We provide instructions for
using Minitab, SPSS, JMP, and R in chapter appendices.
B u s i n e s s s tat i s t i c s PaRt tHRee Probability and Probability Distributions
162 06/26/18 04:58 PM
Hypergeometric
P(X = x) =HYPGeOM.Dist(x, n, S, N, 0)
P(X ≤ x) =HYPGeOM.Dist(x, n, S, N, 1)
EXAMPLE 5.7
In the past decade, the use of technology has skyrocketed, with social media
blooming into one of the most valuable methods of communication. People are
turning to social media to stay in touch with friends and family members, connect
with old friends, catch the news, look for employment, and be entertained. Accord-
ing to a 2016 Pew Research survey, 68% of all U.S. adults are Facebook users.
Consider a sample of 100 randomly selected American adults.
a. What is the probability that exactly 70 American adults are Facebook users?
b. What is the probability that no more than 70 American adults are
Facebook users?
c. What is the probability that at least 70 American adults are Facebook users?
SOLUTION: We let X denote the number of American adults who are Facebook
users. We also know that p = 0.68 and n = 100.
Using Excel to Obtain Binomial Probabilities
We use Excel’s BINOM.DIST function to calculate binomial probabili-
ties. In order to find P(X = x), we enter “=BINOM.DIST(x, n, p, 0)” where x
is the number of successes, n is the number of trials, and p is the probability
of success. If we enter a “1” for the last argument in the function, then Excel
returns P(X ≤ x).
a. In order to find the probability that exactly 70 American adults are Facebook
users, P(X = 70), we enter “=BINOM.DIST(70, 100, 0.68, 0)” and Excel
returns 0.0791.
b. In order to find the probability that no more than 70 American adults are
Facebook users, P(X ≤ 70), we enter “=BINOM.DIST(70, 100, 0.68, 1)”
and Excel returns 0.7007.
c. In order to find the probability that at least 70 American adults are
Facebook users, P(X ≥ 70) = 1 − P(X ≤ 69), we enter “=1−BINOM.
DIST(69, 100, 0.68, 1)” and Excel returns 0.3784.
. . . does a solid job of
building the intuition
behind the concepts
and then adding
mathematical rigor
to these ideas before
finally verifying the
results with Excel.
Matthew Dean,
University of
Southern Maine

xiv E S S E N T I A L S O F B usiness S tatistics WALKTHROUGH
Confirming Pages
Chapter 9 hypothesis testing e S S e N t I a L S O F B u S I N e S S S tat I S t I C S 307
18. Consider the following hypothesis test:
H0: μ ≤ −5
HA: μ > −5
A random sample of 50 observations yields a sample mean
of −3. The population standard deviation is 10. Calculate the
p-value. What is the conclusion to the test if α = 0.05?
H0: μ ≤ 75
HA: μ > 75
of 80. The population standard deviation is 30. Calculate the
p-value. What is the conclusion to the test if α = 0.10?
H0: μ = −100
HA: μ ≠ −100
of −125. The population standard deviation is 42. Conduct
the test at α = 0.01.
21. Consider the following hypotheses:
H0: μ = 120
HA: μ ≠ 120
The population is normally distributed with a population
standard deviation of 46.
a. If ¯
x = 132 and n = 50, what is the conclusion at the
5% significance level?
b. If ¯
x = 108 and n = 50, what is the conclusion at the
10% significance level?
22. Excel_1. Given the accompanying sample data, use
Excel’s formula options to determine if the population mean
is less than 125 at the 5% significance level. Assume that the
population is normally distributed and that the population
standard deviation equals 12.
23. Excel_2. Given the accompanying sample data, use
Excel’s formula options to determine if the population mean
differs from 3 at the 5% significance level. Assume that the
population is normally distributed and that the population
standard deviation equals 5.
Applications
24. It is advertised that the average braking distance for a small
car traveling at 65 miles per hour equals 120 feet. A transpor-
tation researcher wants to determine if the statement made in
the advertisement is false. She randomly test drives 36 small
cars at 65 miles per hour and records the braking distance.
The sample average braking distance is computed as 114 feet.
Assume that the population standard deviation is 22 feet.
a. State the null and the alternative hypotheses for the test.
b. Calculate the value of the test statistic and the p-value.
c. Use α = 0.01 to determine if the average breaking
distance differs from 120 feet.
25. Customers at Costco spend an average of $130 per trip (The
Wall Street Journal, October 6, 2010). One of Costco’s rivals
would like to determine whether its customers spend more
per trip. A survey of the receipts of 25 customers found that
the sample mean was $135.25. Assume that the population
standard deviation is $10.50 and that spending follows a
normal distribution.
a. Specify the null and alternative hypotheses to test whether
average spending at the rival’s store is more than $130.
b. Calculate the value of the test statistic and the p-value.
c. At the 5% significance level, what is the conclusion
to the test?
26. In May 2008, CNN reported that sports utility vehicles (SUVs)
are plunging toward the “endangered” list. Due to the uncer-
tainty of oil prices and environmental concerns, consumers are
replacing gas-guzzling vehicles with fuel-efficient smaller cars.
As a result, there has been a big drop in the demand for new
as well as used SUVs. A sales manager of a used car dealer-
ship for SUVs believes that it takes more than 90 days, on
average, to sell an SUV. In order to test his claim, he samples
40 recently sold SUVs and finds that it took an average of
95 days to sell an SUV. He believes that the population
standard deviation is fairly stable at 20 days.
a. State the null and the alternative hypotheses for
the test.
b. What is the p-value?
c. Is the sales manager’s claim justified at α = 0.01?
27. According to the Centers for Disease Control and Prevention
(February 18, 2016), 1 in 3 American adults do not get enough
sleep. A researcher wants to determine if Americans are sleeping
less than the recommended 7 hours of sleep on weekdays. He
takes a random sample of 150 Americans and computes the
average sleep time of 6.7 hours on weekdays. Assume that the
population is normally distributed with a known standard devia-
tion of 2.1 hours. Test the researcher’s claim at α = 0.01.
28. A local bottler in Hawaii wishes to ensure that an average
of 16 ounces of passion fruit juice is used to fill each bottle.
In order to analyze the accuracy of the bottling process, he
takes a random sample of 48 bottles. The mean weight of the
passion fruit juice in the sample is 15.80 ounces. Assume that
the population standard deviation is 0.8 ounce.
a. State the null and the alternative hypotheses to test if the
bottling process is inaccurate.
b. What is the value of the test statistic and the p-value?
c. At α = 0.05, what is the conclusion to the hypothesis
test? Make a recommendation to the bottler.
29. MV_Houses. A realtor in Mission Viejo, California,
believes that the average price of a house is more than
$500,000.
b. The data accompanying this exercise show house prices.
(Data are in $1,000s.) Assume the population standard
Real-World Exercises and Case
Studies that Reinforce the Material
Mechanical and Applied Exercises
Chapter exercises are a well-balanced blend of mechanical, computational-type problems
followed by more ambitious, interpretive-type problems. We have found that simpler drill
problems tend to build students’ confidence prior to tackling more difficult applied prob-
lems. Moreover, we repeatedly use many data sets—including house prices, rents, stock
returns, salaries, and debt—in various chapters of the text. For instance, students first use
these real data to calculate summary measures, make statistical inferences with confi-
dence intervals and hypothesis tests, and finally, perform regression analysis.
Applied exercises from
The Wall Street Journal,
Kiplinger’s, Fortune, The New
York Times, USA Today; various
websites—Census.gov,
Zillow.com, Finance.yahoo.com,
ESPN.com; and more.
Their exercises and problems are excellent!
Erl Sorensen, Bentley University
I especially like the introductory cases, the quality of the end-of-section
problems, and the writing examples.
Dave Leupp, University of Colorado at Colorado Springs

WALKTHROUGH E S S E N T I A L S O F B usiness S tatistics xv
Features that Go Beyond the
Typical
Conceptual Review
At the end of each chapter, we present a conceptual review that provides a more holistic
approach to reviewing the material. This section revisits the learning outcomes and pro-
vides the most important definitions, interpretations, and formulas.
CHAPTER 5 Discrete Probability Distributions B U S I n E S S S TAT I S T I C S 175
jag39519_ch05_144-181 175 06/13/18 07:46 PM
TABLE 5.B Calculating Arroyo’s Expected Bonus
Bonus (in $), xi Probability, P(xi) Weighted Value, xi P(xi)
0 0.20 0 × 0.20 = 0
50,000 0.25 50,000 × 0.25 = 12,500
100,000 0.35 100,000 × 0.35 = 35,000
150,000 0.20 150,000 × 0.20 = 30,000
Total = 77,500
Arroyo’s expected bonus amounts to $77,500. Thus, her salary options are
Option 1: $125,000 + $77,500 = $202,500
Option 2: $150,000 + (1/2 × $77,500) = $188,750
Arroyo should choose Option 1 as her salary plan.
C O n C E P T U A L R E V I E W
LO 5.1 Describe a discrete random variable and its probability distribution.
A random variable summarizes outcomes of an experiment with numerical values. A
discrete random variable assumes a countable number of distinct values, whereas a
continuous random variable is characterized by uncountable values in an interval.
The probability mass function for a discrete random variable X is a list of the values of
X with the associated probabilities; that is, the list of all possible pairs (x, P(X = x)). The
cumulative distribution function of X is defined as P(X ≤ x).
LO 5.2 Calculate and interpret summary measures for a discrete random
variable.
For a discrete random variable X with values x1, x2, x3, . . . , which occur with probabili-
ties P(X = xi), the expected value of X is calculated as E(X) = μ = ΣxiP(X = xi). We
interpret the expected value as the long-run average value of the random variable over
infinitely many independent repetitions of an experiment. Measures of dispersion indi-
cate whether the values of X are clustered about μ or widely scattered from μ. The variance
of X is calculated as Var(X) = σ2
= Σ(xi − μ)2
P(X = xi). The standard deviation of X is
SD(X)= σ = √
__
σ2
.
In general, a risk-averse consumer expects a reward for taking risk. A risk-averse
consumer may decline a risky prospect even if it offers a positive expected gain. A
risk-neutral consumer completely ignores risk and always accepts a prospect that offers
a positive expected gain.
LO 5.3 Calculate and interpret probabilities for a binomial random variable.
A Bernoulli process is a series of n independent and identical trials of an experiment
such that on each trial there are only two possible outcomes, conventionally labeled “suc-
cess” and “failure.” The probabilities of success and failure, denoted p and 1 − p, remain
the same from trial to trial.
For a binomial random variable X, the probability of x successes in n Bernoulli trials is
P(X = x) = (
n
x)px
(1 − p)n−x
= n!
_____
x!(n − x)! px
(1 − p)n−x
for x = 0, 1, 2, . . . , n.
The expected value, the variance, and the standard deviation of a binomial random vari-
able are E(X) = np, Var(X) = σ2
= np(1 − p), and SD(X)= σ = √
_______
np(1 − p), respectively.
They have gone beyond the typical [summarizing formulas] and I like the structure.
This is a very strong feature of this text.
Virginia M. Miori, St. Joseph’s University
Most texts basically list what one should have learned but don’t add much to that. You do a
good job of reminding the reader of what was covered and what was most important about it.
Andrew Koch, James Madison University

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They’ll thank you for it.
Adaptive study resources like SmartBook® help your
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Make it simple, make it affordable.
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xviii E S S E N T I A L S O F B usiness S tatistics WALKTHROUGH
What Resources are Available for
Instructors?
Instructor Library
The Connect Instructor Library is your repository for additional resources to improve stu-
dent engagement in and out of class. You can select and use any asset that enhances your
lecture. The Connect Instructor Library includes:
∙ PowerPoint presentations
∙ Excel Data Files
∙ Test Bank
∙ Instructor’s Solutions Manual
∙ Digital Image Library
Tegrity Campus:
Lectures 24/7
Tegrity Campus is integrated in Connect to help make your class time available 24/7.
With Tegrity, you can capture each one of your lectures in a searchable format for stu-
dents to review when they study and complete assignments using Connect. With a simple
one-click start-and-stop process, you can capture everything that is presented to students
during your lecture from your computer, including audio. Students can replay any part of
any class with easy-to-use browser-based viewing on a PC or Mac.
Educators know that the more students can see, hear, and experience class resources,
the better they learn. In fact, studies prove it. With Tegrity Campus, students quickly
recall key moments by using Tegrity Campus’s unique search feature. This search helps
students efficiently find what they need, when they need it, across an entire semester of
class recordings. Help turn all your students’ study time into learning moments immedi-
ately supported by your lecture. To learn more about Tegrity, watch a two-minute Flash
demo at http://tegritycampus.mhhe.com.

WALKTHROUGH E S S E N T I A L S O F B usiness S tatistics xix
ALEKS
ALEKS is an assessment and learning program that provides individualized instruction
in Business Statistics, Business Math, and Accounting. Available online in partnership
with McGraw-Hill Education, ALEKS interacts with students much like a skilled human
tutor, with the ability to assess precisely a student’s knowledge and provide instruction on
the exact topics the student is most ready to learn. By providing topics to meet individual
students’ needs, allowing students to move between explanation and practice, correcting
and analyzing errors, and defining terms, ALEKS helps students to master course content
quickly and easily.
ALEKS also includes an instructor module with powerful, assignment-driven fea-
tures and extensive content flexibility. ALEKS simplifies course management and allows
instructors to spend less time with administrative tasks and more time directing student
learning. To learn more about ALEKS, visit www.aleks.com.
MegaStat® for Microsoft Excel®
MegaStat®
by J. B. Orris of Butler University is a full-featured Excel add-in that is
available online through the MegaStat website at www.mhhe.com/megastat or through
an access card packaged with the text. It works with Excel 2016, 2013, and 2010 (and
Excel: Mac 2016). On the website, students have 10 days to successfully download and
install MegaStat on their local computer. Once installed, MegaStat will remain active in
Excel with no expiration date or time limitations. The software performs statistical analy-
ses within an Excel workbook. It does basic functions, such as descriptive statistics, fre-
quency distributions, and probability calculations, as well as hypothesis testing, ANOVA,
and regression. MegaStat output is carefully formatted, and its ease-of-use features
include Auto Expand for quick data selection and Auto Label detect. Since
MegaStat
is easy to use, students can focus on learning statistics without being distracted by the
software. MegaStat is always available from Excel’s main menu. Selecting a menu item
pops up a dialog box. Screencam tutorials are included that provide a walkthrough of
major business statistics topics. Help files are built in, and an introductory user’s manual
is also included.

xx E S S E N T I A L S O F B usiness S tatistics WALKTHROUGH
What Resources are Available for
Students?
Integration of Excel Data Sets. A conven-
ient feature is the inclusion of an Excel data file
link in many problems using data files in their
calculation. The link allows students to easily
launch into Excel, work the problem, and return
to Connect to key in the answer and receive
feedback on their results.
Confirming Pages
al Estimation E S S E N T I A L S O F B u S I N E S S S TAT I S T I c S 267
08/22/18 07:00 PM
rtgage rate
sample of
d from this
ar fixed mort-
ulation standard
nfidence inter-
tgage rate.
.S. Racking Up
hat Americans
archer in a
mean weekday
dom sample of
mean sleep time
ard deviation is
the population
dents of this
at the mean
dwestern town
o California.
Louis, it is tak-
is concerned
ir house on
t the last 26
average time of
t based on her
ation is 72 days.
n is necessary
pulation mean?
the mean sale
ards as a con-
rage amount
ger’s, August
a sample of 100
viation is $500.
error?
the population
ard.
ean salary of
en by [$36,080,
sed for the
ary for all
nalysis.
time (in
ant uses a
dence interval
eviation is
a. Find the sample mean time used to compute the
confidence interval.
b. Determine the confidence level used for the analysis.
15. CT_Undergrad_Debt. A study reports that recent
college graduates from New Hampshire face the highest
average debt of $31,048 (The Boston Globe, May 27, 2012).
A researcher from Connecticut wants to determine how
recent undergraduates from that state fare. He collects data
on debt from 40 recent undergraduates. A portion of the
data is shown in the accompanying table. Assume that the
population standard deviation is $5,000.
Debt
24040
19153
⋮
29329
a. Construct the 95% confidence interval for the mean debt
of all undergraduates from Connecticut.
b. Use the 95% confidence interval to determine if the debt
of Connecticut undergraduates differs from that of New
Hampshire undergraduates.
16. Hourly_Wage. An economist wants to estimate
the mean hourly wage (in $) of all workers. She collects
data on 50 hourly wage earners. A portion of the data
is shown in the accompanying table. Assume that the
population standard deviation is $6. Construct and
interpret 90% and 99% confidence intervals for the mean
hourly wage of all workers.
Hourly Wage
37.85
21.72
⋮
24.18
17. Highway_Speeds. A safety officer is concerned about
speeds on a certain section of the New Jersey Turnpike. He
records the speeds of 40 cars on a Saturday afternoon. The
accompanying table shows a portion of the results. Assume
that the population standard deviation is 5 mph. Construct the
95% confidence interval for the mean speed of all cars on that
section of the turnpike. Are the safety officer’s concerns valid if
the speed limit is 55 mph? Explain.
Highway Speeds
70
60
⋮
65
Revised Pages
jag39519_ch09_292-327 308 08/21/18 06:11 PM
308 E S S E N T I A L S O F B u S I N E S S S TAT I S T I C S 9.3 Hypothesis Test for the Population Mean When σ is unknown
9.3 HYPOTHESIS TEST FOR THE POPuLATION
MEAN WHEN σ IS uNKNOWN
So far we have considered hypothesis tests for the population mean μ under the assump-
tion that the population standard deviation σ is known. In most business applications, σ is
not known and we have to replace σ with the sample standard deviation s to estimate the
standard error of ¯
X.
deviation is $100 (in $1,000s). What is the value of the
test statistic and the p-value?
c. At α = 0.05, what is the conclusion to the test? Is the
realtor’s claim supported by the data?
30. Home_Depot. The data accompanying this exercise
show the weekly stock price for Home Depot. Assume that
stock prices are normally distributed with a population stan-
dard deviation of $3.
a. State the null and the alternative hypotheses in order
to test whether or not the average weekly stock price
differs from $30.
b. Find the value of the test statistic and the p-value.
c. At α = 0.05, can you conclude that the average weekly
stock price does not equal $30?
31. Hourly_Wage. An economist wants to test if the aver-
age hourly wage is less than $22. Assume that the population
standard deviation is $6.
b. The data accompanying this exercise show hourly
wages. Find the value of the test statistic and the
p-value.
c. At α = 0.05, what is the conclusion to the test? Is the
average hourly wage less than $22?
32. CT_Undergrad_Debt. On average, a college student
graduates with $27,200 in debt (The Boston Globe, May 27,
2012). The data accompanying this exercise show the debt for
40 recent undergraduates from Connecticut. Assume that the
population standard deviation is $5,000.
a. A researcher believes that recent undergraduates
from Connecticut have less debt than the national
average. Specify the competing hypotheses to test
this belief.
b. Find the value of the test statistic and the p-value.
c. Do the data support the researcher’s claim, at α = 0.10?
Conduct a hypothesis test
for the population mean
when σ is unknown.
LO 9.4
TEST STATISTIC FOR μ WHEN σ IS UNKNOWN
The value of the test statistic for the hypothesis test of the population mean μ when
the population standard deviation σ is unknown is computed as
tdf =
¯
x − μ0
_____
s/√
__
n
,
where μ0 is the hypothesized value of the population mean, s is the sample standard
deviation, n is the sample size, and the degrees of freedom df = n − 1. This formula
is valid only if ¯
X (approximately) follows a normal distribution.
The next two examples show how we use the four-step procedure for hypothesis testing
when we are testing the population mean μ and the population standard deviation σ is
unknown.
EXAMPLE 9.10
In the introductory case to this chapter, the dean at a large university in California
wonders if students at her university study less than the 1961 national average of
24 hours per week. She randomly selects 35 students and asks their average study
time per week (in hours). From their responses, she calculates a sample mean of
16.3714 hours and a sample standard deviation of 7.2155 hours.
FILE
Study_Hours
Guided Examples. These narrated video walk-
throughs provide students with step-by-step guidelines
for solving selected exercises similar to those contained
in the text. The student is given personalized instruction
on how to solve a problem by applying the concepts pre-
sented in the chapter. The video shows the steps to take
to work through an exercise. Students can go through
each example multiple times if needed.
The Connect Student Resource page is the place for
students to access additional resources. The Student
Resource page offers students quick access to the rec-
ommended study tools, data files, and helpful tutorials
on statistical programs.

WALKTHROUGH E S S E N T I A L S O F B usiness S tatistics xxi
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xxii
We would like to acknowledge the following people for providing useful comments and
suggestions for past and present editions of all aspects of Business Statistics.
ACKNOWLEDGMENTS
John Affisco
Hofstra University
Mehdi Afiat
College of Southern Nevada
Mohammad Ahmadi
University of Tennessee—
Chattanooga
Sung Ahn
Washington State University
Mohammad Ahsanullah
Rider University
Imam Alam
University of Northern Iowa
Mostafa Aminzadeh
Towson University
Ardavan Asef-Vaziri
California State University
Antenah Ayanso
Brock University
Scott Bailey
Troy University
Jayanta Bandyopadhyay
Central Michigan University
Samir Barman
University of Oklahoma
Douglas Barrett
University of North Alabama
John Beyers
University of Maryland
Arnab Bisi
Purdue University—West
Lafayette
Gary Black
University of Southern
Indiana
Randy Boan
Aims Community College
Matthew Bognar
University of Iowa
Juan Cabrera
Ramapo College of New
Jersey
Scott Callan
Bentley University
Gregory Cameron
Brigham Young University
Kathleen Campbell
St. Joseph’s University
Alan Cannon
University of Texas—
Arlington
Michael Cervetti
University of Memphis
Samathy Chandrashekar
Salisbury University
Gary Huaite Chao
University of Pennsylvania—
Kutztown
Sangit Chatterjee
Northeastern University
Leida Chen
California Polytechnic State
University
Anna Chernobai
Syracuse University
Alan Chesen
Wright State University
Juyan Cho
Colorado State
University—Pueblo
Alan Chow
University of South Alabama
Bruce Christensen
Howard Clayton
Auburn University
Robert Collins
Marquette University
M. Halim Dalgin
Kutztown University
Tom Davis
University of Dayton
Matthew Dean
University of Maine
Jason Delaney
University of Arkansas—
Little Rock
Ferdinand DiFurio
Tennessee Tech University
Matt Dobra
UMUC
Luca Donno
University of Miami
Joan Donohue
University of South Carolina
David Doorn
University of Minnesota
James Dunne
University of Dayton
Mike Easley
University of New Orleans
Erick Elder
University of Arkansas—
Little Rock
Ashraf ElHoubi
Lamar University
Roman Erenshteyn
Goldey-Beacom College
Grace Esimai
University of
Texas—Arlington
Soheila Fardanesh
Towson University
Carol Flannery
University of Texas—Dallas
Sydney Fletcher
Mississippi Gulf Coast
Community College
Andrew Flight
Portland State University
Samuel Frame
Cal Poly San Luis Obispo
Priya Francisco
Purdue University
Vickie Fry
Westmoreland County
Community College
Ed Gallo
Sinclair Community
College
Glenn Gilbreath
Virginia Commonwealth
University
Robert Gillette
University of Kentucky
Xiaoning Gilliam
Texas Tech University
Mark Gius
Quinnipiac University
Malcolm Gold
Saint Mary’s University of
Minnesota
Michael Gordinier
Washington University

Deborah Gougeon
University of Scranton
Don Gren
Salt Lake Community
College
Thomas G. Groleau
Carthage College
Babita Gupta
CSU Monterey Bay
Robert Hammond
North Carolina State
University
Jim Han
Florida Atlantic University
Elizabeth Haran
Salem State University
Jack Harshbarger
Montreat College
Edward Hartono
University of
Alabama—Huntsville
Clifford Hawley
West Virginia University
Santhi Heejebu
Cornell College
Paul Hong
University of Toledo
Ping-Hung Hsieh
Oregon State University
Marc Isaacson
Augsburg College
Mohammad Jamal
Northern Virginia
Community College
Robin James
Harper College
Molly Jensen
University of Arkansas
Craig Johnson
Brigham Young
University—Idaho
Janine Sanders Jones
University of St. Thomas
Vivian Jones
Bethune—Cookman
University
Jerzy Kamburowski
University of Toledo
Howard Kaplon
Towson University
Krishna Kasibhatla
North Carolina A&T State
University
Mohammad Kazemi
University of North
Carolina—Charlotte
Ken Kelley
University of Notre Dame
Lara Khansa
Virginia Tech
Esther C. Klein
St. Francis College
Ronald Klimberg
Andrew Koch
James Madison University
Subhash Kochar
Brandon Koford
Weber University
Randy Kolb
St. Cloud State University
Vadim Kutsyy
San Jose State University
Francis Laatsch
Mississippi
David Larson
University of South Alabama
John Lawrence
California State
University—Fullerton
Shari Lawrence
Nicholls State University
Radu Lazar
University of Maryland
David Leupp
University of Colorado—
Colorado Springs
Carel Ligeon
Auburn
University—Montgomery
Carin Lightner
University
Constance Lightner
Fayetteville State University
Scott Lindsey
Dixie State College of Utah
Ken Linna
Auburn
University—Montgomery
Andy Litteral
University of Richmond
Jun Liu
Georgia Southern
University
Chung-Ping Loh
University of North Florida
Salvador Lopez
University of West Georgia
John Loucks
St. Edward’s University
Cecilia Maldonado
Georgia Southwestern State
University
Farooq Malik
Mississippi
Ken Mayer
University of
Nebraska—Omaha
Bradley McDonald
Northern Illinois University
Elaine McGivern
Duquesne University
John McKenzie
Babson University
Norbert Michel
Nicholls State University
John Miller
Sam Houston State
University
Virginia Miori
Prakash Mirchandani
University of Pittsburgh
Jason Molitierno
Sacred Heart University
Elizabeth Moliski
University of Texas—Austin
Joseph Mollick
Texas A&M University—
Corpus Christi
James Moran
Oregon State University
Khosrow Moshirvaziri
California State University—
Long Beach
Tariq Mughal
University of Utah
Patricia Mullins
University of
Wisconsin—Madison
Kusum Mundra
Rutgers University—Newark
Anthony Narsing
Macon State College
Robert Nauss
University of Missouri—St.
Louis
Satish Nayak
University of Missouri—St.
Louis
Thang Nguyen
Long Beach
Mohammad Oskoorouchi
San Marcos
Barb Osyk
University of Akron
Bhavik Pathak
Indiana University South
Bend
Scott Paulsen
Illinois Central College
James Payne
Calhoun Community
College
Norman Pence
Metropolitan State College
of Denver
ACKNOWLEDGMENTS E S S E N T I A L S O F B usiness S tatistics xxiii

Dane Peterson
Missouri State University
Joseph Petry
University of
Illinois—Urbana/Champaign
Courtney Pham
Missouri State University
Martha Pilcher
University of Washington
Cathy Poliak
University of
Wisconsin—Milwaukee
Simcha Pollack
St. John’s University
Hamid Pourmohammadi
Dominguez Hills
Tammy Prater
Alabama State University
Zbigniew H. Przasnyski
Loyola Marymount
University
Manying Qiu
Virginia State University
Troy Quast
Sam Houston State
University
Michael Racer
University of Memphis
Srikant Raghavan
Lawrence Technological
University
Bharatendra Rai
University of
Massachusetts—
Dartmouth
Michael Aaron Ratajczyk
Saint Mary’s University of
Minnesota
Tony Ratcliffe
David Ravetch
University of California
Bruce Reinig
San Diego State University
Darlene Riedemann
Eastern Illinois University
David Roach
Arkansas Tech University
Carolyn Rochelle
East Tennessee State
University
Alfredo Romero
University
Ann Rothermel
University of Akron
Jeff Rummel
Emory University
Deborah Rumsey
The Ohio State University
Stephen Russell
William Rybolt
Babson College
Fati Salimian
Salisbury University
Fatollah Salimian
Perdue School of Business
Samuel Sarri
College of Southern Nevada
Jim Schmidt
University of
Nebraska—Lincoln
Patrick Scholten
Bentley University
Bonnie Schroeder
Ohio State University
Pali Sen
University of North Florida
Donald Sexton
Columbia University
Vijay Shah
West Virginia
University—Parkersburg
Dmitriy Shaltayev
Christopher Newport
University
Soheil Sibdari
University of
Massachusetts—
Dartmouth
Prodosh Simlai
University of North Dakota
Harvey Singer
George Mason University
Harry Sink
University
Don Skousen
Salt Lake Community
College
Robert Smidt
California Polytechnic State
University
Gary Smith
Florida State University
Antoinette Somers
Wayne State University
Ryan Songstad
Augustana College
Erland Sorensen
Bentley University
Arun Kumar Srinivasan
Indiana
University—Southeast
Scott Stevens
Alicia Strandberg
Temple University
Linda Sturges
Suny Maritime College
Wendi Sun
Rockland Trust
Bedassa Tadesse
University of Minnesota
Pandu Tadikamalta
University of Pittsburgh
Roberto Duncan Tarabay
University of
Wisconsin—Madison
Faye Teer
Deborah Tesch
Xavier University
Patrick Thompson
University of Florida
Satish Thosar
University of Redlands
Ricardo Tovar-Silos
Lamar University
Quoc Hung Tran
Bridgewater State University
Elzbieta Trybus
California State
University—Northridge
Fan Tseng
University of
Alabama—Huntsville
Silvanus Udoka
University
Shawn Ulrick
Georgetown University
Bulent Uyar
University of Northern Iowa
Ahmad Vakil
Tobin College of Business
Tim Vaughan
University of Wisconsin—
Eau Claire
Raja Velu
Syracuse University
Holly Verhasselt
University of
Houston—Victoria
Zhaowei Wang
Citizens Bank
Rachel Webb
Kyle Wells
Dixie State College
Alan Wheeler
University of Missouri—
St. Louis
Mary Whiteside
University of Texas—
Arlington
Blake Whitten
University of Iowa
Rick Wing
San Francisco
State University
xxiv E S S E N T I A L S O F B usiness S tatistics ACKNOWLEDGMENTS

Jan Wolcott
Wichita State University
Rongning Wu
Baruch College
John Yarber
Northeast Mississippi
Community College
John C. Yi
Kanghyun Yoon
University of Central
Oklahoma
Mark Zaporowski
Canisius College
Ali Zargar
Dewit Zerom
California State University
Eugene Zhang
Midwestern State University
Ye Zhang
Indiana University—Purdue
University—Indianapolis
Yi Zhang
California State
University—Fullerton
Yulin Zhang
Wencang Zhou
Baruch College
Zhen Zhu
University of Central
Oklahoma
The editorial staff of McGraw-Hill Education are deserving of our gratitude for their
guidance throughout this project, especially Noelle Bathurst, Pat Frederickson, Ryan
McAndrews, Harper Christopher, Daryl Horrocks, and Egzon Shaqiri. We would also like
to thank Eric Kambestad and Matt Kesselring for their outstanding research assistance.
ACKNOWLEDGMENTS E S S E N T I A L S O F B usiness S tatistics xxv

CHAPTER 1 Statistics and Data 2
CHAPTER 2 Tabular and Graphical Methods 18
CHAPTER 3 Numerical Descriptive Measures 60
CHAPTER 4 Introduction to Probability 104
CHAPTER 5 Discrete Probability Distributions 144
CHAPTER 6 Continuous Probability Distributions 182
CHAPTER 7 Sampling and Sampling Distributions 218
CHAPTER 8 Interval Estimation 258
CHAPTER 9 Hypothesis Testing 292
CHAPTER 10 Comparisons Involving Means 328
CHAPTER 11 Comparisons Involving Proportions 370
CHAPTER 12 Basics of Regression Analysis 402
CHAPTER 13 More on Regression Analysis 456
APPENDIXES
APPENDIX A Tables 510
APPENDIX B Answers to Selected Even-Numbered Exercises 520
Glossary 537
Index I-1
BRIEF CONTENTS
xxvi

xxvii
CONTENTS
CHAPTER 1
STATISTICS AND DATA 2
1.1 The Relevance of Statistics 4
1.2 What is Statistics? 5
The Need for Sampling 6
Cross-Sectional and Time Series Data 6
Structured and Unstructured Data 7
Big Data 8
Data on the Web 8
1.3
Variables and Scales of Measurement 10
The Nominal Scale 11
The Ordinal Scale 12
The Interval Scale 13
The Ratio Scale 14
Synopsis of Introductory Case 15
Conceptual Review 16
CHAPTER 2
TABULAR AND
GRAPHICAL METHODS 18
2.1 Summarizing Qualitative Data 20
Pie Charts and Bar Charts 21
Cautionary Comments When Constructing
or Interpreting Charts or Graphs 24
Using Excel to Construct a Pie Chart and a Bar Chart 24
A Pie Chart 24
A Bar Chart 25
2.2 Summarizing Quantitative Data 27
Guidelines for Constructing a Frequency Distribution 28
Synopsis Of Introductory Case 32
Histograms, Polygons, and Ogives 32
Using Excel to Construct a Histogram,
a Polygon, and an Ogive 36
A Histogram Constructed from Raw Data 36
A Histogram Constructed from a Frequency
Distribution 37
A Polygon 38
An Ogive 38
2.3 Stem-and-Leaf Diagrams 42
2.4 Scatterplots 44
Using Excel to Construct a Scatterplot 46
Writing with Statistics 47
Additional Exercises And Case Studies 50
Exercises 50
Case Studies 53
Appendix 2.1
Guidelines for Other Software
Packages 55
CHAPTER 3
NUMERICAL DESCRIPTIVE
MEASURES 60
3.1 Measures of Central Location 62
The Mean 62
The Median 64
The Mode 65
The Weighted Mean 66
Using Excel to Calculate Measures of
Central Location 67
Using Excel’s Function Option 67
Using Excel’s Data Analysis Toolpak Option 68
Note on Symmetry 69
3.2 Percentiles and Boxplots 71
Calculating the pth Percentile 72
Note on Calculating Percentiles 73
Constructing and Interpreting a Boxplot 73
3.3 Measures of Dispersion 76
Range 76
The Mean Absolute Deviation 77
The Variance and the Standard Deviation 78
The Coefficient of Variation 79
Using Excel to Calculate Measures of Dispersion 80
Using Excel’s Function Option 80
Using Excel’s Data Analysis Toolpak Option 80
3.4 Mean-Variance Analysis and
the Sharpe Ratio 81
3.5 Analysis of Relative Location 84
Chebyshev’s Theorem 85
The Empirical Rule 85
z-Scores 86
3.6 Summarizing Grouped Data 89
3.7 Measures of Association 92
Using Excel to Calculate Measures of Association 94
Additional Exercises and Case Studies 98
Exercises 98
Case Studies 101
Appendix 3.1:
Packages 102
CHAPTER 4
INTRODUCTION TO PROBABILITY 104
4.1 Fundamental Probability Concepts 106
Events 107
Assigning Probabilities 109

xxviii E S S E N T I A L S O F B usiness S tatistics CONTENTS
Finding a z Value for a Given Probability 193
The Transformation of Normal Random Variables 195
A Note on the Normal Approximation
of the Binomial Distribution 199
Using Excel for the Normal Distribution 199
6.3 The Exponential Distribution 204
Using Excel for the Exponential Distribution 207
Exercises 211
Case Studies 214
Appendix 6.1:
Packages 215
CHAPTER 7
SAMPLING AND SAMPLING
DISTRIBUTIONS 218
7.1 Sampling 220
Classic Case of a “Bad” Sample: The Literary Digest
Debacle of 1936 220
Trump’s Stunning Victory in 2016 221
Sampling Methods 222
Using Excel to Generate a Simple
Random Sample 224
7.2
The Sampling Distribution of the
Sample Mean 225
The Expected Value and the Standard Error
of the Sample Mean 226
Sampling from a Normal Population 227
The Central Limit Theorem 228
7.3
The Sampling Distribution of the Sample
Proportion 232
The Expected Value and the Standard Error
of the Sample Proportion 232
7.4
The Finite Population Correction Factor 237
7.5 Statistical Quality Control 240
Control Charts 241
Using Excel to Create a Control Chart 244
Exercises 250
Case Studies 252
Appendix 7.1:
Derivation of the Mean and
the Variance for  
¯
X and  ¯
P 253
Appendix 7.2: Properties of Point Estimators 254
Appendix 7.3:
Packages 255
CHAPTER 8
INTERVAL ESTIMATION 258
8.1
Confidence Interval for the Population
Mean when σ is Known 260
Constructing a Confidence Interval for μ
When σ Is Known 261
The Width of a Confidence Interval 263
Using Excel to Construct a Confidence Interval
for μ When σ Is Known 265
4.2 Rules of Probability 113
The Complement Rule 113
The Addition Rule 114
The Addition Rule for Mutually
Exclusive Events 115
Conditional Probability 116
Independent and Dependent Events 118
The Multiplication Rule 119
The Multiplication Rule for
Independent Events 119
4.3 Contingency Tables and Probabilities 123
A Note on Independence 126
4.4 The Total Probability Rule and Bayes’
Theorem 128
The Total Probability Rule 128
Bayes’ Theorem 131
Writing With Statistics 135
Exercises 138
Case Studies 142
CHAPTER 5
DISCRETE PROBABILITY
DISTRIBUTIONS 144
5.1
Random Variables and Discrete
Probability Distributions 146
The Discrete Probability Distribution 147
5.2
Expected Value, Variance, and
Standard Deviation 151
Expected Value 152
Variance and Standard Deviation 152
Risk Neutrality and Risk Aversion 153
5.3 The Binomial Distribution 156
Using Excel to Obtain Binomial Probabilities 161
5.4 The Poisson Distribution 164
Using Excel to Obtain Poisson Probabilities 167
5.5 The Hypergeometric Distribution 169
Using Excel to Obtain Hypergeometric
Probabilities 171
Exercises 176
Case Studies 178
Appendix 5.1:
Packages 179
CHAPTER 6
CONTINUOUS PROBABILITY
DISTRIBUTIONS 182
6.1
Continuous Random Variables and the
Uniform Distribution 184
The Continuous Uniform Distribution 185
6.2 The Normal Distribution 188
Characteristics of the Normal Distribution 189
The Standard Normal Distribution 190
Finding a Probability for a Given z Value 191

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lighted Matches to be ty’d between the Mens Fingers, which burnt all
the Flesh off the Bones; then cut them in several Parts of their
Bodies with Knives and Cutlashes; afterwards took all their
Provisions away, and set some of them ashore in an uninhabited Part
of the Country.
The Kingston, Captain Estwick, another Ship, one Burrington
Master, two Brigantines from Carolina to London; a Sloop from
Virginia to Bermudas; a Ship from Glasgow to Virginia; a Scooner
from New-York to South-Carolina; a Pink from Virginia to Dartmouth,
and a Sloop from Philadelphia to Surinam, fell a Prey to these
Villains, upon this Cruize, besides those above-mentioned.
It happened that at this Time one of his Majesty’s Ships was upon
a Cruize, on this Station, and got Intelligence of some of the
mischievous Actions of this Miscreant, by one of the Vessels that had
been plundered by him, who steering as directed, came in Sight of
the Pyrates by break of Day, on the 10th of June, of all Days in the
Year. The Rovers looking out for Prey, soon saw, and gave Chace to
the Man of War, which was called the Greyhound, a Ship of 20 Guns,
and 120 Men, rather inferiour in Force to the two Pyrate Vessels:
The Greyhound finding them so eager, was in no doubt what they
should be, and therefore tack’d and stood from them, giving the
Pyrates an Opportunity to chace her for two Hours, till all Things
were in Readiness for an Engagement, and the Pyrates about Gun-
shot off; then the Greyhound tack’d again, and stood towards the
two Sloops, one of them called the Fancy, commanded by Low
himself, and the other the Ranger, commanded by Harris, both
which hoisted their pyratical Colours, and fired each a Gun. When
the Greyhound came within Musquet-shot, she halled up her Main-
sail, and clapp’d close upon a Wind, to keep the Pyrates from
running to Leeward, and then engaged: But when the Rogues found
who they had to deal with, they edg’d away under the Man of War’s
Stern, and the Greyhound standing after them, they made a running
Fight for about two Hours; but little Wind happening, the Sloops
gained from her, by the help of their Oars; upon which the
Greyhound left off firing, and turned all Hands to her own Oars, and
at three in the Afternoon came up with them. The Pyrates haul’d

upon a Wind to receive the Man of War, and the Fight was
immediately renewed, with a brisk Fire on both Sides, till the
Ranger’s Main-Yard was shot down, and the Greyhound pressing
close upon the disabled Sloop, Low, in the other, thought fit to bear
away and leave his Consort a Sacrifice to his Enemy, who (seing the
Cowardice and Treachery of his Commadore and Leader, having ten
or twelve Men killed and wounded, and that there was no possibility
of escaping,) called out for Quarters, and surrendered themselves to
Justice, which proved severe enough to them a-while afterwards.
The Conduct of Low was surprizing in this Adventure, because his
reputed Courage and Boldness, had, hitherto, so possess’d the Minds
of all People, that he became a Terror, even to his own Men; but his
Behaviour throughout this whole Action, shewed him to be a base
cowardly Villain, for had Low’s Sloop fought half so briskly as Harris’s
had done, (as they were under a solemn Oath to do,) the Man of
War, in my Opinion, could never have hurted them.
The Greyhound carried in their Prize to Rhode Island, to the great
Joy of the whole Province, tho’ it had been more compleat, if the
great LOW himself had grac’d the Triumph. The Prisoners were
strongly secured in a Goal, till a Court of Vice-Admiralty could be
held for their Tryals, which begun on the 10th of July, at Newport,
and continued three Days. The Court was made up of the following
Gentlemen.
William Dummer, Esq; Lieutenant Governor of the Massachusets,
President. Nathaniel Paine, Esq; Addington Davonport, Esq; Thomas
Fitch, Esq; Spencer Phipps, Esq; John Lechmere, Esq; Surveyor-
General. John Valentine, Esq; Advocate-General. Samuel Cranston,
Governor of Rhode-Island. John Menzies, Esq; Judge of the
Admiralty, Richard Ward, Esq; Register. Mr. Jahleel Brinton, Provost-
Marshal.
Robert Auchmuta, Esq; was assigned, by the Court, Council for the
Prisoners here under mention’d.
Prisoners Names. Ages. Places of Birth.
Charles Harris, Captain 25 London.

William Blads 28 Rhode-Island.
Daniel Hide 23 Virginia.
Thomas Powel, jun. 21 Connecticut N. E.
Stephen Mundon 20 London.
Thomas Huggit 30 London.
William Read 35 Londonderry, Ireland.
Peter Kneeves 32 Exeter in Devon.
James Brinkly 28 Suffolk in England.
Joseph Sound 28 City of Westminster.
William Shutfield 40 Lancafter in England.
Edward Eaton 38 Wrexham in Wales.
John Brown 29 County of Durham.
Edward Lawson 20 Isle of Man.
Owen Rice 27 South-Wales.
John Tomkins 23 Gloucestershire.
John Fitzgerrald 21 Limerick in Ireland.
Abraham Lacy 21 Devonshire.
Thomas Linister 21 Lancashire.
Francis Leyton 39 New-York.
John Waters, Quart.-Mr. 35 County of Devon.
William Jones 28 London.
Charles Church 21 St. Margaret's, Westm.
Thomas Hazel 50 — — —
John Bright 25 — — — —
These 25 were found guilty, and executed the 19th of July, 1723,
near Newport in Rhode-Island.
John Brown 17 Liverpoole.
Patrick Cunningham 25 — — —
These two were found guilty, but respited for one Year, and
recommended to the King’s Favour.
John Wilson 23 New-London County
Henry Barnes 22 Barbadoes.
Thomas Jones 17 Flur in Wales.
Joseph Switzer 24 Boston in New-England.
Thomas Mumper Indian. Mather's Vineyard N. E.

T
John Hincher, Doctor 22 Near Edinburgh, Scot.
John Fletcher 17 — — —
Thomas Child 15 — — —
These eight were found Not Guilty.
The destroying this Pyrate was look’d upon by the Province, to be of
such a signal Service to the Publick, and particular Advantage to the
Colony of New-York, that it was thought necessary to make some
handsome Acknowledgement to Captain Peter Solgard for it; and
therefore it was resolved, in an Assembly of the Common-Council, to
compliment him with the Freedom of their Corporation. The
Resolution, together with the Preamble of the Captain’s Freedom,
being curious in their Kind, I subjoin them for the Satisfaction of the
Reader.
Resolution of the Mayor and Common-Council
of the City of New-York, at a Common-Council
held at the City Hall of the said City, on
Thursday the 25th of July, Anno. Dom. 1723.
Present Robert Walter, Esq; Mayor.
City of New-York, ss.
HIS Court having taken into their Consideration the great
Service lately done to this Province in particular, as well as to
all other his Majesty’s good Subjects in general, by Captain
Peter Solgard, Commander of his Majesty’s Ship the Greyhound, the
Station Ship of the Province, who lately in a Cruize upon this Coast,
in due Execution and Discharge of his Duty, upon Intelligence given
him, sought for, pursued and engaged two Pyrate Sloops,
commanded by one Low, (a notorious and inhumane Pyrate,) one of
which Sloops he took, after a resolute Resistance, and very much
shattered the other, who by the Favour of the Night escaped. Twenty
six of which Pyrates so taken, being lately executed at Rhode Island,
not only eased this City and Province of a very great Trouble, but of

T
a very considerable Expence, c. It is therefore resolved (Nemine
Contradicente) that this Corporation do present the said Captain
Solgard with the Freedom of this Corporation, as a Mark of the great
Esteem they have for his Person, as well as for the aforesaid great
and good Services; and that the Seal of the said Freedom be
enclosed in a Gold Box; that Mr. Recorder and Mr. Bickley do draw
the Draught of the said Freedom, signifying therein, the grateful
Sense of this Corporation, for so signal a Service to the Publick, and
Benefit and Advantage of Mankind. That Alderman Kip, and
Alderman Cruger, do prepare the said Box; that the Arms of the
Corporation be engraved on one Side thereof, and a Representation
of the Engagement on the other, with this Motto, (viz.) [Quesitos
Humani Generos Hostes Debellare superbum, 10 Junii, 1723.] That
the Town-Clerk cause the same Freedom to be handsomly engrossed
on Parchment, and that the whole Corporation do wait upon him, to
present the same.
By Order of the Common-Council.
William Sharpas, Clerk.
The Preamble of Captain Peter Solgard’s Copy
of his Freedom.
Robert Walter, Esq; Mayor, and the Aldermen of the City of New-
York.
City of New-York, ss.
O all whom these Persents shall come, send Greeting.
WHEREAS, Captain Peter Solgard, Commander of his Majesty’s
Ship the Greyhound, (the present Station Ship of this
Province,) in his Cruize, having Intelligence of two Pyrate Sloops of
considerable Force in Consortship, under the Command of one Low,
a notorious Pyrate, that had for upward of two Years, committed
many Depredations, Murders and Barbarities, upon many of his
Majesty’s Subjects and Allies, lately come upon this Coast, hath, with
great Diligence, and utmost Application, pursued, overtaken, and

after a stubborn Resistance, vanquished and overcome both of
them, taking one, and driving the other from our Coast; which
Action, as it is glorious in it self, so it is glorious in the publick
Benefits and Advantages that flow from it, (to wit) The Safety and
Freedom of our own Trade and Commerce, and of all the
neighbouring Provinces on this Continent, such signal Service done
against the Enemies of Mankind, merits the Applause of all good
Men, but more immediately from those of this Province, who are
appointed his particular Care and Charge. WE therefore, the Mayor,
Aldermen and Commonalty of the City of New-York, assembled in
Common Council, to express our grateful Sense and
Acknowledgment, to the said Captain Peter Solgard, for so noble and
faithful a Discharge of his Duty, and as a particular Mark of the great
Esteem and just Regard we bear to his kind Acceptance of the
Freedom of the Corporation of this City of New-York, and that he will
please to become a Fellow Citizen with us. These are therefore to
certify and declare, that the said Captain Peter Solgard is hereby
admitted, received and allowed a Freeman and Citizen of the said
City of New-York, to have, hold, enjoy and partake of all and singular
Advantages, Benefits, Liberties, Privileges, Franchises, Freedoms and
Immunities whatsoever, granted or belonging to the same City: In
Testimony thereof, the said Mayor hath hereunto subscribed his
Name, and caused the Seal of the said City to be affix’d the 25th
Day of July, in the ninth Year of the Reign of our Sovereign Lord
George, by the Grace of God, King of Great Britain, France and
Ireland, Defender of the Faith, c. Anno. Dom. 1723.
William Sharpas,
Clerk.
R. Walter Mayor.
This narrow Escape of Low and his Companions, one would have
thought might have brought them to a little Consideration of their
black and horrid Crimes, and to look upon this Interval as an
Opportunity put into their Hands by Providence, to reconcile
themselves to God, by a hearty and sincere Repentance. But alass
they were dead to all Goodness, and had not so much as one Spark

of Virtue to stir them up to be thankful for such an eminent
Deliverance: But instead thereof, vented a Million of Oaths and
Curses upon the Captain of the Greyhound, vowing to execute
Vengeance upon all they should meet with afterwards, for the
Indignity he put upon them.
The first Prey that they met with, after their Flight, was a small
Sloop belonging to Nantucket, a Whale-Fishing, about 80 Miles from
Land; the Master of which, one Nathan Skiff, a brisk young Fellow,
the Pyrates cruelly whipp’d naked about the Deck, making his
Torture their Sport; after which they cut of his Ears, and last of all
shot him through the Head, and then sunk his Vessel; putting the
rest of the Hands into their Whale-Boat, with a Compass, a little
Water, and a few Biskets; and it being good Weather, they
providentially got safe to Nantucket, beyond all Expectation.
There was another Whale-Boat belonging to this Sloop last
mentioned, which happened to be at some Distance from her, and
perceiving what was doing, rowed with all speed to another Sloop
not far off, to acquaint her with the Misfortune, that the Men might
take Care of themselves; and she happily got away in Time. Some
Days after, Low took a Fishing-Boat off of Block Island, but did not
perpetrate so much Cruelty to her, contenting himself with only
cutting off the Master’s Head: But after taking two Whale-Boats near
Rhode Island, he caused one of the Master’s Bodies to be ripp’d up,
and his Intrails to be taken out; and cut off the Ears of the other,
and made him eat them himself with Pepper and Salt; which hard
Injunction he comply’d with, without making a Word. Several other
Persons he would have murthered, but Humanity prevailing in the
tender Hearts of his Companions, they refused to put his savage
Orders in Execution. From the Coast of New-England, Low sailed
directly for Newfoundland, and, near Cape Briton, took two or three
and twenty French Vessels; and one of them of 22 Guns he mann’d
with Pyrates, making a sort of a Man of War of her; with which he
scower’d the Harbours and Banks of Newfoundland, and took sixteen
or eighteen other Ships and Vessels, all which they plundered, and
some destroyed.

Thus these inhumane Wretches went on, who could not be
contented to satisfy their Avarice only, and travel in the common
Road of Wickedness; but, like their Patron, the Devil, must make
Mischief their Sport, Cruelty their Delight, and damning of Souls their
constant Employment. Of all the pyratical Crews that were ever
heard of, none of the English Name came up to this, in Barbarity;
their Mirth and their Anger had much the same Effect, for both were
usually gratified with the Cries and Groans of their Prisoners; so that
they almost as often murthered a Man from the Excess of good
Humour, as out of Passion and Resentment; and the Unfortunate
could never be assured of Safety from them, for Danger lurked in
their very Smiles. An Instance of this had liked to have happened to
one Captain Graves, Master of a Virginia Ship last taken; for as soon
as he came aboard of the Pyrate, Low takes a Bowl of Punch in his
Hand, and drinks to him, saying, Captain Graves, here’s half this to
you. But the poor Gentleman being too sensibly touched at the
Misfortune of falling into his Hands, modestly desired to be excused,
for that he could not drink; whereupon Low draws out a Pistol, cocks
it, and with the Bowl in ’tother Hand, told him, he should either take
one or the other: So Graves, without Hesitation, made Choice of the
Vehicle that contained the Punch, and guttled down about a Quart,
when he had the least Inclination that ever he had in his Life to be
merry.
The latter End of July, (1723,) Low took a large Ship, called the
Merry Christmas, and fitted her for a Pyrate, cut several Ports in her,
and mounted her with 34 Guns. Low goes aboard of this Ship,
assumes the Title of Admiral, and hoists a black Flag, with the Figure
of Death in red, at the Main-topmast Head, and takes another
Voyage to the Western Islands, where he arrived the Beginning of
September. The first Vessel he met with there, was a Brigantine,
formerly an English Sloop, commanded by Elias Wild, but lately
bought by a Portuguese Nobleman, and altered: She was manned
partly with English, and partly Portuguese; the latter Low caused to
be hang’d, by Way of Reprisal, for some of his own Men sent thither
in a Sloop from the Cape de Verd Islands, as has been mentioned:

The English Men he thrust into their own Boat, to shift for
themselves, and set Fire to the Vessel.
At St. Michaels, they sent in their Boats and cut out of the Road, a
new London built Ship of 14 Guns, commanded by Captain
Thompson, who was taken there the Year before, by Low, in the
Rose Pink. The Boats had fewer Men than the Ship, and Captain
Thompson would have defended himself, but his Men through
Cowardize, or too great an Inclination of becoming Pyrates
themselves, refused to stand by him, and he was obliged to
surrender; and when he came aboard the Pyrate, had his Ears cut
off close to his Head, for only proposing to resist Admiral Low’s black
Flag; they gave him one of his own Boats, and burnt his Ship.
The next was a Portuguese Bark that fell into their Hands, whose
Men came off somewhat better than usual, for they only cut them
with their Cutlashes, out of Wantonness, turned them all into their
Boat, and set their Vessel on Fire. When the Boat was going from
the Side of the Ship, one of Low’s Men, who, we may suppose, was
forced into his Gang, was drinking with a Silver Tankard at one of
the Ports, and took his Opportunity to drop into the Boat among the
Portuguese, and lye down in the Bottom, in order to escape along
with them: After he had stowed himself in the Boat, so as not to be
seen, it came into his Head, that the Tankard might prove of some
Use to him, where he was going; so he got up again, laid hold of the
Utensil, and went off, without being discover’d: In which Attempt
had he failed, no doubt his Life, if not the Lives of all the People in
the Boat, would have paid for it: The Name of this Man is Richard
Hains.
Low took his old Tour to the Canaries, Cape de Verd Islands, and
so to the Coast of Guiney; but nothing extraordinary happened till
they arrived near Sierraleon in Africa, where they met with a Ship
call’d the Delight, Captain Hunt Commander; this Ship they thought
fit for their own Purpose, for she had been a small Man of War, and
carried 12 Guns; however, they mounted 16 on Board her, mann’d
her with 60 Men, and appointed one Spriggs, who was then their
Quarter-Master, to be Captain of her, who, two Days after, separated
from the Admiral, and went to the West-Indies a-pyrating, upon his

own, and particular Company’s, Account, where for the present we
shall leave him.
In January last, Low took a Ship, called the Squirrel, Captain
Stephenson; but what became of him afterwards, I can’t tell; we
have had no News concerning him come to England, since this I
have now mentioned; but I have heard that he talk’d of going to
Brazil; and if so, it is likely we may too soon hear of some Exploit or
other; tho’ the best Information we could receive, would be, that he
and all his Crew were at the Bottom of the Sea.

J
CHAP. XIV.
OF
Capt. JOHN EVANS,
And his CREW.
OHN Evans was a Welch Man, had been formerly Master of a
Sloop belonging to Nevis, but losing his Employ there, he sailed
for some Time out of Jamaica as Mate, till happening in
Company of three or four of his Comrades, and Wages not being so
good as formerly, and Births scarce, because of the great Number of
Seamen; they agreed to go abroad in search of Adventures. They
sailed, or rather rowed out of Port Royal in Jamaica, the latter End of
September 1722, in a Canoa; and coming on the North-Side of the
Island, went ashore in the Night, broke open a House or two, and
robb’d them of some Money, and every Thing else they could find
that was portable, and brought the Booty on Board the Canoa.
This was very well for the first Time, but this kind of Robbery did
not please so well, they wanted to get out to Sea, but having no
Vessel but their Canoa, they were prevented in their laudable
Design; however, they kept a good look out, and traversed the
Island, in Expectation that Providence would send some unfortunate
Vessel as a Sacrifice, and in a few Days their Wishes were
accomplished; for at Duns Hole, they found a small Sloop at an
Anchor, belonging to Bermudas: They made bold and went aboard,
and Evans informed the Folks that belonged to her, that he was
Captain of the Vessel, which was a Piece of News they knew not
before. After they had put their Affairs in a proper Disposition
aboard, they went ashore to a little Village for Refreshments, and

lived jovially the remaining Part of the Day, at a Tavern, spending
three Pistols, and then departed. The People of the House admired
at the merry Guests they had got, were mightily pleased, and wished
for their Company at another Time, which happened too soon for
their Profit; for, in the middle of the Night, they came ashore all
Hands, rifled the House, and carried what they could aboard their
Sloop.
The next Day they weighed in the Sloop, aboard of which they
mounted four Guns, called her the Scowerer, and sailed to
Hispaniola; on the North Part of which Island they took a Spanish
Sloop, which proved an extraordinary rich Prize, as it fell among so
few Persons as this Company consisted of, for they shared upwards
of 150 l. a Man.
In Pursuance of the Game, and beating up for the Windward
Islands, the Scowerer met with a Ship from New-England, bound to
Jamaica, 120 Tons, called the Dove, Captain Diamond Master, off
Porto Rico: They plundered her, and strengthened their own
Company, by taking out the Mate, and two or three other Men; they
discharged the Prize, and run into one of the Islands for fresh Water
and Necessaries, and staid there some Time.
The next Prize they made, was the Lucretia and Catherine,
Captain Mills, of 200 Ton Burthen; they came up with her near the
Island Disseada, January 11th. Upon seizing of this Ship, the Pyrates
began to take upon themselves the Distribution of Justice, examining
the Men concerning their Master’s Usage of them, according to the
Custom of other Pyrates; but the Captain over-hearing the Matter,
put an End to the judicial Proceedings, and fell to rumaging the Ship,
saying to them, What have we to do to turn Reformers, ’tis Money
we want? And speaking to the Prisoners, he asked them, Does your
Captain give you Victuals enough? And they answering in the
Affirmative: Why then, said he, he ought to give you Work enough.
After the taking of this Prize, they went to the little Island of Avis,
with a Design to clean, and carried the Lucretia along with them, in
order to heave down the Scowerer by her; but meeting there with a
Sloop, the Pyrate gave Chace till the Evening, when she was within
Gun-Shot of her; but fearing to lose Company with the Lucretia, who

was a heavy Sailor, they left off, and saw her no more. This Chace
brought them to Leeward of their Port, so that they were obliged to
look out for another Place of Retreat, and the Island of Ruby not
being far distant, they steered for that, and anchored there
accordingly; but the next Day a Dutch Sloop coming as it were, into
their Mouths, they could not forbear dealing, and so making her
their Prize, they plundered her of what came, when shared, to fifty
Pounds a Man.
They found this Sloop more for their Purpose than the Lucretia, to
clean their own Sloop by, as being much lower in the Wast, and
therefore capable of heaving her Bottom farther out of the Water, so
she was discharged, and the Dutch Man kept in her Room; but not
thinking it convenient to lay up here, for fear a discovery should be
made, they turned their Thoughts another Way, and steered to the
Coast of Jamaica, where they took a Sugar Drover, and then run to
the Grand Caimanes, about 30 Leagues to Leeward of Jamaica, with
Intention to clean there; but an unhappy Accident put an End to
their Pyracies, which hitherto had proved very successful to them.
The Boatswain of the Pyrate being a noisy surly Fellow, the
Captain had at several Times Words with him, relating to his
Behaviour, who thinking himself ill treated, not only returned ill
Language, but also challenged the Captain to fight him on the next
Shore they came to, with Pistols and Sword, as is the Custom among
these Outlaws. When the Sloop arrived, as abovementioned, the
Captain proposed the Duel; but the cowardly Boatswain refused to
fight, or go ashore, tho’ it was his own Challenge. When Captain
Evans saw there was nothing to be done with him, he took his Cane,
and gave him a hearty drubbing; but the Boatswain not being able
to bear such an Indignity, drew out a Pistol and shot Evans thro’ the
Head, so that he fell down dead; and the Boatswain immediately
jumped over-board, and swam towards the Shore; but the Boat was
quickly mann’d and sent after him, which took him up and brought
him aboard.
The Death of the Captain in that Manner, provoked all the Crew,
and they resolved the Criminal should die by the most exquisite
Tortures; but while they were considering of the Punishment, the

Gunner, transported with Passion, discharged a Pistol, and shot him
thro’ the Body; but not killing him outright, the Delinquent in very
moving Words, desired a Week for Repentance only; but another
stepping up to him, told him, that he should repent and be damned
to him, and without more ado shot him dead.
I should have observed, that when the Lucretia and Katharine was
suffered to go away, the Pyrates detained their Mate, who was now
the only Man aboard, who understood Navigation, and him they
desired to take upon him the Command of the Sloop, in the Room of
Captain Evans deceased; but he desired to be excused that Honour,
and at length positively refused it; so they agreed to break up the
Company, and leave the Mate in Possession of the Vessel:
Accordingly they went ashore at the Caimanes, carrying with them
about nine thousand Pounds among thirty Persons; and it being fair
Weather, the Mate and a Boy brought the Vessel into Port Royal, in
Jamaica.

J
CHAP. XV.
OF
Captain John Phillips,
And his CREW.
OHN Phillips was bred a Carpenter, and sailing to Newfoundland
in a West-Country Ship, was taken by Anstis in the Good Fortune
Brigantine, the next Day after he had left his Consort and
Commadore, Captain Roberts. Phillips was soon reconciled to the
Life of a Pyrate, and being a brisk Fellow, was appointed Carpenter
of the Vessel, for at first his Ambition reach’d no higher; there he
remain’d till they broke up at Tabago, and was one of those who
came home in a Sloop that we have mentioned to be sunk in Bristol
Channel.
His Stay was not long in England, for whilst he was paying his first
Visits to his Friends in Devonshire, he heard of the Misfortune of
some of his Companions, that is, of their being taken and committed
to Bristol Goal; and there being good Reason for his apprehending
Danger from a Wind that blew from the same Quarter, he mov’d off
immediately to Topsham, the nearest Port, and there shipp’d himself
with one Captain Wadham, for a Voyage to Newfoundland, and
home again; which, by the way, Mr. Phillips never design’d to
perform, or to see England any more. When the Ship came to Peter
Harbour in Newfoundland aforesaid, he ran away from her, and hired
himself a Splitter in the Fishery, for the Season: But this was only till
he could have an Opportunity of prosecuting his intended Rogueries;
in order to which, he combined with several others, in the same
Employ, to go off with one of the Vessels that lay in the Harbour,

E
upon the pyratical Account; accordingly the Time was fix’d, viz. the
29th of August 1723, at Night; but whether Remorse or Fear
prevented their coming together, I know not, but of sixteen Men that
were in the Combination, five only kept the Appointment:
Notwithstanding which, Phillips was for pushing forward with that
small Number, assuring his Companions, that they should soon
encrease their Company; and they agreeing, a Vessel was seiz’d on,
and out of the Harbour they sailed.
The first Thing they had now to do, was to chuse Officers, draw
up Articles, and settle their little Commonwealth, to prevent Disputes
and Ranglings afterwards; so John Phillips was made Captain, John
Nutt, Master, (or Navigator) of the Vessel; James Sparks, Gunner;
Thomas Fern, Carpenter; and Wiliam White was the only private Man
in the whole Crew: When this was done, one of them writ out the
following Articles (which we have taken verbatim) and all swore to
’em upon a Hatchet for want of a Bible.
The Articles on Board the Revenge.
1.
Very Man shall obey civil Command; the Captain shall have one
full Share and a half in all Prizes; the Master, Carpenter,
Boatswain and Gunner shall have one Share and quarter.
2.
If any Man shall offer to run away, or keep any Secret from the
Company, he shall be marroon’d, with one Bottle of Powder, one
Bottle of Water, one small Arm, and Shot.
3.

If any Man shall steal any Thing in the Company, or game, to the
Value of a Piece of Eight, he shall be marroon’d or shot.
4.
If at any Time we should meet another Marrooner [that is, Pyrate,]
that Man that shall sign his Articles without the Consent of our
company, shall suffer such Punishment as the Captain and Company
shall think fit.
5.
That Man that shall strike another whilst these Articles are in force,
shall receive Moses’s Law (that is, 40 Stripes lacking one) on the
bare Back.
6.
That Man that shall snap his Arms, or smoak Tobacco in the Hold,
without a Cap to his Pipe, or carry a Candle lighted without a
Lanthorn, shall suffer the same Punishment as in the former Article.
7.
That Man that shall not keep his Arms clean, fit for an Engagement,
or neglect his Business, shall be cut off from his Share, and suffer
such other Punishment as the Captain and the Company shall think
fit.
8.
If any Man shall lose a Joint in time of an Engagement, shall have
400 Pieces of Eight; if a Limb, 800.

9.
If at any time you meet with a prudent Woman, that Man that offers
to meddle with her, without her Consent, shall suffer present Death.
Thus prepar’d, this bold Crew set out, and before they left the
Banks they made Prize of several small Fishing-Vessels, out of which
they got a few Hands, some French and some English, and then
sail’d for the West-Indies; in one of these Vessels they took out one
John Rose Archer, who having been a Pyrate under the famous
Black-beard, was immediately preferr’d over other People’s Heads, to
be Quarter-Master to the Company; which sudden Promotion so
disgusted some of the older Standers, especially Fern, the Carpenter,
that it occasioned some Mischief to follow, as we shall shew by and
by.
The Pyrates came off Barbadoes the beginning of October, and
cruised there, and among other Islands, above three Months,
without speaking with a Vessel, so that they were almost starv’d for
want of Provisions, being reduc’d to a Pound of Meat a Day between
ten; at length they fell in with a Martinico Man of 12 Guns and 35
Hands, far superior in Force, and what they would not have ventur’d
on at another Time, but Hunger will break down Stone Walls; they
were resolved to shew the French Men their black Flag; and if that
would not do, they must seek out elsewhere; accordingly, they
boldly ran up a-long-side of the Sloop, with their pyratical Colours
flying, and told them, if they did not strike immediately, they would
give them no Quarters; which so intimidated the Frenchmen, that
they never fired a Gun. This proved a seasonable Supply; they took
her Provisions, and four of her Men, and let her go. They took
presently after, a Sloop belonging to New-York, and a Virginia Man,
Huffam Master.
Having now occasion to clean their Vessel, Phillips propos’d
Tobago, where the Company he formerly belong’d to, under Anstis
and Fenn, broke up; to induce them to it, he told them when he left
the Island, there was left behind six or eight of their Company that
were not willing to go to England, with three Negroes: Whereupon

they sail’d to the Island, and after a careful Search, found only one
of the Negroes, whose Name was Pedro, who inform’d Captain
Phillips, that those that were left behind were taken by a Man of
War’s Crew, and hang’d at Antegoa, among whom was Fenn, their
Captain.
They took Pedro on Board, and then fell to Business, careening
their Vessel; and just as they had finished their Work, a Man of
War’s Boat came into the Harbour, the Ship being cruising to
Leeward of the Island. It was easily guess’d upon what Errant she
was sent, and therefore they lost no Time, but, as soon as the Boat
went away, warp’d out, and ply’d to Windward for Security, but left
the four French Men, they took out of the Martinico Sloop, behind.
In a few Days they took a Snow with a few Hands, and Fern, the
Carpenter, one William Phillips, Wood and Taylor, went aboard to
take Possession of her. Fern, not forgetting the Affront of having
Archer preferr’d before him, resolv’d to go off with the Prize, and
brought the rest into the same Measures; however Phillips, the
Captain, keeping a good Look-out, perceiv’d their Design, and gave
them Chace, who coming up with the Vessel, a Skirmish ensu’d,
wherein Wood was kill’d and Taylor wounded in his Leg; upon which
the other two surrender’d. There was no Surgeon aboard, and
therefore it was advis’d, upon a learned Consultation, that Phillips’s
Leg should be cut off; but who should perform the Operation was
the Dispute; at length the Carpenter was appointed, as the most
proper Man: Upon which, he fetch’d up the biggest Saw, and taking
the Limb under his Arm, fell to Work, and separated it from the Body
of the Patient, in as little Time as he could have cut a Deal Board in
two; after that he heated his Ax red hot in the Fire, and cauteriz’d
the Wound, but not with so much Art as he perform’d the other Part,
for he so burnt his Flesh distant from the Place of Amputation, that it
had like to have mortify’d; however nature perform’d a Cure at last
without any other Assistance.
From Tobago they stood away to the Northward and took a
Portugueze bound for Brazil, and two or three Sloops from Jamaica,
in one of which, Fern the Carpenter, endeavouring to go off, was
kill’d by Phillips the Captain, pursuant to their Articles; another had

the same Fate some Days after for the like Attempt. These Severities
made it dangerous for any to consult or project an Escape; the
Terror of which made several sign their Articles and set down quietly,
waiting impatiently for Redemption, which as yet they saw no great
likelyhood of, and should they have been taken before such
Circumstances appear’d in their Actions or Characters, as afterwards
happen’d, to denote their Innocence, they might have lost their Lives
upon a Tryal at a Court of Admiralty; for pretty strong Evidence is
expected in their Favour, to ballance that of being taken aboard a
Vessel which is prov’d to be in actual Pyracy, and they assisting
therein.
Thus was many an honest Man’s Case made most desperate by
the consummate Villany of a few hardned Wretches, who fear
neither God or Devil, as this Phillips us’d often blasphemously to
express himself.
On the 25th of March they took two Ships from Virginia for
London, John Phillips, the Pyrate Captain’s Namesake, was Master of
one, and Captain Robert Mortimer, the other, a brisk young Fellow,
that deserv’d a better Fate than he met with. Phillips the Pyrate staid
on Board of Captain Mortimer’s Ship, while they transported the
Crew to the Sloop, and the Boat returning along side, one of the
Pyrates therein calls to Phillips, and tells him, there was a Mutiny
aboard their Vessel, Mortimer had two Men in his Ship, and the
Pyrate Captain had two, therefore thought it a good Opportunity to
recover his Ship, and directly took up a Handspike and struck Phillips
over the Head, giving him a dangerous wound, but not knocking him
down, he recovered and wounded Mortimer with his Sword; and the
two Pyrates that were aboard coming in to Captain Phillips’s
Assistance, Captain Mortimer was presently cut to Pieces, while his
own two Men stood by and did nothing.
This was the first Voyage that Mortimer had the Command of a
Vessel, by whose Death is a poor disconsolate Widow made
miserable, more in regard of the mutual Love and Fidelity they lived
in, than the Loss of what would have been a handsome and
comfortable Provision for themselves and Children, which, I think,
now ought to be made up by the Publick, since ’twas in the publick

Service he fell; for had his Attempt succeeded, in all Probability he
would not only have regained his own Ship, but entirely subdued
and destroy’d the Enemy, there being several, as it afterwards
proved, that would have seconded such an Enterprize when ever
they found a Beginning made.
This Affair ended without any other Consequence than a strict
Search after a Brother of Captain Mortimer, who was on Board, in
order to have put him likewise to death; but he had the good
Fortune to meet with a Townsman among the Crew, who hid him for
four and twenty Hours in a Stay-Sail, till the Heat of their Fury was
over, and by that Means happily missed of the Fate designed him.
Out of the other Virginia Man before spoken of, they took one
Edward Cheeseman, a Carpenter, to supply the Place of their late
Carpenter, Fern. He was a modest sober young Man, very averse to
their unlawful Practice, and a brave gallant Fellow. There was one
John Philmore of Ipswich, formerly taken by them, ordered to row
Cheeseman aboard of Mortimer’s Ship, which the Pyrates possess’d
themselves of, who, seeing with what Reluctance and Uneasiness
Cheeseman was brought away, told him, he would join with him, in
some Measures, to over-throw the pyratical Government, telling him
withal, their present Condition, what Difficulties Phillips had met with
to make up his Company, and how few voluntary Pyrates there were
on Board, and the like. But, however specious this seemed,
Cheeseman out of Prudence rejected his Offers of Assistance, till he
saw some Proofs of his Sincerity, which after a few Days he was
convinced of, and then they often consulted; but as the old Pyrates
were always jealous of the new Comers, and consequently observant
of their Behaviour; this was done with the utmost Caution, chiefly
when they were lying down together, as tho’ asleep, and, at other
Times, when they were playing at Cards; both which they feigned
often to do for that Purpose.
The Pyrates went on all the while, plundering and robbing several
Ships and Vessels, bending their Course towards Newfoundland,
where they designed to raise more Men, and do all the Mischief they
could on the Banks, and in the Harbours.

Newfoundland is an Island on the North Continent of America,
contained between the 46 and 53° of N. Latitude, discovered first by
St. Sebastion Cabot A. D. 1497, but never settled till the Year 1610;
when Mr. Guy of Bristol revived the Affair, and obtained a Patent,
and himself to be Governor. The Island is deserted by the Natives
and neglected by us, being desolate and Woody, and the Coast and
Harbour only held for the Conveniency of the Cod Fishery, for which
alone they were settled.
The Bays and Harbours about it, are very numerous and
convenient, and being deeply indented, makes it easy for any
Intelligence quickly to pass from one Harbour to another over Land;
especially the principal, St. John’s and Placentia, when the
Appearance of an Enemy makes them apprehend Danger.
They are able to cure and export about 100000 Quintals (100
Weight each) of Fish, annually, which returns to England in Money,
or the necessary Commodities of Portugal, Spain and Italy. As it
therefore expends abundance of Rum, Molossus and Sugar, the
Product of our West-India Colonies, and employs a Number of
Fishermen from home every Season, by whose Industry and Labour
only this Fish is purchased, it may very well be reckon’d an
advantagious Branch of Trade.
But the present Design of this Digression being not to give an
exact Description of the Country or Fishery; but rather how it
accidentally contributes to raise, or support the Pyrates already
rais’d, I shall observe,
First, That our West Country Fishing-Ships, viz. from Topsham,
Barnstable and Bristol, who chiefly attend the Fishing Seasons,
transport over a considerable Number of poor Fellows every
Summer, whom they engage at low Wages, and are by their Terms
to pay for Passage back to England. When the Newfoundland Ships
left that Country, towards Winter, in the Year 1720, these Passengers
muster’d 1100, who, during the Season of Business, (the Hardness
of their Labour, and Chilness of the Nights, pinching them very
much) are mostly fond of drinking Black Strap, (a strong Liquor used
there, and made from Rum, Molossus, and Chowder Beer;) by this
the Majority of them out-run the Constable, and then are

necessitated to come under hard Articles of Servitude for their
Maintenance in the Winter; no ordinary Charge, indeed, when the
Barrenness of the Country is consider’d, and the Stock of Provision
laid in, happen to fall short, in Proportion to the Computation made
of the People remaining there the Winter, which are generally about
17 or 1800. The Masters residing there think Advantages taken on
their Necessities, no more than a just and lawful Gain; and either
bind such for the next Summer’s Service, or sell their Provisions out
to them at extravagant Rates; Bread from 15s. to 50, immediately at
the departing of the Ships, and so of other sorts of Food in
Proportion; wherefore not being able to subsist themselves, or in
any likely Way of clearing the Reckoning to the Masters, they
sometimes run away with Shallops and Boats, and begin on pyratical
Exploits, as Phillips and his Companions, whom we are now treating
of, had done.
And secondly (which is more opportunely for them,) they are
visited every Summer, almost, by some Set of Pyrates or other,
already rais’d, who call here for the same Purpose, (if young
Beginners) and to lay in a Store of Water and Provisions, which they
find imported, much or little, by all the Ships that use the Trade.
Towards this Country Phillips was making his Way, and took on the
Voyage, besides those abovementioned, one Salter, in a Sloop off
the Isle of Sables, which Vessel they made use of themselves, and
gave back Mortimer’s Ship to the Mate and Crew. The same Day, viz.
the 4th of April, took a Scooner, one Chadwell, Master, which they
scuttled, in order to sink; but Capt. Phillips understanding that she
belong’d to Mr. Minors at Newfoundland, with whose Vessel they first
went off a pyrating, a Qualm of Conscience came athwart his
Stomach, and he said to his Companions, We have done him Injury
enough already; so order’d the Vessel immediately to be repair’d,
and return’d her to the Master.
That Afternoon they chac’d another Vessel, and at Night came up
with her, the Master of which was a Saint of New-England, nam’d
Dependance Ellery, who taking Phillips for a Pyrate, he told him was
the Reason that he gave him the Trouble of chacing so long; which

being resented by these Men of Honour, they made poor
Dependance dance about the Deck till he was weary.
Within few Days several other Vessels had the same Misfortune,
the Masters Names were as follow, Joshua Elwell, Samuel Elwell, Mr.
Combs, Mr. Lansly, James Babston, Edward Freeman, Mr. Start,
Obediah Beal, Erick Erickson and Benjamin Wheeler.
The 14th of April they took a Sloop belonging to Cape Ann,
Andrew Harradine Master; they look’d upon this Vessel more fit for
their Purpose, and so came aboard, keeping only the Master of her
Prisoner, and sending Harradine’s Crew away in Salter’s Vessel,
which they, till this Time, detain’d. To this Harradine, Cheeseman the
Carpenter, broke his Mind, and brought him into the Confederacy to
destroy the Crew, which was put in Execution four Days afterwards.
Harradine and the rest were for doing the Business in the Night,
as believing they might be more opportunely surpriz’d; for Nut, the
Master, being a Fellow of great Strength, and no less Courage, it was
thought dangerous to attack him without Fire-Arms; however,
Cheeseman was resolute to have it perform’d by Day-light, as the
least liable to Confusion; and as to the Master, he offer’d to lay
Hands on him first: Upon this ’twas concluded on, 12 at Noon was
the appointed Time; in order for the Business Cheeseman leaves his
working Tools on the Deck, as though he had been going to use
them, and walked aft; but perceiving some Signs of Timidity in
Harradine, he comes back, fetches his Brandy Bottle and gives him
and the rest a Dram, then drank to Burril, the Boatswain, and the
Master, To their next merry Meeting, and up he puts the Bottle; then
he takes a Turn with Nut, asking what he thought of the Weather,
and such like. In the mean while Filemore takes up the Axe, and
turns it round upon the Point, as if at Play, then both he and
Harradine wink at him, thereby letting him know they were ready;
upon which Signal he seizes Nut by the Collar, with one Hand
between his Legs, and toss’d him over the Side of the Vessel, but, he
holding by Cheeseman’s Sleeve, said, Lord have Mercy upon me!
what are you going to do, Carpenter? He told him it was an
unnecessary Question, For, says he, Master, you are a dead Man, so

strikes him over the Arm, Nut looses his Hold, tumbles into the Sea,
and never spoke more.
By this time the Boatswain was dead; for as soon as Filemore saw
the Master laid hold of, he raised up the Axe, and divided his
Enemy’s Head in two: The Noise brought the Captain upon Deck,
whom Cheeseman saluted with the Blow of a Mallet, which broke his
Jaw-Bone, but did not knock him down; Harradine came in then with
the Carpenter’s Adds, but Sparks, the Gunner, interposing between
him and Captain Phillips, Cheeseman trips up his Heels, and flung
him into the Arms of Charles Ivymay, one of his Consorts, who that
Instant discharg’d him into the Sea; and at the same Time Harradine
compassed his Business with the Captain aforesaid: Cheeseman lost
no Time, but from the Deck jumps into the Hold, and was about to
beat out the Brains of Archer, the Quarter-Master, having struck him
two or three Blows with his blunt Weapon the Mallet, when Harry
Giles, a young Lad, came down after him, and desir’d his Life might
be spar’d, as an Evidence of their own Innocence; that he having all
the Spoil and Plunder in his Custody, it may appear, that these
tragick Proceedings were not undertaken with any dishonest View of
seizing or appropriating the Effects to themselves; which prudent
Advice prevail’d, and he and three more were made Prisoners, and
secured.
The Work being done, they went about Ship, altered the Course
from Newfoundland to Boston, and arrived safe the 3d of May
following, to the great Joy of that Province.
On the 12th of May, 1724, a special Court of Admiralty was held
for the Tryal of these Pyrates, when John Filmore, Edward
Cheeseman, John Combs, Henry Giles, Charles Ivymay, John
Bootman, and Henry Payne, the seven that confederated together
for the Pyrates Destruction, were honourably acquitted; as also three
French Men, John Baptis, Peter Taffery, and Isaac Lassen, and three
Negroes, Pedro, Francisco, and Pierro. And John Rose Archer, the
Quarter-Master, William White, William Taylor, and William Phillips,
were condemned; the two latter were reprieved for a Year and a
Day, in order to be recommended (though I don’t know for what) as
Objects of his Majesty’s Mercy. The two former were executed on

I
the 2d of June, and dy’d very penitently, making the following
Declarations at the Place of Execution, with the Assistance of two
grave Divines that attended them.
The dying Declarations of John Rose Archer
and William White, on the Day of their
Execution at Boston, June 2, 1724, for the
Crimes of Pyracy.
First, separately, of Archer.
Greatly bewail my Profanations of the Lord’s Day, and my
Disobedience to my Parents.
And my Cursing and Swearing, and my blaspheming the Name
of the glorious God.
Unto which I have added, the Sins of Unchastity. And I have
provoked the Holy One, at length, to leave me unto the Crimes of
Pyracy and Robbery; wherein, at last, I have brought my self under
the Guilt of Murder also.
But one Wickedness that has led me as much as any, to all the
rest, has been my brutish Drunkenness. By strong Drink I have been
heated and hardened into the Crimes that are now more bitter than
Death unto me.
I could wish that Masters of Vessels would not use their Men with
so much Severity, as many of them do, which exposes to great
Temptations.
And then of White.
I am now, with Sorrow, reaping the Fruits of my Disobedience to my
Parents, who used their Endeavours to have me instructed in my
Bible, and my Catechism.

And the Fruits of my neglecting the publick Worship of God, and
prophaning the holy Sabbath.
And of my blaspheming the Name of God, my Maker.
But my Drunkenness has had a great Hand in bringing my Ruin
upon me. I was drunk when I was enticed aboard the Pyrate.
And now, for all the vile Things I did aboard, I own the Justice of
God and Man, in what is done unto me.
Of both together.
We hope, we truly hate the Sins, whereof we have the Burthen lying
so heavy upon our Consciences.
We warn all People, and particularly young People, against such
Sins as these. We wish, all may take Warning by us.
We beg for Pardon, for the sake of Christ, our Saviour; and our
Hope is in him alone. Oh! that in his Blood our Scarlet and Crimson
Guilt may be all washed away!
We are sensible of an hard Heart in us, full of Wickedness. And we
look upon God for his renewing Grace upon us.
We bless God for the Space of Repentance which he has given us;
and that he has not cut us off in the Midst and Heighth of our
Wickedness.
We are not without Hope, that God has been savingly at work
upon our Souls.
We are made sensible of our absolute Need of the Righteousness
of Christ; that we may stand justified before God in that. We
renounce all Dependance on our own.
We are humbly thankful to the Ministers of Christ, for the great
Pains they have taken for our Good. The Lord Reward their
Kindness.
We don’t Despair of Mercy; but hope, through Christ, that when
we dye, we shall find Mercy with God, and be received into his
Kingdom.
We wish others, and especially the Sea-faring, may get Good by
what they see this Day befalling of us.

Declared in the Presence of J. W. D. M.

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