A Homework Supplement
to Accompany
Conversational Statistics for
Business & Economics
Second Edition
L. Van Jones, Ph.D
Texas Christian University
Kendall Hunt Publishing Co.
www.kendallhunt.com/jones
Works Cited:
Over the years, I have used several other author’s works to prepare some materials
in my course, this textbook and the companion workbook. My thanks go the following
who have helped develop even my understanding of the field of statistics.
L. Van Jones, Ph. D.
David R. Anderson, Dennis J. Sweeney, Thomas A. Williams. Statistics for
Business and Economics.
Wayne W. Daniel and James C. Terrell. Business Statistics for Management and Economics.
David M. Levine, Mark L. Berenson and David Stephan. Statistics for Managers.
Douglas A. Lind, Robert D. Mason, William G. Marchal. Basic Statistics for
Business and Economics.
Patrick W. Shannon, David F. Groebner, Phillip C. Fry, Kent D. Smith. A Course
in Business Statistics.
Andrew F. Siegel. Practical Business Statistics.
Allen L. Webster. Applied Statistics for Business and Economics.
Cover image © 2007 Liquid Library
Copyright © 2007, 2009 by L. Van Jones
ISBN 978-0-7575-5672-2
Kendall/Hunt Publishing Company has the exclusive rights to reproduce this work,
to prepare derivative works from this work, to publicly distribute this work,
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All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any
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without the prior written permission of the copyright owner.
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Contents
Preface and Introduction
v
Problems
Chapter 1:
Chapter 2:
Chapter 3:
Chapter 4:
Chapter 5:
Chapter 6:
Chapter 7:
Chapter 8:
Chapter 9:
Chapter 10:
Chapter 11:
Chapter 12:
Chapter 13:
Chapter 14:
Chapter 15:
Introduction to Definitions, Concepts, and Graphics . . . . . . . . . . . . . . . . . . . . . . . .
Descriptive Statistics—Raw Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Descriptive Statistics—Grouped Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Probabilities—The Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Inferential Statistics—The Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Confidence Intervals—One Population Mean and Proportion Testing . . . . . . . . . .
Applying Inferential Statistics—Hypothesis Testing One Population . . . . . . . . . . .
Hypothesis Testing and Confidence Intervals for Two Populations . . . . . . . . . . . .
Applying Inferential Statistics—Chi Square as a Parametric Test,
F-distribution and One-Way ANOVA Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Forecasting—Simple & Multiple Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Smoothing Techniques and Time Series, Qualitative and Quantitative
Methods of Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Index Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Assumption Free Distributions—Chi Square as a Non-parametric Test . . . . . . . . .
Quality Control Including Six Sigma Introduction . . . . . . . . . . . . . . . . . . . . . . . . . .
3
11
13
17
23
29
35
41
47
55
61
67
71
73
77
Solutions
Chapter 1:
Chapter 2:
Chapter 3:
Chapter 4:
Chapter 5:
Chapter 6:
Chapter 7:
Chapter 8:
Chapter 9:
Chapter 10:
Chapter 11:
Chapter 12:
Chapter 13:
Chapter 14:
Chapter 15:
Introduction to Definitions, Concepts, and Graphics . . . . . . . . . . . . . . . . . . . . . . . .
Descriptive Statistics—Raw Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Descriptive Statistics—Grouped Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Probability—The Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Inferential Statistics—The Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Confidence Intervals—One Population Mean and Proportion Testing . . . . . . . . . .
Applying Inferential Statistics—Hypothesis Testing One Population . . . . . . . . . . .
Hypothesis Testing and Confidence Intervals for Two Populations . . . . . . . . . . . .
Applying Inferential Statistics—Chi Square as a Parametric Test,
F-distribution and One-Way ANOVA Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Forecasting—Simple & Multiple Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Smoothing Techniques and Time Series, Qualitative and
Quantitative Methods of Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Index Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Assumption Free Distributions—Chi Square as a Non-parametric Test . . . . . . . . .
Quality Control Including Six Sigma Introduction . . . . . . . . . . . . . . . . . . . . . . . . . .
In Class Examinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iii
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103
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127
139
159
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219
241
265
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307
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Kendall Hunt Publishing Co.
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Preface and Introduction
Initially Arguing My Case
You might ask, why a homework book? Don’t most of the statistics books give you problems and solutions?
Yep, I respond. But you will be given the problem and then the answer. The student will not be given the
steps necessary to determine the answer. This can be further complicated by a problem with the wrong
answer either because of proofing issues or because a problem was changed in the second or third edition,
but the answer was not changed.
If the student is struggling with the concepts, he or she will simply look at the problem, scratch their head,
look at the answer, and then go look for the professor for help in working the problem. Most professors are
challenged with lectures and preparing and grading examinations. Most professors will not have the time
to work through the same problem for each student who needs help.
For the student, a detailed homework solutions manual is a very practical resolution, which is useful in the
repetitive process necessary to understand statistical concepts. For the professor, this is an excellent tool,
which prevents the professor from being tied up in responding to the same question from different students.
I want to mention a few words about the companion textbook, “Conversational Statistics for Business and
Economics”. The textbook is not like other textbooks you have seen or used. The idea behind the companion textbook is to make a statistics book user friendly. You may be thinking, not possible, but hear me
out. Most textbooks, while quite thorough, are not written in a logical step-by-step manner. There are dozens
of intervening examples, which break the logical flow of the student’s leaning process. Most students have
enough trouble focusing on a singular subject and allow themselves to become easily distracted by what I
call “clutter”. My book is written in lecture format, which takes the reader through a step-by-step, logical
flow of the statistical process under consideration. After teaching statistics for over 20 years, I think I have
just about heard every question from students. In my lecture (textbook), I have strategically placed some of
the most often asked questions and then given an answer to what they are most probably thinking at the
time.
This whole idea of a textbook started out with a set of notes I would pass out to my students. The noted
proved to be most helpful and I found the students were quite receptive and complementary. The notes
tended to sufficient slow down the pace of the class so the student could listen to my lecture, rather than
frantically and continuously taking notes. The notes were detailed and took the student through the concepts being studied. I was approached by Kendall-Hunt Publishing to write a textbook. I thought the task
would be rather easy to simply convert my notes to a textbook. The task was much tougher than I first imagined; however, after 6 agonizing months, I finally accomplished my goal.
I have received certain very positive comments about the textbook such as “user friendly, easy to read, really
love the humor, never seen a math book that really explains the process in detail, helps me to read it and
then listen to the lecture, slows down the pace of a tough course”, just to cite a few.
However, as every professor or student knows (but may not want to admit), you only learn the statistical
concepts by repeatedly working problems, which reinforce the concepts being taught. So being the brilliant
professor (and not wanting to hear myself repeat the same thing 140 times), I thought it would make sense
to prepare a step-by-step homework book. Now, after six agonizing months, I have produced what you are
now holding in your hands—a homework book like no other you have ever seen. Oh, I am sure, you, as the
professor, have seen solutions manuals for the instructor, but that is designed to make the professor look
v
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vi
PREFACE AND INTRODUCTION
good and is not for student consumption. This homework book is for student consumption, so the professor does not have to continually repeat his or herself in solving the homework problems for each student.
Developing My Case and Repeating Some Arguments
This manual has been developed for the purpose of providing practicing exercises for each student. The
manual can be used as a homework complement for any good statistic textbook, although the manual follows the chapter sequence of my textbook. If you don’t buy both, I hope you will at least buy this one. All
textbooks have sample problems used as teaching examples in the reading sections. However, it is not
enough for the student of statistics to simply read the material and follow the examples. Statistics like any
mathematically oriented course requires reinforcement of the techniques. As I have already said, textbooks
have problems at the end of a section or a chapter, which, if worked by the student, are helpful in reinforcing the student’s understanding of the material and techniques. As it is quite impossible for any student to
spend his or her time working all the problems in a chapter or section, the professor must take his or her
time and select typical problems to assign to the student. Additionally, the professor must provide some
guidance in working each problem. Most textbooks provide answers to the odd or the even numbers in the
back, but is this enough?
In a word the answer is “No.”
“Why not?” you might ask.
I reply, “One line or one number answers are just that, answers, and will never reveal enough detail for the
student to understand how the answer was developed, and most importantly, how to interpret and apply
the answer.”
I often tell my students, numbers without appropriate application are really useless. Often, the student will
not understand a concept and will seek help from a fellow student (who is often as lost as he or she is) or
seek individual help from the professor (who really cannot deal with 150 students individually) or ask the
professor to work the problems in a classroom setting (which takes away from valuable lecture time). Are
these the ideal solutions or is something else needed?
Because one student may not be able to help another and because the professor will not have ample time
either personally or in class to address all the homework problems, some other approach is necessary.
Fortunately there is a bridge between these three options that smoothes out the rough edges for the student.
“What is that bridge?” you may ask.
“Glad you asked,” I reply. “The magic answer is this very homework solution manual.”
“Wow,” you gasp. “How could I have every guessed that?”
“All seriousness aside,” I say, “let me tell you more about the structure of this manual and why it is the best
answer possible.” This solutions manual provides a bridge between all options. The approach taken in my
manual is to provide very detailed answers to the homework problems including step-by-step calculations,
not just a one-line answer. Additionally, when appropriate, my manual provides very specific interpretations associated with each homework problem.
“Why would this be necessary?” you ask.
“There are several reasons,” I reply (repeating some arguments for emphasis).
Kendall Hunt Publishing Co.
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PREFACE AND INTRODUCTION
vii
First, the one who prepares the textbook will often provide a complete solutions manual for the professor.
However, the entire solutions manual usually remains in the hands of the professor. This certainly aids the
professor, but not the student. It is usually impractical for the professor to make the professor’s manual
available to the student. My solutions manual provides a better option where each student can have his or
her own solutions manual.
Second, no specific detail is provided in textbooks on how to actually work a problem. Many (probably
most) students have forgotten the simplest algebra and cannot seem to correctly execute the order of operation. The professor must work the problem step-by-step in some cases for the student to understand the
process. My manual presents a step-by-step solution for each assigned problem. Where appropriate, Excel
becomes the method of choice (ANOVA and Regression and Time Series to name a few of the obvious ones).
Third, my solutions manual contains a clear and concise interpretation of the numbers, which is totally
missing in other textbooks. My solution manual addresses this issue with very specific detailed interpretations.
For example, solutions to business problems regarding a hypothesis test are of little value to simply arriving at the conclusion of rejecting or not rejecting the null hypothesis. The business executive must understand the impact of the decision. Should more or less product be placed in the container? Can a company’s
advertising claim be supported or is the claim false? Is there a difference between the mean life of one company’s product when compared with the mean life of their competitor’s product? Actually the interpretation is more important than the numbers themselves.
Most professors will not have time to adequately address each and every problem solution with each and
every student either personally or in a class-room setting. Most professors would rather use the class period for lecture time rather than working homework problems. Either personal attention to each student or
class time usually creates a time crunch for the professor. This can be especially difficult, if the professor has
two or three sections and several hundred students. Using my homework manual as the assigned problems
associated with a single semester course in Statistics, the professor should be able to concentrate on lectures,
teaching, grading and attending never ending meetings. Of course, use of this manual does not preclude
individual student contact, but again this is often impractical for the professor to provide individual personal contact with all students.
My manual is not designed for the mathematics major and will not dwell on the use of calculus in the solutions. This homework manual does not ignore software, but also requires solutions using a lot of pen and
paper. The theory is that ideas and concepts flow into the brain much more rapidly and permanently
when pen and paper are used rather than always depending on software. Old fashion? Perhaps, but in
realty pen and paper can be a very effective tool useful in transferring foreign ideas (translated statistical
processes) to the student’s mind in a logical sequence. The use of software is certainly encouraged and is
often shown in my manual. However, first, the student is encouraged to learn with pen and paper and then
learn how to apply the software. Sometimes (okay, most of the time) manual solutions can prove to be very
tedious; however, the enriched learning experiences outweigh the momentary tedium. Additionally, this
manual cannot cover all subjects, although by reviewing the Table of Contents, one can easily see the student will be challenged in a one-semester course. To cover other subjects such as Decision Theory or spend
more time on Multiple Regression Model Building or Decision Trees is quite often a two-semester statistics
course. My solutions manual is designed to cover relevant, basic, and essential subjects in a one-semester
course.
Kendall Hunt Publishing Co.
www.kendallhunt.com/jones
viii
PREFACE AND INTRODUCTION
In Class Examinations (Pop Quizzes)
You will note that at the back of the homework solutions manual, I have included a “pop quiz” section.
I need to mention the purpose of my including an in-class examination section. If you will go to that section
and read the instructions, you will see that I give 5 out of the 10 examination at anytime during the course.
Most often, the pop quizzes take approximately 10-15 minutes to complete. My classes are structured with
lecture and lab time. I may have two or three lecture periods followed by a lab period, in which the problems at the end of each chapter are worked in class. At that time, I also provide solutions for all of those
problems. I use an in-class examination to encourage attendance, to encourage completion of homework,
and to encourage reading by the student. I only use the examinations as 5% of their total grade. While the
threat of a pop quiz by itself will not force a student to be responsible and attend class, this seems to encourage them to be responsible, attend class with the proper materials, be on time, remain at their desk for the
full class period, and, God forbid, read the textbook and do the homework.
Try both the textbook and the companion homework solutions manual or try the homework solutions manual with your companion textbook. I can hear you think about that statement and wonder if I am a bit off
my rocker. Try them and then let me know if I am a wee-bit crazy. Since I have been using them, I find the
flow and pace of the class is better, class participation (yes, I said class participation) has increased and
grades have actually improved. I find fewer class cuts or absences except for the omnipresent “official
excused absence”, which proves to be a distraction from teaching, but something I presume is necessary to
make the student feel a part of the university community.
Both the textbook and the companion homework solutions manual will be useful for you. If you will
also make use of the tear out pages in the textbook at the back of each chapter and have them turned in and
you make them tear out pop quizzes, you will make both books unsalable on the secondary market thus
increasing my royalty income. I really like that idea. Try them and I think you will find them most helpful
to you as the professor and more especially useful to your students.
—L. Van Jones, Ph.D.
Kendall Hunt Publishing Co.
www.kendallhunt.com/jones