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All rights reserved. Manufactured in the United States of America. This publication is protected by Copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. Many of the designations by manufacturers and seller to distinguish their products are claimed as trademarks.
Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps or all caps. Hogg, Elliot A. Tanis, Dale Zimmerman.
Mathematical statistics. Hogg, Robert V. Tanis, Elliot A. H59 In this Ninth Edition of Probability and Statistical Inference, Bob Hogg and Elliot Tanis are excited to add a third person to their writing team to contribute to the continued success of this text. Dale Zimmerman is the Robert V. Dale has rewritten several parts of the text, making the terminology more consistent and contributing much to a substantial revision. The text is designed for a two-semester course, but it can be adapted for a one-semester course.
A good calculus background is needed, but no previous study of probability or statistics is required. The greatest change to this edition is in the statistical inference coverage, now Chapters 6—9. The first two of these chapters provide an excellent presentation of estimation. Chapter 6 covers point estimation, including descriptive and order statistics, maximum likelihood estimators and their distributions, sufficient statis- tics, and Bayesian estimation.
Interval estimation is covered in Chapter 7, including the topics of confidence intervals for means and proportions, distribution-free con- fidence intervals for percentiles, confidence intervals for regression coefficients, and resampling methods in particular, bootstrapping. The last two chapters are about tests of statistical hypotheses. The topics in Chapter 9 are standard chi-square tests, analysis of variance including general factorial designs, and some procedures associated with regression, correlation, and statistical quality control.
The first semester of the course should contain most of the topics in Chapters 1—5. The second semester includes some topics omitted there and many of those in Chapters 6—9. A more basic course might omit some of the optional starred sections, but we believe that the order of topics will give the instructor the flexibility needed in his or her course. The usual nonparametric and Bayesian techniques are placed at appropriate places in the text rather than in separate chapters.
We find that many persons like the applications associated with statistical quality control in the last section. Overall, one of the authors, Hogg, believes that the presentation at a somewhat reduced mathematical level is much like that given in the earlier editions of Hogg and Craig see References.
The Prologue suggests many fields in which statistical methods can be used. In the Epilogue, the importance of understanding variation is stressed, particularly for its need in continuous quality improvement as described in the usual Six-Sigma pro- grams.
At the end of each chapter we give some interesting historical comments, which have proved to be very worthwhile in the past editions. The answers given in this text for questions that involve the standard distribu- tions were calculated using our probability tables which, of course, are rounded off for printing.
If you use a statistical package, your answers may differ slightly from those given. Some of the numer- ical exercises were solved with Maple.
Several exercises in that manual also make use of the power of Maple as a computer algebra system. In particular, we would like to thank the reviewers of the eighth edition who made suggestions for this edition. They are Steven T.
Mark Mills from Central College in Iowa also made some helpful com- ments. We also acknowledge the excellent suggestions from our copy editor, Kristen Cassereau Ng, and the fine work of our accuracy checkers, Kyle Siegrist and Steven Garren.
We also thank the University of Iowa and Hope College for providing office space and encouragement. Finally, our families, through nine editions, have been most understanding during the preparation of all of this material. We would espe- cially like to thank our wives, Ann, Elaine, and Bridget.
We truly appreciate their patience and needed their love. Elliot A. Dale L. The discipline of statistics deals with the collection and analysis of data. Advances in computing technology, particularly in relation to changes in science and business, have increased the need for more statistical scientists to examine the huge amount of data being collected. We know that data are not equivalent to information.
Once data hopefully of high quality are collected, there is a strong need for statisticians to make sense of them. That is, data must be analyzed in order to provide informa- tion upon which decisions can be made. In light of this great demand, opportunities for the discipline of statistics have never been greater, and there is a special need for more bright young persons to go into statistical science.
If we think of fields in which data play a major part, the list is almost endless: accounting, actuarial science, atmospheric science, biological science, economics, educational measurement, environmental science, epidemiology, finance, genetics, manufacturing, marketing, medicine, pharmaceutical industries, psychology, sociol- ogy, sports, and on and on.
Because statistics is useful in all of these areas, it really should be taught as an applied science. Nevertheless, to go very far in such an applied science, it is necessary to understand the importance of creating models for each sit- uation under study. Now, no model is ever exactly right, but some are extremely useful as an approximation to the real situation. Most appropriate models in statis- tics require a certain mathematical background in probability.
Accordingly, while alluding to applications in the examples and the exercises, this textbook is really about the mathematics needed for the appreciation of probabilistic models necessary for statistical inferences. In a sense, statistical techniques are really the heart of the scientific method. Observations are made that suggest conjectures. These conjectures are tested, and data are collected and analyzed, providing information about the truth of the conjectures.
Sometimes the conjectures are supported by the data, but often the conjectures need to be modified and more data must be collected to test the mod- ifications, and so on. Clearly, in this iterative process, statistics plays a major role with its emphasis on the proper design and analysis of experiments and the resulting inferences upon which decisions can be made.
Through statistics, information is pro- vided that is relevant to taking certain actions, including improving manufactured products, providing better services, marketing new products or services, forecasting energy needs, classifying diseases better, and so on.
Statisticians recognize that there are often small errors in their inferences, and they attempt to quantify the probabilities of those mistakes and make them as small as possible. That these uncertainties even exist is due to the fact that there is variation in the data. Even though experiments are repeated under seemingly the same condi- tions, the results vary from trial to trial. We try to improve the quality of the data by making them as reliable as possible, but the data simply do not fall on given patterns.
In light of this uncertainty, the statistician tries to determine the pattern in the best possible way, always explaining the error structures of the statistical estimates. This is an important lesson to be learned: Variation is almost everywhere.
Often, as in manufacturing, the desire is to reduce variation because the products will be more consistent. In other words, car. This need is based upon three points two of which have been mentioned in the preceding paragraph : 1 Variation exists in all processes; 2 understanding and reducing undesirable variation is a key to success; and 3 all work occurs in a system of interconnected processes.
He would carefully note that you could not maximize the total operation by maximizing the individual components unless they are inde- pendent of each other. However, in most instances, they are highly dependent, and persons in different departments must work together in creating the best products and services.
If not, what one unit does to better itself could very well hurt others. He often cited an orchestra as an illustration of the need for the members to work together to create an outcome that is consistent and desirable. Any student of statistics should understand the nature of variability and the necessity for creating probabilistic models of that variability. We cannot avoid mak- ing inferences and decisions in the face of this uncertainty; however, these inferences and decisions are greatly influenced by the probabilistic models selected.
Some persons are better model builders than others and accordingly will make better infer- ences and decisions. The assumptions needed for each statistical model are carefully examined; it is hoped that thereby the reader will become a better model builder. Finally, we must mention how modern statistical analyses have become depen- dent upon the computer.
In light of this growing relationship between these two fields, it is good advice for bright students to take substantial offerings in statistics and in computer science. Students majoring in statistics, computer science, or a joint program are in great demand in the workplace and in graduate programs. Clearly, they can earn advanced degrees in statistics or computer science or both.
But, more important, they are highly desirable candidates for graduate work in other areas: actuarial science, indus- trial engineering, finance, marketing, accounting, management science, psychology, economics, law, sociology, medicine, health sciences, etc.
We truly hope that we can interest students enough that they want to study more statistics. If they do, they will find that the opportunities for very successful careers are numerous. And there is some truth to that concept.
But if we consider the bigger picture, many recognize that statisticians can be extremely helpful in many investigations. There is some problem or situation that needs to be considered; so statisticians are often asked to work with investigators or research scientists. Suppose that some measure or measures is needed to help us understand the situation better.
The measurement problem is often extremely difficult, and creating good measures is a valuable skill. As an illustration, in higher educa- tion, how do we measure good teaching?
This is a question to which we have not found a satisfactory answer, although several measures, such as student evaluations, have been used in the past. After the measuring instrument has been developed, we must collect data through observation, possibly the results of a survey or an experiment.
Using these data, statisticians summarize the results, often with descriptive statistics and graphical methods. These summaries are then used to analyze the situation. Here it is possible that statisticians make what are called statistical inferences. Finally, a report is presented, along with some recommendations that are based upon the data and the analysis of them.
Probability and Statistical Inference 9th Edition Hogg Solutions Manual
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PROBABILITY AND STATISTICAL INFERENCE. Ninth Edition. Robert V. Hogg. Elliot A. Tanis. Dale L. Zimmerman. Boston Columbus Indianapolis NewYork.
Probability and Statistical Inference, 9th Edition
This chapter contains many useful examples of parametric distributions, one- and two-parameter exponential families, location—scale families, maximum likelihood estimators, method of moment estimators, transformations t Y , E Y , V Y , moment generating functions, and confidence intervals. Sixth edition: Freeman. Meeden, Statistical Science , A.
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs. Reproduced by Pearson from electronic files supplied by the author.
Probability and Statistical Inference. Ed.9
Written by three veteran statisticians, this applied introduction to probability and statistics emphasizes the existence of variation in almost every process, and how the study of probability and statistics helps us understand this variation. Designed for students with a background in calculus, this book continues to reinforce basic mathematical concepts with numerous real-world examples and applications to illustrate the relevance of key concepts. Probability and Statistical Inference. Hogg, Elliot Tanis, Dale Zimmerman. Informasi Dasar.
All rights reserved. Manufactured in the United States of America. This publication is protected by Copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. Many of the designations by manufacturers and seller to distinguish their products are claimed as trademarks. Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps or all caps. Hogg, Elliot A.
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This user-friendly introduction to the mathematics of probability and statistics for readers with a background in calculus uses numerous applications--drawn from biology, education, economics, engineering, environmental studies, exercise science, health science, manufacturing, opinion polls, psychology, sociology, and sports--to help explain and motivate the concepts. A review of selected mathematical techniques is included, and an accompanying CD-ROM contains many of the figures many animated , and the data included in the examples and exercises stored in both Minitab compatible format and ASCII. Empirical and Probability Distributions. Discrete Distributions. Continuous Distributions. Multivariable Distributions.
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