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Business Statistics in Practice: Using Data, Modeling, and Analytics, 9th Edition Bruce L. Bowerman
Page i
Bruce L. Bowerman
Miami University
Anne M. Drougas
Dominican University
William M. Duckworth
Creighton University
Amy G. Froelich
Iowa State University
Ruth M. Hummel
JMP
Kyle B. Moninger
Bowling Green State University
Patrick J. Schur
Miami University
Business Statistics and
Analytics in Practice
NINTH EDITION
with major contributions by
Steven C. Huchendorf
University of Minnesota
Dawn C. Porter
University of Southern California
Business Statistics in Practice: Using Data, Modeling, and Analytics, 9th Edition Bruce L. Bowerman
Page ii
BUSINESS STATISTICS AND ANALYTICS IN PRACTICE, NINTH
EDITION
Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY
10121. Copyright © 2019 by McGraw-Hill Education. All rights
reserved. Printed in the United States of America. Previous editions
© 2017, 2014, and 2011. No part of this publication may be
reproduced or distributed in any form or by any means, or stored in
a database or retrieval system, without the prior written consent of
McGraw-Hill Education, including, but not limited to, in any network
or other electronic storage or transmission, or broadcast for distance
learning.
Some ancillaries, including electronic and print components, may not
be available to customers outside the United States.
This book is printed on acid-free paper.
1 2 3 4 5 6 7 8 9 LWI/LWI 21 20 19 18
ISBN 978-1-260-18749-6
MHID 1-260-18749-7
Portfolio Manager: Noelle Bathurst
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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
Bowerman, Bruce L., author. | Duckworth, William Maury, author. |
Froelich, Amy Goodwin, author.
Business statistics in practice / Bruce L. Bowerman, Miami
University,
William M. Duckworth, Creighton University, Amy Froelich, Iowa
State University.
Ninth Edition. | Dubuque : McGraw-Hill Education, [2019] |
Revised edition of Business statistics in practice, [2017]
LCCN 2018012294 | ISBN 9781260187496 (alk. paper)
LCSH: Commercial statistics. | Statistics.
LCC HF1017 .B654 2018 | DDC 519.5024/65—dc23
LC record available at https://lccn.loc.gov/2018012294
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
Page iii
The McGraw-Hill/Irwin Series in
Operations and Decision Sciences
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Twelfth Edition
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BUSINESS STATISTICS
Bowerman, et. al.
Business Statistics and Analytics in Practice
Ninth Edition
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Essentials of Business Statistics
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Page iv
ABOUT THE AUTHORS
Bruce L. Bowerman Bruce L. Bowerman is emeritus professor of
information systems and analytics at Miami University in Oxford,
Ohio. He received his Ph.D. degree in statistics from Iowa State
University in 1974, and he has over 40 years of experience teaching
basic statistics, regression analysis, time series forecasting, survey
sampling, and design of experiments to both undergraduate and
graduate students. In 1987 Professor Bowerman received an
Outstanding Teaching award from the Miami University senior class,
and in 1992 he received an Effective Educator award from the
Richard T. Farmer School of Business Administration. Together with
Richard T. O’Connell, Professor Bowerman has written 25 textbooks.
These include Forecasting, Time Series, and Regression: An Applied
Approach (also coauthored with Anne B. Koehler); Linear Statistical
Models: An Applied Approach; Regression Analysis: Unified
Concepts, Practical Applications, and Computer Implementation (also
coauthored with Emily S. Murphree); and Experimental Design:
Unified Concepts, Practical Applications, and Computer
Implementation (also coauthored with Emily S. Murphree). The first
edition of Forecasting and Time Series earned an Outstanding
Academic Book award from Choice magazine. Professor Bowerman
has also published a number of articles in applied stochastic process,
time series forecasting, and statistical education. In his spare time,
Professor Bowerman enjoys watching movies and sports, playing
tennis, and designing houses.
Anne Drougas Anne M. Drougas is a Professor of Finance and
Quantitative Methods at Dominican University in River Forest,
Illinois. Over the course of her academic career, she has received
three teaching awards and has developed and taught online and
hybrid business statistics and finance courses. Her research is
primarily in the areas of corporate finance, simulation, and business
analytics with publications in a number of journals including the
Journal of Financial Education and Journal of Applied Business and
Economics. She spends her spare time with her family and serving
on the board of directors for Hephzibah House, a social service
agency for children in Oak Park, Illinois.
William Duckworth William M. Duckworth specializes in statistics
education and business applications of statistics. His professional
affiliations have included the American Statistical Association (ASA),
the International Association for Statistical Education (IASE), and the
Decision Sciences Institute (DSI). Dr. Duckworth was also a member
of the Undergraduate Statistics Education Initiative (USEI), which
developed curriculum guidelines for undergraduate programs in
statistical science that were officially adopted by the ASA. Dr.
Duckworth has published research papers, been an invited speaker
at professional meetings, and taught company training workshops, in
addition to providing consulting and expert witness services to a
variety of companies. During his tenure in the Department of
Statistics at Iowa State University, his main responsibility was
coordinating, teaching, and improving introductory business statistics
courses. Dr. Duckworth currently teaches business analytics to both
undergraduate and graduate students in the Heider College of
Business at Creighton University.
Page v
Amy Froelich Amy G. Froelich received her Ph.D. in Statistics from
the University of Illinois, Urbana-Champaign, and currently is
Associate Professor and Director of Undergraduate Education in the
Department of Statistics at Iowa State University. A specialist in
undergraduate statistics education, she has taught over 2,700
students at Iowa State in the last 18 years, primarily in introductory
statistics, probability and mathematical statistics, and categorical
data analysis. Her research in statistics education and psychometrics
and educational measurement has appeared in The American
Statistician, the Journal of Statistics Education, Teaching Statistics,
and the Journal of Educational Measurement, and she and her
colleagues have received research funding from the National
Science Foundation, the U.S. Department of Agriculture, and
the U.S. Department of Education. Dr. Froelich has received several
teaching and advising awards at Iowa State University and was the
2010 recipient of the Waller Education Award from the American
Statistical Association. When not working, she enjoys reading,
spending time with her family, and supporting her daughters’
extracurricular activities.
Ruth Hummel Ruth M. Hummel is an Academic Ambassador with
JMP, a division of SAS specializing in desktop software for dynamic
data visualization and analysis. As a technical advocate for the use
of JMP®
in academic settings, she supports professors and
instructors who use JMP for teaching and research. She has been
teaching and consulting since 2002, when she started her career as
a high school math teacher. She has taught high school,
undergraduate, and graduate courses in mathematics and statistics,
and directed statistical research and analysis in a variety of fields.
Ruth holds a Ph.D. in statistics from the Pennsylvania State
University.
Kyle Moninger Kyle B. Moninger instructs the Quantitative
Business Curriculum at Bowling Green State University in Bowling
Green, Ohio. He teaches and plans undergraduate courses in
statistics and business calculus, serves on the Quantitative Business
Curriculum committee, and supervises the college’s math and
statistics tutoring center. Kyle has been a visiting instructor three
times at Tianjin Polytechnic University in Tianjin, China, and was
previously a data scientist at Owens Corning in Toledo, Ohio, where
he designed and implemented a corporate training program on
business intelligence and analytics.
Pat Schur Patrick J. Schur is a Senior Clinical Professor in the
Department of Information Systems and Analytics in the Farmer
School of Business at Miami University in Oxford, Ohio. He received
his master’s degree in statistics from Purdue University. He has been
at Miami University for 11 years, teaching introductory statistics
courses and advanced statistics courses including regression
modeling, time series modeling, design of experiments, and
statistical process control. Before joining Miami University, he worked
at Procter & Gamble as a statistical consultant and also worked with
multiple startup companies cutting across multiple industries.
Page vi
AUTHORS’ PREVIEW
Business Statistics and Analytics in Practice, Ninth Edition, provides a
unique and flexible framework for teaching the introductory course
in business statistics. This framework consists of
A complete presentation of traditional business statistics, with
improved discussions of introductory concepts, probability
modeling, classical statistical inference (including a much clearer
explanation of hypothesis testing), and regression and time series
modeling.
A complete presentation of business analytics, with topic coverage
in six optional sections and two optional chapters: a section in
Chapter 1 introducing analytics, five sections in Chapters 2 and 3
discussing descriptive analytics, and Chapters 5 and 16 discussing
predictive analytics.
Continuing case studies that facilitate student learning by
presenting new concepts in the context of familiar situations.
Business improvement conclusions—highlighted in yellow and
designated by icons BI in the page margins—that explicitly show
how statistical analysis leads to practical business decisions.
Many new exercises.
Use of Excel (including the Excel add-in MegaStat), Minitab, and
JMP to carry out traditional statistical analysis. Use of JMP (and
Excel and Minitab where possible) to carry out descriptive and
predictive analytics.
We now discuss how these features are implemented in the book’s
20 chapters.
Chapters 1, 2, and 3: Introductory concepts. Graphical and
numerical descriptive methods. In an improved and simpler
Chapter 1 we discuss data, variables, populations, and how to select
random and other types of samples. Three case studies—The Cell
Phone Case, The Marketing Research Case, and The Car
Mileage Case—are used to illustrate sampling and how samples
can be used to make statistical inferences.
In Chapters 2 and 3 we begin to formally discuss the statistical
analysis used in making statistical inferences. For example, in
Chapter 2 (graphical descriptive methods) we show how to construct
a histogram of the car mileages that were sampled in The Car
Mileage Case of Chapter 1. In Chapter 3 (numerical descriptive
methods) we then use this histogram to help explain the Empirical
Rule. As illustrated in Figure 3.15, this rule gives tolerance intervals
providing estimates of the “lowest” and “highest” mileages that a
new midsize car model should be expected to get in combined city
and highway driving.
Page vii
Chapters 1, 2, and 3: Six optional sections introducing
business analytics and data mining and discussing
descriptive analytics. In an optional section of Chapter 1 The
Disney Parks Case introduces how business analytics and data
mining are used to analyze big data. This case is then used in an
optional section of Chapter 2 to help begin the book’s discussion of
descriptive analytics. Here, the optional section of Chapter 2
discusses what we call graphical descriptive analytics, and four
optional sections in Chapter 3 (Part 2 of Chapter 3) discuss what we
call numerical descriptive analytics. Included in the discussion of
graphical descriptive analytics are gauges and dashboards (see
Figure 2.35), bullet graphs and treemaps (see the Disney examples
in Figures 2.36 and 2.37), and sparklines and data drill-down
graphics. Included in the discussion of numerical descriptive
analytics are association rules (see Figure 3.25), text mining (see
Figure 3.27), hierarchical and k-means cluster analysis (see Figures
3.38 and 3.40), multidimensional scaling (which is part of the cluster
analysis section), and factor analysis.
Business Statistics in Practice: Using Data, Modeling, and Analytics, 9th Edition Bruce L. Bowerman
Business Statistics in Practice: Using Data, Modeling, and Analytics, 9th Edition Bruce L. Bowerman
Page viii
We believe that an early introduction to descriptive analytics will
make statistics seem more useful and relevant from the
beginning and thus motivate students to be more
interested in the entire course. However, our presentation gives
instructors various choices. This is because, after covering the
optional introduction to business analytics in Chapter 1, the five
optional sections on descriptive analytics in Chapters 2 and 3 can be
covered in any order without loss of continuity. Therefore, the
instructor can choose which of the six optional business analytics
sections to cover early, as part of the main flow of Chapters 1–3,
and which to discuss later—perhaps with the predictive analytics
discussed in Chapters 5 and 16. For courses with limited time to
spend on descriptive analytics, we might recommend covering
graphical descriptive analytics, association rules, and text mining.
These topics are both very useful and easy to understand.
Chapters 4 and 5: Probability and probability modeling.
Predictive analytics I (optional). Chapter 4 discusses probability
and probability modeling by using motivating examples—The
Page ix
Crystal Cable Case and a real-world example of gender
discrimination at a pharmaceutical company—to illustrate the
probability rules. Optional Chapter 5 then uses the probability
concepts of Chapter 4 and the descriptive statistics of Chapters 2
and 3 to discuss four predictive analytics: classification trees (see
Figure 5.1), regression trees (see Figure 5.17). k-nearest neighbors
(see Figure 5.28), and naive Bayes’ classification (see Figure 5.36).
These predictive analytics are called nonparametric predictive
analytics and differ from the parametric predictive analytics
discussed in Chapter 16. Parametric predictive analytics make
predictions by using parametric equations that are evaluated by
using the statistical inference techniques of Chapters 6 through 15.
Nonparametric predictive analytics make predictions without using
such equations and can be understood (from an applied standpoint)
with a background of only descriptive statistics and probability.
Chapters 5 and 16 are independent of each other and of the
descriptive analytics sections in Chapters 2 and 3. Therefore, the
instructor has the option to try to motivate student interest by
covering Chapter 5 early, in the main flow of the course, or
wait to cover Chapter 5 until later, perhaps with (before or
after) the parametric predictive analytics in Chapter 16. For courses
with limited time to spend on nonparametric predictive analytics, we
might suggest covering just classification trees and regression trees.
Business Statistics in Practice: Using Data, Modeling, and Analytics, 9th Edition Bruce L. Bowerman
Chapters 6–9: Discrete and continuous probability
distributions. Sampling distributions and confidence
intervals. Chapters 6 and 7 give discussions of discrete and
continuous probability distributions (models) and feature practical
examples illustrating the “rare event approach” to making a
statistical inference. In Chapter 8, The Car Mileage Case is used to
introduce sampling distributions and motivate the Central Limit
Theorem (see Figures 8.1, 8.3, and 8.5). In Chapter 9, the
automaker in The Car Mileage Case uses a confidence interval
procedure specified by the Environmental Protection Agency (EPA) to
find the EPA estimate of a new midsize model’s true mean mileage
and determine if the new midsize model deserves a federal tax credit
(see Figure 9.2).
Business Statistics in Practice: Using Data, Modeling, and Analytics, 9th Edition Bruce L. Bowerman
Business Statistics in Practice: Using Data, Modeling, and Analytics, 9th Edition Bruce L. Bowerman
Page x
Chapters 10–13: Hypothesis testing. Two-sample
procedures. Experimental design and analysis of
variance. Chi-square tests. Chapter 10 discusses hypothesis
testing and begins with a new section on formulating statistical
hypotheses and the meanings of Type I and Type II errors. Three
case studies—The Trash Bag Case, The e-Billing Case, and The
Valentine’s Day Chocolate Case—are then used in the next
section to give a more unified and clearer discussion of the critical
value rule and p-value approaches to performing a z test about the
population mean. Specifically, for each type of alternative
hypothesis, this discussion first illustrates the appropriate critical
value rule in a graphical figure and then, in the same graphical
figure, shows the appropriate p-value and explains why it is the
more informative way to carry out the hypothesis test.
For example, the above Figures 10.1 and 10.2 are presented
side-by-side in the text and illustrate testing a “greater than”
alternative hypothesis in The Trash Bag Case. These figures show
the different a’s specified by two television networks evaluating a
trash bag advertising claim, the different critical values that would
have table looked up by an hypothesis tester using the critical value
rule approach, and have the p-value immediately tells the hypothesis
tester the results of the hypothesis test for any and all values of a.
Similarly, Figures 10.3 and 10.4 illustrate the appropriate critical
value rules and p-values for testing “less than” and “not equal to”
alternative hypotheses.
In addition, as the case studies are used to illustrate hypothesis
testing, the z test about a population mean summary box and the
five-step hypothesis testing procedure shown in the upper portion of
the next page are developed. Here, although the true value of the
population standard deviation is rarely known, the z test about a
population mean summary box serves as an easily modifiable model
for the book’s other more practically useful hypothesis testing
summary boxes—for example, for the t test about a population
mean summary box and the z test about a population proportion
summary box shown in the lower portion of the next page.
Moreover, the five-step hypothesis testing procedure emphasizes
that to successfully use a hypothesis testing summary box, we
simply identify the alternative hypothesis being tested and then
Page xi
looking the summary box for the appropriate critical value rule
and/or p-value.
Page xii
Hypothesis testing summary boxes are featured
throughout Chapter 10, Chapter 11 (two-sample
procedures), Chapter 12 (one-way, randomized block, and two-way
analysis of variance), Chapter 13 (chi-square tests of goodness of fit
and independence), and the remainder of the book. Furthermore,
emphasis is placed throughout on assessing practical importance
after testing for statistical significance. For example, as illustrated in
Figure 12.12, if an F test finds a significant factor in an analysis of
variance, we assess practical importance by finding point estimates
of and confidence intervals for the differences in the effects of the
different levels of the factor. As another example (see Figure 13.2), if
a chi-square test rejects the hypothesis of independence between
two variables, we assess practical importance by using the
contingency table upon which the chi-square test is based to analyze
the nature of the dependence between the variables.
Chapters 14–17: Simple linear regression. Multiple
regression and model building. Predictive analytics II
(optional). Time series forecasting and index
numbers. Chapter 14 discusses simple linear regression and
illustrates the results of a simple linear regression analysis by using
The Tastee Sub Shop (revenue prediction) Case. This same case
is then used by the first seven sections of Chapter 15 (multiple
regression and model building) to illustrate the results of a basic
multiple regression analysis (see Figure 15.4). The last four sections
of Chapter 15 continue the regression discussion by presenting four
modeling topics that can be covered in any order without loss of
continuity: dummy variables (including a discussion of interaction);
Page xiii
quadratic variables and quantitative interaction variables; model
building and the effects of multicollinearity (including model building
for big data—see Figure 15.31); and residual analysis and
diagnosing outlying and influential observations.
With the regression concepts of Chapters 14 and 15 as
background, optional Chapter 16 extends these concepts and
discusses three parametric predictive analytics: logistic regression
(see Figure 16.5), linear discriminate analysis (see Figure 16.12),
and neural networks (see Figures 16.17 and 16.19). Moreover,
Chapter 17 extends the regression concepts in a different way and
discusses time series forecasting methods, including an expanded
presentation of exponential smoothing and a new and fuller (but
understandable) presentation of the Box–Jenkins methodology.
Business Statistics in Practice: Using Data, Modeling, and Analytics, 9th Edition Bruce L. Bowerman
Note that although we have used the term predictive analytics to
refer only to the prediction methods of Chapters 5 and 16, the
regression and time series methods of Chapters 14, 15, and 17 all
predict (using a parametric equation) values of a response variable
and thus are all (parametric) predictive analytics. We have used the
term predictive analytics to refer only to the predictive methods of
Chapters 5 and 16 because these methods are (for the most part)
more modern methods that have been found to be particularly
successful in analyzing big data. Together, the more classical
parametric predictive analytics of Chapters 14, 15, and 17, along
with the more modern nonparametric and parametric predictive
analytics of Chapters 5 and 16 and the descriptive analytics of
Chapters 2 and 3, make up a full second statistics course in business
analytics.
Chapters 18–20: Concluding chapters. The book concludes
with Chapters 18 (nonparametric statistics), Chapter 19 (decision
theory), and website Chapter 20 (process improvement using control
charts).
Page xiv
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He thought better of this, however, and continued to creep forward
carefully and silently.
"If he hits you again," he said, speaking to Hal but muttering
the words to himself, "it can't be helped; but we'll repay those blows
with interest."
Hal, standing erect before his captors, did not flinch as
Lieutenant Steinz drew back his arm for another blow. But his eyes
flashed dangerously.
"You'll be sorry for this, my friends," he said quietly.
"Threats, eh?" sneered the German. "You're in no position to
threaten, pig."
"Perhaps not," admitted Hal, "but just the same I am warning
you."
There was something so menacing in the lad's voice, that for a
moment the German hesitated; but for a moment only, then he drew
back his arm and struck.
Once more Hal staggered under the blow, but he did not flinch.
The German raised his arm and would have struck again but for
a sudden interruption.
When Chester saw the German strike Hal a second time, it was
more than his blood could stand. He forgot, for the moment, his
mission, that his first duty was to pass beyond the German camp. He
threw caution to the winds.
With a wild cry he leaped to his feet and dashed forward, a
revolver levelled in each hand.
Startled, the Germans turned to face their new foe. One look at
Chester's angry features and they recoiled involuntarily.
At the same moment Chester fired—both weapons at once. Two
of the enemy toppled over in their tracks.
Now Hal had a quick mind. At Chester's first cry he knew what
was up and he grew instantly alert, ready to take advantage of the
first opportunity that presented itself.
The opportunity was not long coming.
Lieutenant Steinz, turning to get a view of Chester, for a
moment left Hal unguarded. In that instant Hal sprang. Both hands
he locked about the German's throat, and squeezed with all his
strength. In vain the Teuton squirmed, struck and kicked.
Suddenly Hal released his right hand and drove it into the man's
face. At the same moment his left hand shot out and seized the
German's revolver. Then he stepped quickly back, levelled the
weapon and fired.
"Come on, Chester!" he shouted.
Chester needed no urging.
In a few quick strides he was at Hal's side.
"Let's get out of here," he cried. "It's getting too warm."
Together the lads dashed toward the trench.
A cry of alarm went up from the Germans behind.
"Shoot them!" cried a voice that Hal recognized as that of the
German colonel.
"Zig-zag, Chester!" cried Hal, and suited the action to the word.
Chester followed his chum's example and the first volley from
behind failed to find a mark.
By this time the lads were at the edge of the trench.
"Up and over with you, quick!" cried Chester.
Hal leaped to the top of the trench and toppled to the ground
beyond even as half a score of bullets sang across the spot where
his head had been a moment before.
Chester also sprang for the top of the trench. But he had leaped
too soon, and instead of reaching the top he fell short, and dropped
down inside the trench again.
Germans were almost upon him when he regained his feet.
Chester realized that a second leap was out of the question at
the minute, so guns in hand he turned and faced his foes.
"Crack! Crack! Crack! Crack!"
His automatics spoke angrily and all four bullets found human
targets.
Hal, meanwhile, safely over the trench, looked around for
Chester. When he failed to see him he realized on the instant what
had happened.
"What shall I do?" he asked himself. "Duty says to hurry to a
place of safety, but friendship says help Chester."
He wasted little time in thought.
He scrambled back to the top of the earthen embankment and
took in the sight about him.
There Chester stood at bay, his automatics held in steady
hands. Hal drew his own weapons.
"Jump up here quick, Chester!" he called. "I'll cover you."
"Don't bother about me," Chester called back. "Get away from
here. Remember you must get through. I'll hold 'em off."
"Don't be a fool," shouted Hal, discharging his revolver at a big
German who was about to shoot Chester down with his rifle. "Come
up here."
Chester paid no further heed to his chum.
Hal gritted his teeth, dropped one revolver in his pocket, and
reaching down grasped Chester by the shoulder.
"Come on," he called.
Chester shook off his chum's hand.
"Let me alone." he shouted angrily. "I'll get a few of these
boches before they down me."
His revolvers spoke as he talked, and two Germans dropped.
Meanwhile bullets were striking on all sides of the two lads, and
it seemed a miracle that they were not touched.
Hal considered the situation in a flash.
"There's one chance," he said.
Deliberately he sheathed his other revolver, thus leaving himself
unarmed in the face of his foes. Then, bracing himself as best he
could on the embankment, he reached down and seized Chester by
both shoulders.
Putting forth all his strength, Hal heaved mightily, and drew his
chum to the top of the embankment with him. There he released
him and drew his revolvers again.
Came a cry of rage from inside the trench as the Germans saw
their prey about to escape. Two men dropped on their knees and
sighted their rifles carefully.
But before they could fire Hal had accounted for one and
Chester for the other.
Again a howl of rage went up from the German trench.
"Kill them! Kill them!" screamed the German colonel. "What a lot
of dunderheads! Can't you shoot?"
He seized a revolver from a young officer close by and dashed
forward himself.
Hal, in the act of tumbling from the embankment, smiled slightly
and faced the colonel, unmindful of all other dangers.
"So you're the man responsible for those blows a moment ago,
eh?" he muttered. "Well, you'll never do it again. Take that!"
He sighted carefully and fired.
The German colonel staggered in his onward rush, reeled
crazily, threw up his arms, casting his revolver a dozen paces away,
then fell to the ground.
"So much for you," Hal muttered. "You won't bully another
American, I'll bet on that."
"Come on," said Chester, who had stuck close to his chum all
the time. "It's too warm here. Let's move."
"Right. Suits me," said Hal quietly.
"Down we go, then," said Chester.
He rolled rather than leaped to the ground on the outside of the
trench. Hal did likewise.
Both lads were slightly bruised by this method of descent, but
they were not injured seriously. They scrambled to their feet.
"Now, let's see you run!" shouted Hal to Chester.
They ran.
CHAPTER XIV
THE CLOSING OF THE NET
Bullets flew thick and fast after the two lads as they clashed for the
shelter of the American lines beyond. Fortunately, however, none
touched them.
The Germans, it appeared, were so bewildered by the
suddenness of Chester's appearance, single-handed attack and the
flight of the two chums that followed, that they forgot all about their
searchlights, which would have made it possible for them to have
picked off fugitives at will; or else they had no searchlights in that
section of the field.
Zig-zagging from right to left, the lads ran at top speed. For a
time bullets whistled unpleasantly close, but soon they became few
and far between.
Hal slowed down. Chester followed his example.
"Whew!" said Chester. "Pretty close, but we're safe enough now,
I guess."
"By George! I hope so," declared Hal. "But there is just one job
that I would have liked to complete before getting away from there."
"What's that?" demanded Chester.
"I would like to have let a little lead into that big German
lieutenant who battered me up with his fist."
"Don't blame you," said Chester. "I'd like a shot at him myself."
"Well," said Hal, "I left my mark on his throat, and that's some
satisfaction. Also, I disposed of the colonel who was responsible, and
there's more satisfaction there, too."
"I saw you," replied Chester. "It was a neat shot."
"Well," said Hal, "we've done something that a couple of other
couriers sent out by General Rhodes failed to accomplish—we have
passed through the German lines. The general's plans will not go
wrong if we can help it."
"Right," agreed Chester. "And I figure that the sooner we report
to General Lejeune the better."
"Correct as usual. But I don't know that I care to try and repeat
the feat of getting through. Besides, we have General Rhodes'
permission to stay here until after the big battle if we like."
"And I vote that we stay," said Chester.
"Think I'll cast my own ballot that way," declared Hal. "We'll
stick, unless something turns up to change our minds."
"Now for the American lines, then," said Chester.
They hurried on through the darkness and directly the dim
outline of the American trenches loomed up ahead.
"Here we are," said Hal. "Now to get over."
As they would have climbed up, however, the figure of a soldier
appeared above them. He saw them instantly and levelling his rifle
cried:
"Halt! Who goes there?"
"Friends," said Hal briefly.
"Advance, friends, and be recognized," said the sentinel.
Hal and Chester obeyed and the sentinel scanned them closely.
"You look all right," he growled at last, "but I'm not sure of
you."
"Do you think we'd be coming in here if we didn't belong?"
demanded Chester.
"I don't know about that; but I can't see any good reason why
you should be prowling around out in No Man's Land if you are not
bent on mischief."
"Don't be absurd, man," said Hal. "We come from General
Rhodes with a message for General Lejeune."
"A likely story," said the sentry. "How'd you get through the
Germans?"
"Walking and running," said Chester. "But are you going to keep
us standing here all night? I tell you we bear an important message
from General Rhodes."
"What'd you both come for?" the sentry wanted to know.
"That," said Chester, thoroughly exasperated, "is none of your
business, my man! Will you call the sergeant of the guard, or shall
I?"
"Oh, I'll call him," said the sentry, "but I'll tell you right now I
don't think it will do you any good. Kindly step up here, will you?"
Hal and Chester did so. Then, for the first time, the sentry saw
that they were officers in the American army. He looked
flabbergasted.
"I—I—I beg pardon, gentlemen," he said. "I didn't know you
were officers. Why didn't you tell me?"
"You didn't give us a chance," said Hal shortly. "Kindly summon
the sergeant of the guard."
The sentry argued no longer. He raised his voice in a shout that
brought the sergeant of the guard on the dead run.
"What's the matter with you, you bonehead?" demanded the
sergeant as he came lumbering forward. "Want to arouse the whole
camp?"
"It's all right, sergeant," said Hal. "He only did as ordered. We
have come from General Rhodes with an important message for
General Lejeune. Will you direct us to his quarters?"
The sergeant saluted stiffly.
"Follow me, sirs," he said briefly.
Five minutes walk brought the three to the headquarters of the
commander of the Second American division. There the lads were
accosted by a member of the general's staff, Colonel O'Shea.
"We desire to see the general at once on a very urgent matter,"
said Hal.
Colonel O'Shea scowled.
"The general left orders that he was not to be disturbed unless
upon a very important matter," he replied.
"But this is urgent," said Chester. "We are instructed by General
Rhodes to deliver the message at once."
"But how am I to know the matter is so urgent?" asked the
colonel.
"Because I say so, sir," said Hal quietly. "I am not in the habit of
lying, nor of having my word doubted."
"Oh, is that so," said the colonel, though somewhat taken
aback. "Well, I'm not sure the general will care to be disturbed. You
may deliver your message, and then I shall consider whether your
business is of such importance as to justify waking the general."
"We were not instructed to deliver our message to you, sir," said
Hal simply. "I have to request again that we be given immediate
audience of General Lejeune."
The colonel hesitated. Apparently he was on the point of
refusing to arouse the general, but he thought better of it, shrugged
his shoulders and turned away.
"One moment," he said brusquely.
He returned a moment later, however, followed by a second
figure, attired in a suit of pajamas and rubbing sleepy eyes.
"General Lejeune?" asked Hal.
"Yes," was the sharp reply. "What is it?"
"We bear a message from General Rhodes, sir," said Hal.
"Well, let's have it, let's have it," exclaimed the general. "I've
got to get back to bed and get some sleep."
"First, sir," said Hal, "I must explain that we came through the
German lines where two or three other couriers lost their lives.
General Rhodes wishes you to understand, sir, that the success of
the campaign depends upon your acting in accordance with his
message."
"I have no doubt of it," said General Lejeune. "I have been
unable, since the German wedge was driven between our forces, to
get into communication with General Rhodes or other divisional
commanders. I am isolated here, but at the same time I consider my
position impregnable, so I am standing pat."
Hal and Chester bowed in understanding of the general's
explanation, and the commander of the Second division added:
"Come, sirs, what is the message you bring?"
"General Rhodes' message, sir," said Hal, "is that he requests
you to attack the enemy before Sedan in full force on the evening of
November 6, the attack to begin precisely at 6 o'clock."
"Very well," said General Lejeune, "and just what is at the
bottom of this plan—what is to be gained by it?"
"That I do not know, sir," said Hal. "General Rhodes simply
asked us to carry that message. He said that the success of the
campaign against Sedan depended upon you doing your part."
"Well, I'll do it, never fear," said General Lejeune. "I've got one
of the best fighting units in France, and there's not a man in it who's
not dead anxious to get another chance at the Huns. You may take
back word to General Rhodes for me, that I shall act in accordance
with his wishes."
"If it is all the same to you, sir," said Chester with a slight smile,
"we're not going back—not, at least, until the battle of Sedan is
over."
"How's that? How's that?" asked the general in some surprise.
"Why, sir," said Chester, "General Rhodes gave us permission to
stay with you if we deemed it imprudent to try and pierce the
enemy's lines again."
"And you think it would be imprudent?" asked General Lejeune
with a slight smile.
"In view of the trouble we had getting here, yes, sir," replied
Chester.
"Very well, then," said the general, "you may remain with us.
Colonel O'Shea, will you find quarters for these gentlemen? By the
way, I did not catch your names."
"Crawford, sir," said Chester.
"Paine, sir," said Hal.
"Very well," General Lejeune continued, "Colonel O'Shea, will
you please see that Major Paine and Major Crawford are provided
with suitable quarters? And will you both report to me at 8 o'clock in
the morning, gentlemen? I may have need of you. The Second
division is an hospitable unit, but you'll find that guests are required
to work as well as home folks."
"We shall be more than glad to do our parts, sir," said Hal.
"Very well. Now you have kept me out of bed long enough. I'll
leave you both to the good graces of Colonel O'Shea, and if he
doesn't find suitable quarters for you, you let me know and I'll have
him court-martialed."
With this, and a smile on his face, the good-natured commander
took his leave.
"By George!" said Hal, as the lads followed Colonel O'Shea from
the general's quarters, "he's the most lively commander I ever did
see."
"Full of 'pep' eh?" said Chester with a laugh.
"Yes," Hal agreed, "and I'll bet he's full of the same old 'pep'
when it comes down to business."
And Hal was right.
CHAPTER XV
THE CAPTURE OF SEDAN
The American advance against Sedan was in full blast. All night the
fighting had raged. Promptly at 6 o'clock on the evening of
November 6 General Lejeune had hurled the Second division forward
in accordance with the plans outlined by General Rhodes of the
Forty-second.
Apparently the Germans had anticipated the attack, for they
were braced to receive it when the first Yankee troops began to
move. The enemy stood firm—and was continuing to stand firm
almost twelve hours after the assault was launched.
There was a slight chill in the early November air as it grew
light. The air was filled with shrieking shells and shrapnel. Rifle and
machine-gun fire rose even above the noise of the field and siege
guns. Shrill whistles punctuated intervals of seeming silence as
American officers gave orders to their men. In the midst of battle,
whistles are depended upon mainly for signals—also there are
signals given with the hands. The confusion is usually too great to
permit verbal orders being understood.
At the same time that General Lejeune attacked the enemy,
General Rhodes, to the south, also had advanced. But the enemy
was holding stubbornly in that section of the field also, and at 6
o'clock on the morning of November 7 the American forces had
made only slight progress. However, they were still hammering hard
at the German lines.
With a gallantry not exceeded in the annals of the war, the
Second division kept at its task. When one enemy machine-gun nest
was captured, they found themselves targets for others, whose
gunners, discovered, had withheld their fire until the moment when
it would be the most effective.
Another grand assault was ordered by General Lejeune.
The Germans made a determined resistance. They put in fresh
troops and subjected the American lines to a terrific artillery
bombardment of high explosives and gas shells. Directly in the path
of the advancing Americans was a large wood. Although the wood
was not yet cleared of the enemy, the American line here was
farther advanced. Many prisoners had been taken.
A third attack resulted in the capture of still more prisoners and
many machine-guns. In the meantime the Ninth infantry, on the
right of that part of the field where Hal and Chester found
themselves, had advanced its position to the northern edge of the
Bois de la Jardin and was digging in to beat off a possible counter-
attack. In fact, the entire Third brigade, assisted by a battalion of
the Second engineers, was strengthening its lines as well as possible
under heavy enemy machine-gun and artillery fire.
The defensive part played by this brigade was very difficult. Its
losses were heavy as a result of enemy shell fire and gas
bombardments, to which the Third brigade could not at the moment
reply. Its duty now was to hold its lines. Its present action was
confined to a rifle and machine-gun duel with the enemy.
To the south, the First brigade also was hotly engaged. It had
advanced in the face of a terrible artillery and machine-gun fire until
at hand grips with the foe. Then ensued one of the fiercest struggles
of the war.
As in other encounters, the Germans proved no match for the
Yankees at hand-to-hand fighting. They resisted desperately, but
gradually were driven back. The Americans, with wild cheers,
pursued them closely.
General Lejeune's center, composed of the Second brigade, with
an additional battalion or two of artillery, also was meeting with
greater success than the Third brigade, which, for the moment, had
been checked.
The advance was pushed with desperate energy, and the
Germans could not hold their ground in the face of the withering
American fire. The German center faltered, then broke.
Taking advantage of this success, General Lejeune pushed
Brigadier General Abernathy's Second division into the breach.
Immediately, also, he ordered the First brigade forward in an effort
to break through to the south, while orders were rushed to the hard-
pressed Third brigade to make a final effort.
The task of the Third brigade was easier now. Bereft of its
supports, the German center was obliged to yield ground to the
Third brigade or risk being cut off and surrounded.
The Germans gave ground slowly.
To the south, the First brigade also began to drive the foe more
swiftly. It appeared for a moment that the Germans would suffer a
rout. Under the direction of their officers, however, they braced
perhaps half a mile farther back, and again showed a determined
front.
Trenches dug by the Americans were abandoned now as the
Yankees poured forth in pursuit of the enemy. Not a man in the
whole Second division who was not sure that the trenches would
never be needed for defensive purposes. No one knew better the
morale of the American troops than did the men themselves.
Nevertheless, the advance slowed down in the face of the
resistance being offered by the enemy. For a time it appeared that
the fighting had reached a deadlock.
The deciding touch to the battle was furnished by General
Rhodes.
Sweeping up from the south, the Fifth, Sixth and Seventh
brigades of the Forty-second division bore off a trifle to the east and
then turned north again, thus catching the enemy on the left flank.
This maneuver, apparently, had not been anticipated by the
enemy's general staff, for it took the Germans by surprise. True, they
received warning in time to wheel machine-guns into position and to
place big guns to rake the Americans as they dashed forward. But
the warning had not been received in time to permit the general
staff to alter its plan of defense, and for this reason proved the blow
that broke the backbone of the enemy's resistance.
The enemy, closely pressed by General Lejeune, had no time to
make changes in his defensive plan necessitated by General Rhodes'
sudden attack. Reinforcements could not be sent to check General
Rhodes without weakening the front opposed to General Lejeune.
General Schindler, after a hasty conference with his staff,
ordered a retreat to the lines just before Sedan. The Germans fell
back rapidly.
Neither General Rhodes nor General Lejeune was content to rest
with this advantage, but each decided to push on.
During all this time, the enemy had been successful in keeping a
wedge between the Second and Forty-second American divisions.
General Schindler realized that if he hoped to extricate his men from
the trap sprung by the Americans he must prevent a juncture of the
Second and Forty-second at all hazards.
Now, however, as the attack seemed on the verge of success,
General Lejeune decided that the German wedge separating him
from General Rhodes must be pierced.
Accordingly, without permitting the advance to slacken
elsewhere, he threw the First brigade against it.
For perhaps fifteen minutes the fighting was fast and furious. In
vain the Germans tried to stem the tide in khaki that rushed forward
against them. General Schindler further weakened his center to rush
reinforcements in order to retain the wedge intact.
But it was no use. The Americans were not to be denied. They
fought with the courage and desperation of lions. Little heed did
they pay to the hail of machine-gun bullets that swept them as they
advanced. Artillery and explosive shells failed to stop them. Rifle fire
was no more effective.
Suddenly from the German lines sallied a regiment of cavalry.
The American infantry braced to receive the charge.
At the same time Hal found himself before Colonel Taylor of the
First brigade with dispatches from General Lejeune. He had just
delivered them as the German cavalry sallied forth.
"Great Scott! What a chance to take!" the lad muttered under
his breath. "The Germans must be licked. This move can be for no
other purpose than to give infantry time to withdraw."
The American infantry stood firm as the German cavalry hurled
itself upon them. Not an inch of ground did they give. Horses and
men fell in heaps. Other chargers reeled back, throwing their riders
beneath their hoofs. At the same time the Yankee infantry poured in
a hail of rifle fire.
The Germans retired a pace, reformed and charged again. The
result was the same. Not an inch did the Americans give, and the
execution in the enemy's ranks was fearful to behold.
"I guess that will stop that," Hal told himself.
He was right.
When the enemy's cavalry withdrew a second time it did not
reform for a third charge. Instead, it fell back upon its infantry and
artillery supports, apparently fearing that the American infantry
would pursue and annihilate it.
"I thought so," said Hal.
In the meantime, the German retirement in other parts of the
field had become more rapid. The lines before Sedan were
abandoned gradually and at last there was nothing to keep the
Americans from entering the city save the cannonading of the
German artillery from far to the rear of the town.
But although the bulk of the German army had retired safely to
the east of Sedan, fortune had not been so kind to the two brigades
which had formed the wedge between the Second and Forty-second
American divisions.
When General Lejeune's men had pushed back the cavalry
attack, General Rhodes, to the south, had gained an inkling of what
was going on. Accordingly he had ordered an attack upon the hard-
pressed foes.
Caught thus between two fires, the Germans tried first to hold
their ground, and, finding this could not be done, to retreat orderly.
But they had delayed too long.
Three regiments of the First brigade of General Lejeune's
division had been hurried forward to cut off a movement, and the
Germans, when they found flight blocked, became disheartened. In
spite of the fact that they outnumbered the little force between them
and the bulk of their army, thousands of men threw down their arms
and surrendered. This forced the others to follow suit or be
annihilated.
Less than two hours later, with German shells still falling among
them, American troops entered Sedan.
And the French population, virtual prisoners for many months,
received them with wild acclaim. It was a joyous day for the citizens,
indeed.
CHAPTER XVI
AN UNEXPECTED HONOR
"Sedan at last! This settles the war."
It was Chester who spoke.
"Right you are," replied Hal. "The poor old kaiser's goose is
cooked. Even the most sanguine German can no longer hope for
victory."
"I think the kaiser gave up hope a long while ago," said Chester.
"He—Hello, what's up now, I wonder?"
He broke off suddenly and pointed to a horseman who came
galloping into the town from the east, gesticulating excitedly as he
rode along. Words that he shouted as he dashed forward seemed to
create great excitement among the villagers, who, all day, had been
parading the streets in celebration of the American occupation of the
city.
"Don't know," said Hal. "We'll try and get close enough to hear
what he says."
As the man drew close, the lads saw that he was a German
cavalryman. It appeared strange to both boys that he was thus
permitted to ride free, as the feelings of the villagers were very
strong against the Germans. But it soon became apparent that the
message he brought secured him immunity.
"What's that he said?" asked Chester, with hand to his ear.
"I didn't catch it," said Hal. "Here, get in front of him. We'll stop
his wild ride."
Chester needed no urging. The lads stepped directly in front of
the galloping horse. Hal produced his revolvers.
The rider checked his steed. Hal approached him.
"Dismount," said the lad in German.
The rider did so.
"Now," said Hal, "what's all the excitement? You seem to have
something on your mind. What is it?"
"Haven't you heard the news?" demanded the rider.
"I wouldn't be asking you if I had," said Hal. "What is it?"
"The kaiser has abdicated!"
Hal and Chester started back in pure amazement.
"What!" they exclaimed in a single voice.
"So I am informed," declared the German. "It is true that my
information has not been substantiated, but I know enough of
conditions in Germany to credit the report."
"Well, you come with me," said Hal. "We'll take this matter to
General Lejeune."
The German accompanied them without objection.
General Lejeune received the report with skepticism.
"Nothing to it, in my opinion," he said. "It is true that conditions
in Germany are fast approaching a crisis, but I believe this report is
premature. However, I have no doubt that something like that will
happen within the next thirty days. But what are you doing in our
lines, man?"
This last to the German soldier.
"Well, I'm tired of fighting," was the soldier's reply. "I want to
live to go home again some day. I've a family in Hamburg that will
need me. I am content to remain a prisoner until the war is over."
"And so you shall," said General Lejeune. "Whether your report
is true or not, it has given me an interesting moment. Colonel
O'Shea, will you turn this man over to the corporal of the guard?"
The prisoner was led away. General Lejeune turned to Hal and
Chester.
"I am sorry to lose your services, gentlemen," he said, "but I
have just been in communication with General Rhodes, and he
wishes you to report to him at once."
The lads saluted the commander of the Second division and left
his quarters.
Half an hour later they reported to General Rhodes as he rode
into Sedan to establish his own quarters, as the Second division was
soon to advance again. General Rhodes greeted the lads warmly.
"I am certainly glad that you both came through safely," he
said, after returning their salutes, "and I must say that I didn't
expect it. You have been in luck. Now I have another important
matter in hand."
"We shall be glad to offer our services, sir," said Hal.
General Rhodes smiled.
"I've no doubt of it," he replied. "However, this mission is not
likely to be so dangerous. Don't worry, though," he added, as the
faces of the lads fell, "I believe I may safely promise you some
interesting moments."
"We're glad of that, sir," declared Chester.
"I wonder," said General Rhodes, "whether you have heard of
the reported upheaval in Germany?"
"Yes, sir," said Hal. "Only a few moments ago we captured a
man who declared the kaiser had abdicated."
"That," said General Rhodes, "is probably untrue; however, I
know that the kaiser has considered abdicating. In fact, his
abdication is being urged by his military leaders—his erstwhile
friends, Hindenburg and Ludendorff."
"Can that be possible, sir?" asked Hal.
"Yes, we have authentic information to that effect. I understand,
too, Germany is preparing to ask Marshal Foch for an armistice
preliminary to signing a declaration of peace."
"By Jove, sir!" exclaimed Chester, carried away in spite of
himself.
General Rhodes smiled again.
"It is good news," he said quietly. "Of course, I am not
absolutely positive of that, but in view of recent German reverses I
do not see how the enemy can do aught else."
"Well, sir," said Chester, "we'll impose terms on them that will
make their hair curl."
For a third time General Rhodes smiled.
"We won't be too severe," he said. "Remember, we are not
German."
"That's true, too, sir," said Chester. "But all the same, it should
be done, if you ask me."
"Perhaps," said General Rhodes. "Now, I suppose you are
wondering why I called you here?"
"Yes, sir," returned Hal.
"Well," said General Rhodes, "I have been summoned to report
to the commander-in-chief and I want a couple of officers to go with
me who can be useful as well as ornamental."
Both lads flushed.
"I know that you drive an automobile exceedingly well, Major
Paine," the general continued, "and for that reason I am selecting
you as my chauffeur on this trip."
"But I am afraid I shall not be so useful, sir," said Chester.
"Well," said the general, "I am taking you along because I
thought you'd like to go."
"And so I would, sir," answered Chester.
"It may be," General Rhodes continued, "that before our return
we shall be present at a very momentous gathering."
"You mean, sir—" asked Hal.
General Rhodes nodded.
"Exactly," he replied. "I mean that the commander-in-chief is
summoning me for some purpose other than because he wants to
see me. It would seem that matters have reached a point where
something is likely to break at any minute."
"By George! I hope so, sir," declared Chester.
"I shall expect you to be ready in an hour," said General Rhodes
ending the interview suddenly. "I shall have a car here at that time."
Chester and Hal saluted and departed.
"Now, this is what I call a regular mission," declared Hal, as
they hurried to their quarters.
"It is if it develops," replied Chester.
"Something tells me it will develop," said Hal.
"Let's hope so."
The lads were back at General Rhodes' headquarters well within
the time allowed them. A large army automobile stood without.
"Guess this is our steed," said Hal.
He was right.
General Rhodes appeared a few moments later and took his
seat. He motioned Chester to a place beside him. Hal took the
wheel.
"Where to, sir?" he asked of the general.
"Rheims," was the reply. "The commander-in-chief is there now.
You know the road, of course?"
"Yes, sir."
"Then you will take us there as speedily as possible."
The machine shot forward with a lurch.
Now if there was one thing Hal did better than anything else it
was to drive an automobile. He was a fast though careful driver and
his hands and nerves both were like steel when he clutched a wheel.
He had been over the road before, and his excellent memory
served him in good stead now.
It was after 3 o'clock on the afternoon of November 7 when the
automobile flashed into the outskirts of Rheims. Hal stopped the car
long enough to inquire the way to General Pershing's headquarters,
then moved forward again.
"You are a good driver, Major," said General Rhodes, as he
alighted and motioned both boys to follow him.
"Thank you, sir," returned Hal. "I've had experience enough, sir,
I should be, at all events."
General Rhodes vouchsafed no reply, as he mounted the short
flight of steps to General Pershing's offices, with Hal and Chester at
his heels.
Apparently his arrival was expected, for an orderly saluted and
told him that he was to proceed to the commander-in-chief
immediately.
"You gentlemen stay here until I send for you, or return," he
instructed the two lads.
Hal and Chester stood stiffly at attention as he walked away.
"We're in luck, if you ask me," said Chester after their
commander had gone.
"It would seem so," Hal agreed. "If anything happens, I'd like to
be in at the finish."
"So would I. We've been in the war from the first. It would be
no more than right for us to see the finale."
"Maybe we will," said Hal. "Here's hoping."
They sat quietly for some time. Two hours later an orderly
approached.
"Major Paine! Major Crawford!" he said, "the commander-in-
chief desires your presence at once. Kindly follow me."
CHAPTER XVII
STUBBS AGAIN
General Pershing greeted the lads cordially.
"Glad to see you again," he said. "General Rhodes informs me
that you have been up to your old tricks and have again been cited
for gallantry in action. However, it is no more than I would have
expected of you."
The lads bowed in response to this praise, but neither spoke.
"It is fortunate that General Rhodes brought you with him,"
General Pershing continued. "Still, it may not be so fortunate for
him, for I am about to deprive him of your services. I take it that
you will survive the separation, though," and the commander-in-
chief smiled.
"We are always glad to serve in whatever way we may, sir," said
Hal.
"Good!" said General Pershing. "Then I shall avail myself of your
services. Several hours ago I was in communication with Marshal
Foch, who is now in Soissons. General Rhodes informs me that he
has made you acquainted with the facts that seem to indicate an
early cessation of hostilities, so I need not amplify here. Now,
Marshal Foch, anticipating that Germany may really sue for peace,
has asked my advice in the matter of armistice terms pending a final
treaty of peace. These I have written out. As you will readily
recognize, they are not to be trusted to careless hands. I have
confidence in you, however, gentlemen, so I shall ask you to carry
this paper to Marshal Foch."
"We shall be glad to do it, sir," said Chester.
"Very well. Then I intrust this paper to you, and I need not warn
you to guard it carefully and keep the matter secret."
General Pershing extended a document to Hal. The lad took it
and put it carefully in his inside coat pocket.
"It will be safe there, your excellency," he said quietly.
"Now," said the commander-in-chief, "it is my wish that that
paper be placed in Marshal Foch's hands at the earliest possible
moment. The car in which you drove General Rhodes is at your
disposal."
"We shall make all possible haste, sir," said Chester.
Both lads saluted their commander and left the room.
"By Jove!" said Hal, as he sprang into the car, "there is no use
talking, important developments are pending. It begins to look like
peace to me."
"And to me," Chester agreed. "Well, the sooner the better. Four
years of war is enough to satisfy Mars himself."
Soon the car was speeding westward.
It was a long drive to Soissons and it was after nightfall when
Hal saw the lights of the city in the distance. A few moments later
they entered the town.
Hal had no difficulty ascertaining where Marshal Foch made his
headquarters and he drove there at once. A few words to a guard
before the building brought forth a member of Marshal Foch's staff
and the lads explained their mission to him briefly.
"You are expected," said the French officer. "Follow me."
He led the way into the house and through a long hall. At the
far end he tapped on a door.
"Who's there?" came a voice, that Hal at once recognized as
belonging to the French commander-in-chief.
"Colonel Murrat," said the lads' guide. "The messengers from
General Pershing have arrived."
"Show them in at once," said Marshal Foch.
A moment later Hal and Chester were in the presence of the
generalissimo of all the allied forces. They saluted him respectfully.
"I may be mistaken," said Marshal Foch, eyeing them
searchingly, "but I'll wager you are Majors Paine and Crawford. Am I
right?"
"Yes, your excellency," said Hal. "We are honored that you
remember us."
"I never forget a face," replied Marshal Foch; "and seldom a
name. Then you bring me a communication from General Pershing?"
For answer Hal produced the document given him by the
American commander-in-chief earlier in the day. He passed it to
Marshal Foch without a word. The French commander took it and
laid it carefully on his desk.
"That will be all for to-night, gentlemen," he said. "I shall be
pleased if you will avail yourself of our hospitality. Colonel Murrat will
find quarters for you. Will you report to me in the morning at 8
o'clock? I may have a reply for your commander-in-chief."
The lads saluted again and withdrew. Colonel Murrat showed
them to excellent quarters in a house next to the one in which the
French commander had his headquarters and left them.
"Well," said Chester, after he had gone, "looks like we are right
in among things, doesn't it?"
"It certainly does," Hal agreed. "But say, I'm hungry. Let's step
out and round up something to eat."
"Suits me," declared Chester, "I'm half starved myself."
At a little restaurant only three or four blocks away they were
soon comfortably filled. Hal was on the point of suggesting that they
turn in for the night when a figure entering the door caught his eye.
"By all that's wonderful," he exclaimed, "here comes Anthony
Stubbs."
Hal was right. The little war correspondent espied the lads at
the same moment and hurried toward them with outstretched hand.
"I'm awfully glad to see you boys again," he exclaimed. "What
brings you here, if I may ask?"
"Sit down, Mr. Stubbs," said Hal. "Have something to eat with
us."
"Thanks: don't mind if I do. But I repeat, what are you doing
here?"
"How long have you been in town, Mr. Stubbs?" asked Chester,
ignoring the little man's question.
"About fifteen minutes, more or less. But I say, what are you
doing here? This is the third time I've asked that question."
"Then don't ask it again, Mr. Stubbs," replied Chester.
"Oh, I see," smiled Stubbs. "Can't answer, eh? Well, I'll wager
another hat with somebody that I can tell you why you're here."
"You'd lose this time, Mr. Stubbs," said Hal.
"Oh, no I wouldn't. You're here in connection with the signing of
an armistice by Germany and the allies."
Chester started to his feet.
"Sh-h-h! Not so loud, Stubbs," he exclaimed.
Stubbs smiled, but he lowered his voice when he spoke again.
"Well, would I lose the bet?" he asked.
"I can't say a thing, Mr. Stubbs," was Hal's response.
"Well, I'm bound by no such orders," said Stubbs, "so I can.
First, however, I want you to understand that whatever I do say is in
confidence."
"Of course," said Hal.
"Certainly, Mr. Stubbs," agreed Chester.
"Well, then," said Stubbs, "I want to tell you I'm on the trail of
the biggest scoop in newspaper history. I'm going to be the first war
correspondent to flash the news that the armistice is signed."
"You mean you think you are," said Chester.

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Business Statistics in Practice: Using Data, Modeling, and Analytics, 9th Edition Bruce L. Bowerman

  • 1. Read Anytime Anywhere Easy Ebook Downloads at ebookmeta.com Business Statistics in Practice: Using Data, Modeling, and Analytics, 9th Edition Bruce L. Bowerman https://ebookmeta.com/product/business-statistics-in- practice-using-data-modeling-and-analytics-9th-edition- bruce-l-bowerman/ OR CLICK HERE DOWLOAD EBOOK Visit and Get More Ebook Downloads Instantly at https://ebookmeta.com
  • 3. Page i Bruce L. Bowerman Miami University Anne M. Drougas Dominican University William M. Duckworth Creighton University Amy G. Froelich Iowa State University Ruth M. Hummel JMP Kyle B. Moninger Bowling Green State University Patrick J. Schur Miami University Business Statistics and Analytics in Practice NINTH EDITION with major contributions by Steven C. Huchendorf University of Minnesota Dawn C. Porter University of Southern California
  • 5. Page ii BUSINESS STATISTICS AND ANALYTICS IN PRACTICE, NINTH EDITION Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2019 by McGraw-Hill Education. All rights reserved. Printed in the United States of America. Previous editions © 2017, 2014, and 2011. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 LWI/LWI 21 20 19 18 ISBN 978-1-260-18749-6 MHID 1-260-18749-7 Portfolio Manager: Noelle Bathurst Product Developer: Tobi Philips Marketing Manager: Harper Christopher Content Project Managers: Fran Simon/Jamie Koch Buyer: Laura Fuller Design: Egzon Shaqiri Content Licensing Specialists: Brianna Kirschbaum
  • 6. Cover Image: ©hxdyl/Shutterstock Compositor: MPS Limited 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 Bowerman, Bruce L., author. | Duckworth, William Maury, author. | Froelich, Amy Goodwin, author. Business statistics in practice / Bruce L. Bowerman, Miami University, William M. Duckworth, Creighton University, Amy Froelich, Iowa State University. Ninth Edition. | Dubuque : McGraw-Hill Education, [2019] | Revised edition of Business statistics in practice, [2017] LCCN 2018012294 | ISBN 9781260187496 (alk. paper) LCSH: Commercial statistics. | Statistics. LCC HF1017 .B654 2018 | DDC 519.5024/65—dc23 LC record available at https://lccn.loc.gov/2018012294 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
  • 7. Page iii The McGraw-Hill/Irwin Series in Operations and Decision Sciences SUPPLY CHAIN MANAGEMENT Benton Purchasing and Supply Chain Management Second Edition Burt, Petcavage, and Pinkerton Supply Management Eighth Edition Bowersox, Closs, Cooper, and Bowersox Supply Chain Logistics Management Fourth Edition Johnson and Flynn Purchasing and Supply Management Fifteenth Edition Simchi-Levi, Kaminsky, and Simchi-Levi Designing and Managing the Supply Chain: Concepts, Strategies, Case Studies Third Edition PROJECT MANAGEMENT Brown and Hyer Managing Projects: A Team-Based Approach
  • 8. First Edition Larson and Gray Project Management: The Managerial Process Seventh Edition SERVICE OPERATIONS MANAGEMENT Bordoloi, Fitzsimmons, and Fitzsimmons Service Management: Operations, Strategy, Information Technology Ninth Edition MANAGEMENT SCIENCE Hillier and Hillier Introduction to Management Science: A Modeling and Case Studies Approach with Spreadsheets Sixth Edition BUSINESS RESEARCH METHODS Schindler Business Research Methods Thirteenth Edition BUSINESS FORECASTING Keating and Wilson Forecasting and Predictive Analytics with ForecastXTM Seventh Edition LINEAR STATISTICS AND REGRESSION
  • 9. Kutner, Nachtsheim, and Neter Applied Linear Regression Models Fourth Edition BUSINESS SYSTEMS DYNAMICS Sterman Business Dynamics: Systems Thinking and Modeling for a Complex World First Edition OPERATIONS MANAGEMENT Cachon and Terwiesch Operations Management First Edition Cachon and Terwiesch Matching Supply with Demand: An Introduction to Operations Management Fourth Edition Jacobs and Chase Operations and Supply Chain Management Fifteenth Edition Jacobs and Chase Operations and Supply Chain Management: The Core Fourth Edition Schroeder and Goldstein Operations Management in the Supply Chain: Decisions and Cases Seventh Edition
  • 10. Stevenson Operations Management Thirteenth Edition Swink, Melnyk, Hartley, and Cooper Managing Operations Across the Supply Chain Third Edition BUSINESS MATH Slater and Wittry Practical Business Math Procedures Twelfth Edition Slater and Wittry Math for Business and Finance: An Algebraic Approach Second Edition BUSINESS STATISTICS Bowerman, et. al. Business Statistics and Analytics in Practice Ninth Edition Bowerman, O’Connell, Murphree, and Orris Essentials of Business Statistics Fifth Edition Doane and Seward Applied Statistics in Business and Economics Sixth Edition Doane and Seward
  • 11. Essential Statistics in Business and Economics Second Edition Jaggia and Kelly Business Statistics: Communicating with Numbers Third Edition Jaggia and Kelly Essentials of Business Statistics: Communicating with Numbers First Edition Lind, Marchal, and Wathen Basic Statistics for Business and Economics Ninth Edition Lind, Marchal, and Wathen Statistical Techniques in Business and Economics Seventeenth Edition McGuckian Connect Master: Business Statistics
  • 12. Page iv ABOUT THE AUTHORS Bruce L. Bowerman Bruce L. Bowerman is emeritus professor of information systems and analytics at Miami University in Oxford, Ohio. He received his Ph.D. degree in statistics from Iowa State University in 1974, and he has over 40 years of experience teaching basic statistics, regression analysis, time series forecasting, survey sampling, and design of experiments to both undergraduate and graduate students. In 1987 Professor Bowerman received an Outstanding Teaching award from the Miami University senior class, and in 1992 he received an Effective Educator award from the Richard T. Farmer School of Business Administration. Together with Richard T. O’Connell, Professor Bowerman has written 25 textbooks. These include Forecasting, Time Series, and Regression: An Applied Approach (also coauthored with Anne B. Koehler); Linear Statistical Models: An Applied Approach; Regression Analysis: Unified Concepts, Practical Applications, and Computer Implementation (also coauthored with Emily S. Murphree); and Experimental Design: Unified Concepts, Practical Applications, and Computer
  • 13. Implementation (also coauthored with Emily S. Murphree). The first edition of Forecasting and Time Series earned an Outstanding Academic Book award from Choice magazine. Professor Bowerman has also published a number of articles in applied stochastic process, time series forecasting, and statistical education. In his spare time, Professor Bowerman enjoys watching movies and sports, playing tennis, and designing houses. Anne Drougas Anne M. Drougas is a Professor of Finance and Quantitative Methods at Dominican University in River Forest, Illinois. Over the course of her academic career, she has received three teaching awards and has developed and taught online and hybrid business statistics and finance courses. Her research is primarily in the areas of corporate finance, simulation, and business analytics with publications in a number of journals including the Journal of Financial Education and Journal of Applied Business and Economics. She spends her spare time with her family and serving on the board of directors for Hephzibah House, a social service agency for children in Oak Park, Illinois.
  • 14. William Duckworth William M. Duckworth specializes in statistics education and business applications of statistics. His professional affiliations have included the American Statistical Association (ASA), the International Association for Statistical Education (IASE), and the Decision Sciences Institute (DSI). Dr. Duckworth was also a member of the Undergraduate Statistics Education Initiative (USEI), which developed curriculum guidelines for undergraduate programs in statistical science that were officially adopted by the ASA. Dr. Duckworth has published research papers, been an invited speaker at professional meetings, and taught company training workshops, in addition to providing consulting and expert witness services to a variety of companies. During his tenure in the Department of Statistics at Iowa State University, his main responsibility was coordinating, teaching, and improving introductory business statistics courses. Dr. Duckworth currently teaches business analytics to both undergraduate and graduate students in the Heider College of Business at Creighton University.
  • 15. Page v Amy Froelich Amy G. Froelich received her Ph.D. in Statistics from the University of Illinois, Urbana-Champaign, and currently is Associate Professor and Director of Undergraduate Education in the Department of Statistics at Iowa State University. A specialist in undergraduate statistics education, she has taught over 2,700 students at Iowa State in the last 18 years, primarily in introductory statistics, probability and mathematical statistics, and categorical data analysis. Her research in statistics education and psychometrics and educational measurement has appeared in The American Statistician, the Journal of Statistics Education, Teaching Statistics, and the Journal of Educational Measurement, and she and her colleagues have received research funding from the National Science Foundation, the U.S. Department of Agriculture, and the U.S. Department of Education. Dr. Froelich has received several teaching and advising awards at Iowa State University and was the 2010 recipient of the Waller Education Award from the American Statistical Association. When not working, she enjoys reading, spending time with her family, and supporting her daughters’ extracurricular activities. Ruth Hummel Ruth M. Hummel is an Academic Ambassador with JMP, a division of SAS specializing in desktop software for dynamic data visualization and analysis. As a technical advocate for the use of JMP® in academic settings, she supports professors and instructors who use JMP for teaching and research. She has been teaching and consulting since 2002, when she started her career as a high school math teacher. She has taught high school,
  • 16. undergraduate, and graduate courses in mathematics and statistics, and directed statistical research and analysis in a variety of fields. Ruth holds a Ph.D. in statistics from the Pennsylvania State University. Kyle Moninger Kyle B. Moninger instructs the Quantitative Business Curriculum at Bowling Green State University in Bowling Green, Ohio. He teaches and plans undergraduate courses in statistics and business calculus, serves on the Quantitative Business Curriculum committee, and supervises the college’s math and statistics tutoring center. Kyle has been a visiting instructor three times at Tianjin Polytechnic University in Tianjin, China, and was previously a data scientist at Owens Corning in Toledo, Ohio, where he designed and implemented a corporate training program on business intelligence and analytics. Pat Schur Patrick J. Schur is a Senior Clinical Professor in the Department of Information Systems and Analytics in the Farmer School of Business at Miami University in Oxford, Ohio. He received
  • 17. his master’s degree in statistics from Purdue University. He has been at Miami University for 11 years, teaching introductory statistics courses and advanced statistics courses including regression modeling, time series modeling, design of experiments, and statistical process control. Before joining Miami University, he worked at Procter & Gamble as a statistical consultant and also worked with multiple startup companies cutting across multiple industries.
  • 18. Page vi AUTHORS’ PREVIEW Business Statistics and Analytics in Practice, Ninth Edition, provides a unique and flexible framework for teaching the introductory course in business statistics. This framework consists of A complete presentation of traditional business statistics, with improved discussions of introductory concepts, probability modeling, classical statistical inference (including a much clearer explanation of hypothesis testing), and regression and time series modeling. A complete presentation of business analytics, with topic coverage in six optional sections and two optional chapters: a section in Chapter 1 introducing analytics, five sections in Chapters 2 and 3 discussing descriptive analytics, and Chapters 5 and 16 discussing predictive analytics. Continuing case studies that facilitate student learning by presenting new concepts in the context of familiar situations. Business improvement conclusions—highlighted in yellow and designated by icons BI in the page margins—that explicitly show how statistical analysis leads to practical business decisions. Many new exercises.
  • 19. Use of Excel (including the Excel add-in MegaStat), Minitab, and JMP to carry out traditional statistical analysis. Use of JMP (and Excel and Minitab where possible) to carry out descriptive and predictive analytics. We now discuss how these features are implemented in the book’s 20 chapters. Chapters 1, 2, and 3: Introductory concepts. Graphical and numerical descriptive methods. In an improved and simpler Chapter 1 we discuss data, variables, populations, and how to select random and other types of samples. Three case studies—The Cell Phone Case, The Marketing Research Case, and The Car Mileage Case—are used to illustrate sampling and how samples can be used to make statistical inferences. In Chapters 2 and 3 we begin to formally discuss the statistical analysis used in making statistical inferences. For example, in Chapter 2 (graphical descriptive methods) we show how to construct a histogram of the car mileages that were sampled in The Car Mileage Case of Chapter 1. In Chapter 3 (numerical descriptive methods) we then use this histogram to help explain the Empirical Rule. As illustrated in Figure 3.15, this rule gives tolerance intervals providing estimates of the “lowest” and “highest” mileages that a new midsize car model should be expected to get in combined city and highway driving.
  • 20. Page vii Chapters 1, 2, and 3: Six optional sections introducing business analytics and data mining and discussing descriptive analytics. In an optional section of Chapter 1 The Disney Parks Case introduces how business analytics and data mining are used to analyze big data. This case is then used in an optional section of Chapter 2 to help begin the book’s discussion of descriptive analytics. Here, the optional section of Chapter 2 discusses what we call graphical descriptive analytics, and four optional sections in Chapter 3 (Part 2 of Chapter 3) discuss what we call numerical descriptive analytics. Included in the discussion of graphical descriptive analytics are gauges and dashboards (see Figure 2.35), bullet graphs and treemaps (see the Disney examples in Figures 2.36 and 2.37), and sparklines and data drill-down graphics. Included in the discussion of numerical descriptive analytics are association rules (see Figure 3.25), text mining (see Figure 3.27), hierarchical and k-means cluster analysis (see Figures 3.38 and 3.40), multidimensional scaling (which is part of the cluster analysis section), and factor analysis.
  • 23. Page viii We believe that an early introduction to descriptive analytics will make statistics seem more useful and relevant from the beginning and thus motivate students to be more interested in the entire course. However, our presentation gives instructors various choices. This is because, after covering the optional introduction to business analytics in Chapter 1, the five optional sections on descriptive analytics in Chapters 2 and 3 can be covered in any order without loss of continuity. Therefore, the instructor can choose which of the six optional business analytics sections to cover early, as part of the main flow of Chapters 1–3, and which to discuss later—perhaps with the predictive analytics discussed in Chapters 5 and 16. For courses with limited time to spend on descriptive analytics, we might recommend covering graphical descriptive analytics, association rules, and text mining. These topics are both very useful and easy to understand. Chapters 4 and 5: Probability and probability modeling. Predictive analytics I (optional). Chapter 4 discusses probability and probability modeling by using motivating examples—The
  • 24. Page ix Crystal Cable Case and a real-world example of gender discrimination at a pharmaceutical company—to illustrate the probability rules. Optional Chapter 5 then uses the probability concepts of Chapter 4 and the descriptive statistics of Chapters 2 and 3 to discuss four predictive analytics: classification trees (see Figure 5.1), regression trees (see Figure 5.17). k-nearest neighbors (see Figure 5.28), and naive Bayes’ classification (see Figure 5.36). These predictive analytics are called nonparametric predictive analytics and differ from the parametric predictive analytics discussed in Chapter 16. Parametric predictive analytics make predictions by using parametric equations that are evaluated by using the statistical inference techniques of Chapters 6 through 15. Nonparametric predictive analytics make predictions without using such equations and can be understood (from an applied standpoint) with a background of only descriptive statistics and probability. Chapters 5 and 16 are independent of each other and of the descriptive analytics sections in Chapters 2 and 3. Therefore, the instructor has the option to try to motivate student interest by covering Chapter 5 early, in the main flow of the course, or wait to cover Chapter 5 until later, perhaps with (before or after) the parametric predictive analytics in Chapter 16. For courses with limited time to spend on nonparametric predictive analytics, we might suggest covering just classification trees and regression trees.
  • 26. Chapters 6–9: Discrete and continuous probability distributions. Sampling distributions and confidence intervals. Chapters 6 and 7 give discussions of discrete and continuous probability distributions (models) and feature practical examples illustrating the “rare event approach” to making a statistical inference. In Chapter 8, The Car Mileage Case is used to introduce sampling distributions and motivate the Central Limit Theorem (see Figures 8.1, 8.3, and 8.5). In Chapter 9, the automaker in The Car Mileage Case uses a confidence interval procedure specified by the Environmental Protection Agency (EPA) to find the EPA estimate of a new midsize model’s true mean mileage and determine if the new midsize model deserves a federal tax credit (see Figure 9.2).
  • 29. Page x Chapters 10–13: Hypothesis testing. Two-sample procedures. Experimental design and analysis of variance. Chi-square tests. Chapter 10 discusses hypothesis testing and begins with a new section on formulating statistical hypotheses and the meanings of Type I and Type II errors. Three case studies—The Trash Bag Case, The e-Billing Case, and The Valentine’s Day Chocolate Case—are then used in the next section to give a more unified and clearer discussion of the critical value rule and p-value approaches to performing a z test about the population mean. Specifically, for each type of alternative hypothesis, this discussion first illustrates the appropriate critical value rule in a graphical figure and then, in the same graphical figure, shows the appropriate p-value and explains why it is the more informative way to carry out the hypothesis test. For example, the above Figures 10.1 and 10.2 are presented side-by-side in the text and illustrate testing a “greater than” alternative hypothesis in The Trash Bag Case. These figures show the different a’s specified by two television networks evaluating a trash bag advertising claim, the different critical values that would have table looked up by an hypothesis tester using the critical value rule approach, and have the p-value immediately tells the hypothesis tester the results of the hypothesis test for any and all values of a. Similarly, Figures 10.3 and 10.4 illustrate the appropriate critical
  • 30. value rules and p-values for testing “less than” and “not equal to” alternative hypotheses.
  • 31. In addition, as the case studies are used to illustrate hypothesis testing, the z test about a population mean summary box and the five-step hypothesis testing procedure shown in the upper portion of the next page are developed. Here, although the true value of the population standard deviation is rarely known, the z test about a population mean summary box serves as an easily modifiable model for the book’s other more practically useful hypothesis testing summary boxes—for example, for the t test about a population mean summary box and the z test about a population proportion summary box shown in the lower portion of the next page. Moreover, the five-step hypothesis testing procedure emphasizes that to successfully use a hypothesis testing summary box, we simply identify the alternative hypothesis being tested and then
  • 32. Page xi looking the summary box for the appropriate critical value rule and/or p-value.
  • 33. Page xii Hypothesis testing summary boxes are featured throughout Chapter 10, Chapter 11 (two-sample procedures), Chapter 12 (one-way, randomized block, and two-way analysis of variance), Chapter 13 (chi-square tests of goodness of fit and independence), and the remainder of the book. Furthermore, emphasis is placed throughout on assessing practical importance after testing for statistical significance. For example, as illustrated in Figure 12.12, if an F test finds a significant factor in an analysis of variance, we assess practical importance by finding point estimates of and confidence intervals for the differences in the effects of the different levels of the factor. As another example (see Figure 13.2), if a chi-square test rejects the hypothesis of independence between two variables, we assess practical importance by using the contingency table upon which the chi-square test is based to analyze the nature of the dependence between the variables.
  • 34. Chapters 14–17: Simple linear regression. Multiple regression and model building. Predictive analytics II (optional). Time series forecasting and index numbers. Chapter 14 discusses simple linear regression and illustrates the results of a simple linear regression analysis by using The Tastee Sub Shop (revenue prediction) Case. This same case is then used by the first seven sections of Chapter 15 (multiple regression and model building) to illustrate the results of a basic multiple regression analysis (see Figure 15.4). The last four sections of Chapter 15 continue the regression discussion by presenting four modeling topics that can be covered in any order without loss of continuity: dummy variables (including a discussion of interaction);
  • 35. Page xiii quadratic variables and quantitative interaction variables; model building and the effects of multicollinearity (including model building for big data—see Figure 15.31); and residual analysis and diagnosing outlying and influential observations.
  • 36. With the regression concepts of Chapters 14 and 15 as background, optional Chapter 16 extends these concepts and discusses three parametric predictive analytics: logistic regression (see Figure 16.5), linear discriminate analysis (see Figure 16.12), and neural networks (see Figures 16.17 and 16.19). Moreover, Chapter 17 extends the regression concepts in a different way and discusses time series forecasting methods, including an expanded presentation of exponential smoothing and a new and fuller (but understandable) presentation of the Box–Jenkins methodology.
  • 38. Note that although we have used the term predictive analytics to refer only to the prediction methods of Chapters 5 and 16, the regression and time series methods of Chapters 14, 15, and 17 all predict (using a parametric equation) values of a response variable and thus are all (parametric) predictive analytics. We have used the term predictive analytics to refer only to the predictive methods of Chapters 5 and 16 because these methods are (for the most part) more modern methods that have been found to be particularly successful in analyzing big data. Together, the more classical parametric predictive analytics of Chapters 14, 15, and 17, along with the more modern nonparametric and parametric predictive analytics of Chapters 5 and 16 and the descriptive analytics of Chapters 2 and 3, make up a full second statistics course in business analytics. Chapters 18–20: Concluding chapters. The book concludes with Chapters 18 (nonparametric statistics), Chapter 19 (decision theory), and website Chapter 20 (process improvement using control charts).
  • 39. Page xiv Students—study more efficiently, retain more and achieve better outcomes. Instructors— focus on what you love— teaching. SUCCESSFUL SEMESTERS INCLUDE CONNECT For Instructors You’re in the driver’s seat. Want to build your own course? No problem. Prefer to use our turnkey, prebuilt course? Easy. Want to make changes throughout the semester? Sure. And you’ll save time with Connect’s auto- grading too. They’ll thank you for it.
  • 40. Adaptive study resources like SmartBook® help your students be better prepared in less time. You can transform your class time from dull definitions to dynamic debates. Hear from your peers about the benefits of Connect at www.mheducation.com/highered/connect Make it simple, make it affordable. Connect makes it easy with seamless integration using any of the major Learning Management Systems—Blackboard®, Canvas, and D2L, among others—to let you organize your course in one convenient location. Give your students access to digital materials at a discount with our inclusive access program. Ask your McGraw-Hill representative for more information. Solutions for your challenges.
  • 41. Page xv A product isn’t a solution. Real solutions are affordable, reliable, and come with training and ongoing support when you need it and how you want it. Our Customer Experience Group can also help you troubleshoot tech problems—although Connect’s 99% uptime means you might not need to call them. See for yourself at status.mheducation.com For Students Effective, efficient studying. Connect helps you be more productive with your study time and get better grades using tools like SmartBook, which highlights key concepts and creates a personalized study plan. Connect sets you up for success, so you walk into class with confidence and walk out with better grades.
  • 42. Another Random Scribd Document with Unrelated Content
  • 43. He thought better of this, however, and continued to creep forward carefully and silently. "If he hits you again," he said, speaking to Hal but muttering the words to himself, "it can't be helped; but we'll repay those blows with interest." Hal, standing erect before his captors, did not flinch as Lieutenant Steinz drew back his arm for another blow. But his eyes flashed dangerously. "You'll be sorry for this, my friends," he said quietly. "Threats, eh?" sneered the German. "You're in no position to threaten, pig." "Perhaps not," admitted Hal, "but just the same I am warning you." There was something so menacing in the lad's voice, that for a moment the German hesitated; but for a moment only, then he drew back his arm and struck. Once more Hal staggered under the blow, but he did not flinch. The German raised his arm and would have struck again but for a sudden interruption. When Chester saw the German strike Hal a second time, it was more than his blood could stand. He forgot, for the moment, his mission, that his first duty was to pass beyond the German camp. He threw caution to the winds. With a wild cry he leaped to his feet and dashed forward, a revolver levelled in each hand. Startled, the Germans turned to face their new foe. One look at Chester's angry features and they recoiled involuntarily.
  • 44. At the same moment Chester fired—both weapons at once. Two of the enemy toppled over in their tracks. Now Hal had a quick mind. At Chester's first cry he knew what was up and he grew instantly alert, ready to take advantage of the first opportunity that presented itself. The opportunity was not long coming. Lieutenant Steinz, turning to get a view of Chester, for a moment left Hal unguarded. In that instant Hal sprang. Both hands he locked about the German's throat, and squeezed with all his strength. In vain the Teuton squirmed, struck and kicked. Suddenly Hal released his right hand and drove it into the man's face. At the same moment his left hand shot out and seized the German's revolver. Then he stepped quickly back, levelled the weapon and fired. "Come on, Chester!" he shouted. Chester needed no urging. In a few quick strides he was at Hal's side. "Let's get out of here," he cried. "It's getting too warm." Together the lads dashed toward the trench. A cry of alarm went up from the Germans behind. "Shoot them!" cried a voice that Hal recognized as that of the German colonel. "Zig-zag, Chester!" cried Hal, and suited the action to the word. Chester followed his chum's example and the first volley from behind failed to find a mark. By this time the lads were at the edge of the trench. "Up and over with you, quick!" cried Chester.
  • 45. Hal leaped to the top of the trench and toppled to the ground beyond even as half a score of bullets sang across the spot where his head had been a moment before. Chester also sprang for the top of the trench. But he had leaped too soon, and instead of reaching the top he fell short, and dropped down inside the trench again. Germans were almost upon him when he regained his feet. Chester realized that a second leap was out of the question at the minute, so guns in hand he turned and faced his foes. "Crack! Crack! Crack! Crack!" His automatics spoke angrily and all four bullets found human targets. Hal, meanwhile, safely over the trench, looked around for Chester. When he failed to see him he realized on the instant what had happened. "What shall I do?" he asked himself. "Duty says to hurry to a place of safety, but friendship says help Chester." He wasted little time in thought. He scrambled back to the top of the earthen embankment and took in the sight about him. There Chester stood at bay, his automatics held in steady hands. Hal drew his own weapons. "Jump up here quick, Chester!" he called. "I'll cover you." "Don't bother about me," Chester called back. "Get away from here. Remember you must get through. I'll hold 'em off." "Don't be a fool," shouted Hal, discharging his revolver at a big German who was about to shoot Chester down with his rifle. "Come up here."
  • 46. Chester paid no further heed to his chum. Hal gritted his teeth, dropped one revolver in his pocket, and reaching down grasped Chester by the shoulder. "Come on," he called. Chester shook off his chum's hand. "Let me alone." he shouted angrily. "I'll get a few of these boches before they down me." His revolvers spoke as he talked, and two Germans dropped. Meanwhile bullets were striking on all sides of the two lads, and it seemed a miracle that they were not touched. Hal considered the situation in a flash. "There's one chance," he said. Deliberately he sheathed his other revolver, thus leaving himself unarmed in the face of his foes. Then, bracing himself as best he could on the embankment, he reached down and seized Chester by both shoulders. Putting forth all his strength, Hal heaved mightily, and drew his chum to the top of the embankment with him. There he released him and drew his revolvers again. Came a cry of rage from inside the trench as the Germans saw their prey about to escape. Two men dropped on their knees and sighted their rifles carefully. But before they could fire Hal had accounted for one and Chester for the other. Again a howl of rage went up from the German trench. "Kill them! Kill them!" screamed the German colonel. "What a lot of dunderheads! Can't you shoot?"
  • 47. He seized a revolver from a young officer close by and dashed forward himself. Hal, in the act of tumbling from the embankment, smiled slightly and faced the colonel, unmindful of all other dangers. "So you're the man responsible for those blows a moment ago, eh?" he muttered. "Well, you'll never do it again. Take that!" He sighted carefully and fired. The German colonel staggered in his onward rush, reeled crazily, threw up his arms, casting his revolver a dozen paces away, then fell to the ground. "So much for you," Hal muttered. "You won't bully another American, I'll bet on that." "Come on," said Chester, who had stuck close to his chum all the time. "It's too warm here. Let's move." "Right. Suits me," said Hal quietly. "Down we go, then," said Chester. He rolled rather than leaped to the ground on the outside of the trench. Hal did likewise. Both lads were slightly bruised by this method of descent, but they were not injured seriously. They scrambled to their feet. "Now, let's see you run!" shouted Hal to Chester. They ran. CHAPTER XIV THE CLOSING OF THE NET
  • 48. Bullets flew thick and fast after the two lads as they clashed for the shelter of the American lines beyond. Fortunately, however, none touched them. The Germans, it appeared, were so bewildered by the suddenness of Chester's appearance, single-handed attack and the flight of the two chums that followed, that they forgot all about their searchlights, which would have made it possible for them to have picked off fugitives at will; or else they had no searchlights in that section of the field. Zig-zagging from right to left, the lads ran at top speed. For a time bullets whistled unpleasantly close, but soon they became few and far between. Hal slowed down. Chester followed his example. "Whew!" said Chester. "Pretty close, but we're safe enough now, I guess." "By George! I hope so," declared Hal. "But there is just one job that I would have liked to complete before getting away from there." "What's that?" demanded Chester. "I would like to have let a little lead into that big German lieutenant who battered me up with his fist." "Don't blame you," said Chester. "I'd like a shot at him myself." "Well," said Hal, "I left my mark on his throat, and that's some satisfaction. Also, I disposed of the colonel who was responsible, and there's more satisfaction there, too." "I saw you," replied Chester. "It was a neat shot." "Well," said Hal, "we've done something that a couple of other couriers sent out by General Rhodes failed to accomplish—we have
  • 49. passed through the German lines. The general's plans will not go wrong if we can help it." "Right," agreed Chester. "And I figure that the sooner we report to General Lejeune the better." "Correct as usual. But I don't know that I care to try and repeat the feat of getting through. Besides, we have General Rhodes' permission to stay here until after the big battle if we like." "And I vote that we stay," said Chester. "Think I'll cast my own ballot that way," declared Hal. "We'll stick, unless something turns up to change our minds." "Now for the American lines, then," said Chester. They hurried on through the darkness and directly the dim outline of the American trenches loomed up ahead. "Here we are," said Hal. "Now to get over." As they would have climbed up, however, the figure of a soldier appeared above them. He saw them instantly and levelling his rifle cried: "Halt! Who goes there?" "Friends," said Hal briefly. "Advance, friends, and be recognized," said the sentinel. Hal and Chester obeyed and the sentinel scanned them closely. "You look all right," he growled at last, "but I'm not sure of you." "Do you think we'd be coming in here if we didn't belong?" demanded Chester. "I don't know about that; but I can't see any good reason why you should be prowling around out in No Man's Land if you are not bent on mischief."
  • 50. "Don't be absurd, man," said Hal. "We come from General Rhodes with a message for General Lejeune." "A likely story," said the sentry. "How'd you get through the Germans?" "Walking and running," said Chester. "But are you going to keep us standing here all night? I tell you we bear an important message from General Rhodes." "What'd you both come for?" the sentry wanted to know. "That," said Chester, thoroughly exasperated, "is none of your business, my man! Will you call the sergeant of the guard, or shall I?" "Oh, I'll call him," said the sentry, "but I'll tell you right now I don't think it will do you any good. Kindly step up here, will you?" Hal and Chester did so. Then, for the first time, the sentry saw that they were officers in the American army. He looked flabbergasted. "I—I—I beg pardon, gentlemen," he said. "I didn't know you were officers. Why didn't you tell me?" "You didn't give us a chance," said Hal shortly. "Kindly summon the sergeant of the guard." The sentry argued no longer. He raised his voice in a shout that brought the sergeant of the guard on the dead run. "What's the matter with you, you bonehead?" demanded the sergeant as he came lumbering forward. "Want to arouse the whole camp?" "It's all right, sergeant," said Hal. "He only did as ordered. We have come from General Rhodes with an important message for General Lejeune. Will you direct us to his quarters?"
  • 51. The sergeant saluted stiffly. "Follow me, sirs," he said briefly. Five minutes walk brought the three to the headquarters of the commander of the Second American division. There the lads were accosted by a member of the general's staff, Colonel O'Shea. "We desire to see the general at once on a very urgent matter," said Hal. Colonel O'Shea scowled. "The general left orders that he was not to be disturbed unless upon a very important matter," he replied. "But this is urgent," said Chester. "We are instructed by General Rhodes to deliver the message at once." "But how am I to know the matter is so urgent?" asked the colonel. "Because I say so, sir," said Hal quietly. "I am not in the habit of lying, nor of having my word doubted." "Oh, is that so," said the colonel, though somewhat taken aback. "Well, I'm not sure the general will care to be disturbed. You may deliver your message, and then I shall consider whether your business is of such importance as to justify waking the general." "We were not instructed to deliver our message to you, sir," said Hal simply. "I have to request again that we be given immediate audience of General Lejeune." The colonel hesitated. Apparently he was on the point of refusing to arouse the general, but he thought better of it, shrugged his shoulders and turned away. "One moment," he said brusquely.
  • 52. He returned a moment later, however, followed by a second figure, attired in a suit of pajamas and rubbing sleepy eyes. "General Lejeune?" asked Hal. "Yes," was the sharp reply. "What is it?" "We bear a message from General Rhodes, sir," said Hal. "Well, let's have it, let's have it," exclaimed the general. "I've got to get back to bed and get some sleep." "First, sir," said Hal, "I must explain that we came through the German lines where two or three other couriers lost their lives. General Rhodes wishes you to understand, sir, that the success of the campaign depends upon your acting in accordance with his message." "I have no doubt of it," said General Lejeune. "I have been unable, since the German wedge was driven between our forces, to get into communication with General Rhodes or other divisional commanders. I am isolated here, but at the same time I consider my position impregnable, so I am standing pat." Hal and Chester bowed in understanding of the general's explanation, and the commander of the Second division added: "Come, sirs, what is the message you bring?" "General Rhodes' message, sir," said Hal, "is that he requests you to attack the enemy before Sedan in full force on the evening of November 6, the attack to begin precisely at 6 o'clock." "Very well," said General Lejeune, "and just what is at the bottom of this plan—what is to be gained by it?" "That I do not know, sir," said Hal. "General Rhodes simply asked us to carry that message. He said that the success of the campaign against Sedan depended upon you doing your part."
  • 53. "Well, I'll do it, never fear," said General Lejeune. "I've got one of the best fighting units in France, and there's not a man in it who's not dead anxious to get another chance at the Huns. You may take back word to General Rhodes for me, that I shall act in accordance with his wishes." "If it is all the same to you, sir," said Chester with a slight smile, "we're not going back—not, at least, until the battle of Sedan is over." "How's that? How's that?" asked the general in some surprise. "Why, sir," said Chester, "General Rhodes gave us permission to stay with you if we deemed it imprudent to try and pierce the enemy's lines again." "And you think it would be imprudent?" asked General Lejeune with a slight smile. "In view of the trouble we had getting here, yes, sir," replied Chester. "Very well, then," said the general, "you may remain with us. Colonel O'Shea, will you find quarters for these gentlemen? By the way, I did not catch your names." "Crawford, sir," said Chester. "Paine, sir," said Hal. "Very well," General Lejeune continued, "Colonel O'Shea, will you please see that Major Paine and Major Crawford are provided with suitable quarters? And will you both report to me at 8 o'clock in the morning, gentlemen? I may have need of you. The Second division is an hospitable unit, but you'll find that guests are required to work as well as home folks." "We shall be more than glad to do our parts, sir," said Hal.
  • 54. "Very well. Now you have kept me out of bed long enough. I'll leave you both to the good graces of Colonel O'Shea, and if he doesn't find suitable quarters for you, you let me know and I'll have him court-martialed." With this, and a smile on his face, the good-natured commander took his leave. "By George!" said Hal, as the lads followed Colonel O'Shea from the general's quarters, "he's the most lively commander I ever did see." "Full of 'pep' eh?" said Chester with a laugh. "Yes," Hal agreed, "and I'll bet he's full of the same old 'pep' when it comes down to business." And Hal was right. CHAPTER XV THE CAPTURE OF SEDAN The American advance against Sedan was in full blast. All night the fighting had raged. Promptly at 6 o'clock on the evening of November 6 General Lejeune had hurled the Second division forward in accordance with the plans outlined by General Rhodes of the Forty-second. Apparently the Germans had anticipated the attack, for they were braced to receive it when the first Yankee troops began to move. The enemy stood firm—and was continuing to stand firm almost twelve hours after the assault was launched.
  • 55. There was a slight chill in the early November air as it grew light. The air was filled with shrieking shells and shrapnel. Rifle and machine-gun fire rose even above the noise of the field and siege guns. Shrill whistles punctuated intervals of seeming silence as American officers gave orders to their men. In the midst of battle, whistles are depended upon mainly for signals—also there are signals given with the hands. The confusion is usually too great to permit verbal orders being understood. At the same time that General Lejeune attacked the enemy, General Rhodes, to the south, also had advanced. But the enemy was holding stubbornly in that section of the field also, and at 6 o'clock on the morning of November 7 the American forces had made only slight progress. However, they were still hammering hard at the German lines. With a gallantry not exceeded in the annals of the war, the Second division kept at its task. When one enemy machine-gun nest was captured, they found themselves targets for others, whose gunners, discovered, had withheld their fire until the moment when it would be the most effective. Another grand assault was ordered by General Lejeune. The Germans made a determined resistance. They put in fresh troops and subjected the American lines to a terrific artillery bombardment of high explosives and gas shells. Directly in the path of the advancing Americans was a large wood. Although the wood was not yet cleared of the enemy, the American line here was farther advanced. Many prisoners had been taken. A third attack resulted in the capture of still more prisoners and many machine-guns. In the meantime the Ninth infantry, on the
  • 56. right of that part of the field where Hal and Chester found themselves, had advanced its position to the northern edge of the Bois de la Jardin and was digging in to beat off a possible counter- attack. In fact, the entire Third brigade, assisted by a battalion of the Second engineers, was strengthening its lines as well as possible under heavy enemy machine-gun and artillery fire. The defensive part played by this brigade was very difficult. Its losses were heavy as a result of enemy shell fire and gas bombardments, to which the Third brigade could not at the moment reply. Its duty now was to hold its lines. Its present action was confined to a rifle and machine-gun duel with the enemy. To the south, the First brigade also was hotly engaged. It had advanced in the face of a terrible artillery and machine-gun fire until at hand grips with the foe. Then ensued one of the fiercest struggles of the war. As in other encounters, the Germans proved no match for the Yankees at hand-to-hand fighting. They resisted desperately, but gradually were driven back. The Americans, with wild cheers, pursued them closely. General Lejeune's center, composed of the Second brigade, with an additional battalion or two of artillery, also was meeting with greater success than the Third brigade, which, for the moment, had been checked. The advance was pushed with desperate energy, and the Germans could not hold their ground in the face of the withering American fire. The German center faltered, then broke. Taking advantage of this success, General Lejeune pushed Brigadier General Abernathy's Second division into the breach.
  • 57. Immediately, also, he ordered the First brigade forward in an effort to break through to the south, while orders were rushed to the hard- pressed Third brigade to make a final effort. The task of the Third brigade was easier now. Bereft of its supports, the German center was obliged to yield ground to the Third brigade or risk being cut off and surrounded. The Germans gave ground slowly. To the south, the First brigade also began to drive the foe more swiftly. It appeared for a moment that the Germans would suffer a rout. Under the direction of their officers, however, they braced perhaps half a mile farther back, and again showed a determined front. Trenches dug by the Americans were abandoned now as the Yankees poured forth in pursuit of the enemy. Not a man in the whole Second division who was not sure that the trenches would never be needed for defensive purposes. No one knew better the morale of the American troops than did the men themselves. Nevertheless, the advance slowed down in the face of the resistance being offered by the enemy. For a time it appeared that the fighting had reached a deadlock. The deciding touch to the battle was furnished by General Rhodes. Sweeping up from the south, the Fifth, Sixth and Seventh brigades of the Forty-second division bore off a trifle to the east and then turned north again, thus catching the enemy on the left flank. This maneuver, apparently, had not been anticipated by the enemy's general staff, for it took the Germans by surprise. True, they received warning in time to wheel machine-guns into position and to
  • 58. place big guns to rake the Americans as they dashed forward. But the warning had not been received in time to permit the general staff to alter its plan of defense, and for this reason proved the blow that broke the backbone of the enemy's resistance. The enemy, closely pressed by General Lejeune, had no time to make changes in his defensive plan necessitated by General Rhodes' sudden attack. Reinforcements could not be sent to check General Rhodes without weakening the front opposed to General Lejeune. General Schindler, after a hasty conference with his staff, ordered a retreat to the lines just before Sedan. The Germans fell back rapidly. Neither General Rhodes nor General Lejeune was content to rest with this advantage, but each decided to push on. During all this time, the enemy had been successful in keeping a wedge between the Second and Forty-second American divisions. General Schindler realized that if he hoped to extricate his men from the trap sprung by the Americans he must prevent a juncture of the Second and Forty-second at all hazards. Now, however, as the attack seemed on the verge of success, General Lejeune decided that the German wedge separating him from General Rhodes must be pierced. Accordingly, without permitting the advance to slacken elsewhere, he threw the First brigade against it. For perhaps fifteen minutes the fighting was fast and furious. In vain the Germans tried to stem the tide in khaki that rushed forward against them. General Schindler further weakened his center to rush reinforcements in order to retain the wedge intact.
  • 59. But it was no use. The Americans were not to be denied. They fought with the courage and desperation of lions. Little heed did they pay to the hail of machine-gun bullets that swept them as they advanced. Artillery and explosive shells failed to stop them. Rifle fire was no more effective. Suddenly from the German lines sallied a regiment of cavalry. The American infantry braced to receive the charge. At the same time Hal found himself before Colonel Taylor of the First brigade with dispatches from General Lejeune. He had just delivered them as the German cavalry sallied forth. "Great Scott! What a chance to take!" the lad muttered under his breath. "The Germans must be licked. This move can be for no other purpose than to give infantry time to withdraw." The American infantry stood firm as the German cavalry hurled itself upon them. Not an inch of ground did they give. Horses and men fell in heaps. Other chargers reeled back, throwing their riders beneath their hoofs. At the same time the Yankee infantry poured in a hail of rifle fire. The Germans retired a pace, reformed and charged again. The result was the same. Not an inch did the Americans give, and the execution in the enemy's ranks was fearful to behold. "I guess that will stop that," Hal told himself. He was right. When the enemy's cavalry withdrew a second time it did not reform for a third charge. Instead, it fell back upon its infantry and artillery supports, apparently fearing that the American infantry would pursue and annihilate it. "I thought so," said Hal.
  • 60. In the meantime, the German retirement in other parts of the field had become more rapid. The lines before Sedan were abandoned gradually and at last there was nothing to keep the Americans from entering the city save the cannonading of the German artillery from far to the rear of the town. But although the bulk of the German army had retired safely to the east of Sedan, fortune had not been so kind to the two brigades which had formed the wedge between the Second and Forty-second American divisions. When General Lejeune's men had pushed back the cavalry attack, General Rhodes, to the south, had gained an inkling of what was going on. Accordingly he had ordered an attack upon the hard- pressed foes. Caught thus between two fires, the Germans tried first to hold their ground, and, finding this could not be done, to retreat orderly. But they had delayed too long. Three regiments of the First brigade of General Lejeune's division had been hurried forward to cut off a movement, and the Germans, when they found flight blocked, became disheartened. In spite of the fact that they outnumbered the little force between them and the bulk of their army, thousands of men threw down their arms and surrendered. This forced the others to follow suit or be annihilated. Less than two hours later, with German shells still falling among them, American troops entered Sedan. And the French population, virtual prisoners for many months, received them with wild acclaim. It was a joyous day for the citizens, indeed.
  • 61. CHAPTER XVI AN UNEXPECTED HONOR "Sedan at last! This settles the war." It was Chester who spoke. "Right you are," replied Hal. "The poor old kaiser's goose is cooked. Even the most sanguine German can no longer hope for victory." "I think the kaiser gave up hope a long while ago," said Chester. "He—Hello, what's up now, I wonder?" He broke off suddenly and pointed to a horseman who came galloping into the town from the east, gesticulating excitedly as he rode along. Words that he shouted as he dashed forward seemed to create great excitement among the villagers, who, all day, had been parading the streets in celebration of the American occupation of the city. "Don't know," said Hal. "We'll try and get close enough to hear what he says." As the man drew close, the lads saw that he was a German cavalryman. It appeared strange to both boys that he was thus permitted to ride free, as the feelings of the villagers were very strong against the Germans. But it soon became apparent that the message he brought secured him immunity. "What's that he said?" asked Chester, with hand to his ear. "I didn't catch it," said Hal. "Here, get in front of him. We'll stop his wild ride."
  • 62. Chester needed no urging. The lads stepped directly in front of the galloping horse. Hal produced his revolvers. The rider checked his steed. Hal approached him. "Dismount," said the lad in German. The rider did so. "Now," said Hal, "what's all the excitement? You seem to have something on your mind. What is it?" "Haven't you heard the news?" demanded the rider. "I wouldn't be asking you if I had," said Hal. "What is it?" "The kaiser has abdicated!" Hal and Chester started back in pure amazement. "What!" they exclaimed in a single voice. "So I am informed," declared the German. "It is true that my information has not been substantiated, but I know enough of conditions in Germany to credit the report." "Well, you come with me," said Hal. "We'll take this matter to General Lejeune." The German accompanied them without objection. General Lejeune received the report with skepticism. "Nothing to it, in my opinion," he said. "It is true that conditions in Germany are fast approaching a crisis, but I believe this report is premature. However, I have no doubt that something like that will happen within the next thirty days. But what are you doing in our lines, man?" This last to the German soldier. "Well, I'm tired of fighting," was the soldier's reply. "I want to live to go home again some day. I've a family in Hamburg that will need me. I am content to remain a prisoner until the war is over."
  • 63. "And so you shall," said General Lejeune. "Whether your report is true or not, it has given me an interesting moment. Colonel O'Shea, will you turn this man over to the corporal of the guard?" The prisoner was led away. General Lejeune turned to Hal and Chester. "I am sorry to lose your services, gentlemen," he said, "but I have just been in communication with General Rhodes, and he wishes you to report to him at once." The lads saluted the commander of the Second division and left his quarters. Half an hour later they reported to General Rhodes as he rode into Sedan to establish his own quarters, as the Second division was soon to advance again. General Rhodes greeted the lads warmly. "I am certainly glad that you both came through safely," he said, after returning their salutes, "and I must say that I didn't expect it. You have been in luck. Now I have another important matter in hand." "We shall be glad to offer our services, sir," said Hal. General Rhodes smiled. "I've no doubt of it," he replied. "However, this mission is not likely to be so dangerous. Don't worry, though," he added, as the faces of the lads fell, "I believe I may safely promise you some interesting moments." "We're glad of that, sir," declared Chester. "I wonder," said General Rhodes, "whether you have heard of the reported upheaval in Germany?" "Yes, sir," said Hal. "Only a few moments ago we captured a man who declared the kaiser had abdicated."
  • 64. "That," said General Rhodes, "is probably untrue; however, I know that the kaiser has considered abdicating. In fact, his abdication is being urged by his military leaders—his erstwhile friends, Hindenburg and Ludendorff." "Can that be possible, sir?" asked Hal. "Yes, we have authentic information to that effect. I understand, too, Germany is preparing to ask Marshal Foch for an armistice preliminary to signing a declaration of peace." "By Jove, sir!" exclaimed Chester, carried away in spite of himself. General Rhodes smiled again. "It is good news," he said quietly. "Of course, I am not absolutely positive of that, but in view of recent German reverses I do not see how the enemy can do aught else." "Well, sir," said Chester, "we'll impose terms on them that will make their hair curl." For a third time General Rhodes smiled. "We won't be too severe," he said. "Remember, we are not German." "That's true, too, sir," said Chester. "But all the same, it should be done, if you ask me." "Perhaps," said General Rhodes. "Now, I suppose you are wondering why I called you here?" "Yes, sir," returned Hal. "Well," said General Rhodes, "I have been summoned to report to the commander-in-chief and I want a couple of officers to go with me who can be useful as well as ornamental." Both lads flushed.
  • 65. "I know that you drive an automobile exceedingly well, Major Paine," the general continued, "and for that reason I am selecting you as my chauffeur on this trip." "But I am afraid I shall not be so useful, sir," said Chester. "Well," said the general, "I am taking you along because I thought you'd like to go." "And so I would, sir," answered Chester. "It may be," General Rhodes continued, "that before our return we shall be present at a very momentous gathering." "You mean, sir—" asked Hal. General Rhodes nodded. "Exactly," he replied. "I mean that the commander-in-chief is summoning me for some purpose other than because he wants to see me. It would seem that matters have reached a point where something is likely to break at any minute." "By George! I hope so, sir," declared Chester. "I shall expect you to be ready in an hour," said General Rhodes ending the interview suddenly. "I shall have a car here at that time." Chester and Hal saluted and departed. "Now, this is what I call a regular mission," declared Hal, as they hurried to their quarters. "It is if it develops," replied Chester. "Something tells me it will develop," said Hal. "Let's hope so." The lads were back at General Rhodes' headquarters well within the time allowed them. A large army automobile stood without. "Guess this is our steed," said Hal. He was right.
  • 66. General Rhodes appeared a few moments later and took his seat. He motioned Chester to a place beside him. Hal took the wheel. "Where to, sir?" he asked of the general. "Rheims," was the reply. "The commander-in-chief is there now. You know the road, of course?" "Yes, sir." "Then you will take us there as speedily as possible." The machine shot forward with a lurch. Now if there was one thing Hal did better than anything else it was to drive an automobile. He was a fast though careful driver and his hands and nerves both were like steel when he clutched a wheel. He had been over the road before, and his excellent memory served him in good stead now. It was after 3 o'clock on the afternoon of November 7 when the automobile flashed into the outskirts of Rheims. Hal stopped the car long enough to inquire the way to General Pershing's headquarters, then moved forward again. "You are a good driver, Major," said General Rhodes, as he alighted and motioned both boys to follow him. "Thank you, sir," returned Hal. "I've had experience enough, sir, I should be, at all events." General Rhodes vouchsafed no reply, as he mounted the short flight of steps to General Pershing's offices, with Hal and Chester at his heels. Apparently his arrival was expected, for an orderly saluted and told him that he was to proceed to the commander-in-chief immediately.
  • 67. "You gentlemen stay here until I send for you, or return," he instructed the two lads. Hal and Chester stood stiffly at attention as he walked away. "We're in luck, if you ask me," said Chester after their commander had gone. "It would seem so," Hal agreed. "If anything happens, I'd like to be in at the finish." "So would I. We've been in the war from the first. It would be no more than right for us to see the finale." "Maybe we will," said Hal. "Here's hoping." They sat quietly for some time. Two hours later an orderly approached. "Major Paine! Major Crawford!" he said, "the commander-in- chief desires your presence at once. Kindly follow me." CHAPTER XVII STUBBS AGAIN General Pershing greeted the lads cordially. "Glad to see you again," he said. "General Rhodes informs me that you have been up to your old tricks and have again been cited for gallantry in action. However, it is no more than I would have expected of you." The lads bowed in response to this praise, but neither spoke. "It is fortunate that General Rhodes brought you with him," General Pershing continued. "Still, it may not be so fortunate for
  • 68. him, for I am about to deprive him of your services. I take it that you will survive the separation, though," and the commander-in- chief smiled. "We are always glad to serve in whatever way we may, sir," said Hal. "Good!" said General Pershing. "Then I shall avail myself of your services. Several hours ago I was in communication with Marshal Foch, who is now in Soissons. General Rhodes informs me that he has made you acquainted with the facts that seem to indicate an early cessation of hostilities, so I need not amplify here. Now, Marshal Foch, anticipating that Germany may really sue for peace, has asked my advice in the matter of armistice terms pending a final treaty of peace. These I have written out. As you will readily recognize, they are not to be trusted to careless hands. I have confidence in you, however, gentlemen, so I shall ask you to carry this paper to Marshal Foch." "We shall be glad to do it, sir," said Chester. "Very well. Then I intrust this paper to you, and I need not warn you to guard it carefully and keep the matter secret." General Pershing extended a document to Hal. The lad took it and put it carefully in his inside coat pocket. "It will be safe there, your excellency," he said quietly. "Now," said the commander-in-chief, "it is my wish that that paper be placed in Marshal Foch's hands at the earliest possible moment. The car in which you drove General Rhodes is at your disposal." "We shall make all possible haste, sir," said Chester. Both lads saluted their commander and left the room.
  • 69. "By Jove!" said Hal, as he sprang into the car, "there is no use talking, important developments are pending. It begins to look like peace to me." "And to me," Chester agreed. "Well, the sooner the better. Four years of war is enough to satisfy Mars himself." Soon the car was speeding westward. It was a long drive to Soissons and it was after nightfall when Hal saw the lights of the city in the distance. A few moments later they entered the town. Hal had no difficulty ascertaining where Marshal Foch made his headquarters and he drove there at once. A few words to a guard before the building brought forth a member of Marshal Foch's staff and the lads explained their mission to him briefly. "You are expected," said the French officer. "Follow me." He led the way into the house and through a long hall. At the far end he tapped on a door. "Who's there?" came a voice, that Hal at once recognized as belonging to the French commander-in-chief. "Colonel Murrat," said the lads' guide. "The messengers from General Pershing have arrived." "Show them in at once," said Marshal Foch. A moment later Hal and Chester were in the presence of the generalissimo of all the allied forces. They saluted him respectfully. "I may be mistaken," said Marshal Foch, eyeing them searchingly, "but I'll wager you are Majors Paine and Crawford. Am I right?" "Yes, your excellency," said Hal. "We are honored that you remember us."
  • 70. "I never forget a face," replied Marshal Foch; "and seldom a name. Then you bring me a communication from General Pershing?" For answer Hal produced the document given him by the American commander-in-chief earlier in the day. He passed it to Marshal Foch without a word. The French commander took it and laid it carefully on his desk. "That will be all for to-night, gentlemen," he said. "I shall be pleased if you will avail yourself of our hospitality. Colonel Murrat will find quarters for you. Will you report to me in the morning at 8 o'clock? I may have a reply for your commander-in-chief." The lads saluted again and withdrew. Colonel Murrat showed them to excellent quarters in a house next to the one in which the French commander had his headquarters and left them. "Well," said Chester, after he had gone, "looks like we are right in among things, doesn't it?" "It certainly does," Hal agreed. "But say, I'm hungry. Let's step out and round up something to eat." "Suits me," declared Chester, "I'm half starved myself." At a little restaurant only three or four blocks away they were soon comfortably filled. Hal was on the point of suggesting that they turn in for the night when a figure entering the door caught his eye. "By all that's wonderful," he exclaimed, "here comes Anthony Stubbs." Hal was right. The little war correspondent espied the lads at the same moment and hurried toward them with outstretched hand. "I'm awfully glad to see you boys again," he exclaimed. "What brings you here, if I may ask?"
  • 71. "Sit down, Mr. Stubbs," said Hal. "Have something to eat with us." "Thanks: don't mind if I do. But I repeat, what are you doing here?" "How long have you been in town, Mr. Stubbs?" asked Chester, ignoring the little man's question. "About fifteen minutes, more or less. But I say, what are you doing here? This is the third time I've asked that question." "Then don't ask it again, Mr. Stubbs," replied Chester. "Oh, I see," smiled Stubbs. "Can't answer, eh? Well, I'll wager another hat with somebody that I can tell you why you're here." "You'd lose this time, Mr. Stubbs," said Hal. "Oh, no I wouldn't. You're here in connection with the signing of an armistice by Germany and the allies." Chester started to his feet. "Sh-h-h! Not so loud, Stubbs," he exclaimed. Stubbs smiled, but he lowered his voice when he spoke again. "Well, would I lose the bet?" he asked. "I can't say a thing, Mr. Stubbs," was Hal's response. "Well, I'm bound by no such orders," said Stubbs, "so I can. First, however, I want you to understand that whatever I do say is in confidence." "Of course," said Hal. "Certainly, Mr. Stubbs," agreed Chester. "Well, then," said Stubbs, "I want to tell you I'm on the trail of the biggest scoop in newspaper history. I'm going to be the first war correspondent to flash the news that the armistice is signed." "You mean you think you are," said Chester.