Student Workbook for use with Statistical Methods For Business and Economics [antikvár]

Preface to the First Edition of the Workbook This student workbook is designed to be a companion to Pfaffenberger and Patterson, Statistical Methods for Business and Economics (revised edition, 1981). The content of the workbook parallels that ofthe Pfaffenberger-Patterson text, and the individual chapters expound upon the more elementary concepts. Individual chapters contain step-by-step work-through problems, and the student can verify that his calculations are correct as he goes along. In addition, exercises are appended at the end of most chapters. These exercises may be used as supplementary homework or for student practice. For the convenience of the student, we include at the end of this workbook all of the statistical tables. The numbering of these tables corresponds to that in Appendix B ofthe Pfaffenberger-Patterson textbook. Appendix A ofthe textbook (Special Topics: Calculus-Based Statistical Procedures) is not included in the workbook. It is best to study the appropriate chapter in the Pfaffenberger-Patterson text before reading a corresponding chapter in the workbook. In our opinion, this procedure will be most efficient in absorbing the material. Though we have striven to make this workbook error-free, it is inevitable that some errors would remain. The authors would very much appreciate being informed of these. Finally, the authors wish to express their deepest thanks to those who typed this manuscript: Ildiko Schall, Sharalyn Bowersox, and Pat Habjouka. We are indebted to them for their patience with the innumerable corrections and revisions and for their great skill. Jack C. Hayya Roger C. Pfaffenberger July 1981 Preface to the Revised Edition of the Workbook We now have revised this workbook to parallel the revisions in the third edition of Pfaffenberger and Patterson, Statistical Methods for Business and Economics. In particular, we increased the number of end-of-chapter exercises and included Minitab solutions in end-of-chapter appendices. The use of some Minitab computer solutions is designed to enrich the presentation, and an individual instructor can easily substitute some other statistical package or can avoid it altogether. Mrs. Ildiko Schall typed the revisions. To her we again express our deepest thanks. It is inevitable that a new manuscript would contain typographical errors. It is also quite possible that some material could be presented better. As the object is clarity and ease of comprehension by the student, we encourage the reader, student, or teacher to communicate these errors to us with a promise on our part of suitable remuneration or acknowledgement. Any errors will be corrected in subsequent printings. Please write to: Professor Jack C. Hayya, College of Business Administration, The Pennsylvania State University, University Park, PA 16802. Phone: (814) 865-1461. Jack C. Hayya Roger C. Pfaffenberger August 1986 Chapter 1 Introduction 1.1. WHAT IS STATISTICS? The object of serious study is the truth, and statistics is one of the methods used by scientists to pursue the truth. Statistics is a practical application of mathematics. Statistics may then be thought of as one ofthe branchlets of philosophy ("Love of Wisdom"), the critical examination of the grounds for fundamental beliefs and an analysis of the basic concepts employed in the expression of such beliefs. Nevertheless, the word statistics means different things to different people. As a noncount noun, it is used to indicate a subject of study; as a singular or plural noun, it is used to indicate numerical facts. For example, it may interest you to know that the heaviest man alive is "Fat Albert" and that his weight varies between 872 and 891 pounds. It may also interest you to know that the tallest people are the Tutsis in Central Africa, the average height for an adult male being more than six feet. Having read that, you will probably wonder about the shortest people, the pygmies: the shortest pygmies are the Mbutis of Zaire, some of whose women average 4 feet-1 inch in height. You can find many of these entertaining statistics in the Guinness Book of World Records. There is also the term vital statistics, associated with births, deaths, marriages, and divorces. In 1984, for example, there were in Pennsylvania 159,911 births, 122,204 deaths, 92,596 marriages, and 40,581 divorces. California, our leading state, had 455,075 births, 195,430 deaths, and 226,560 marriages. (For some mysterious reason, the divorce rate data for California were not available.) It is obvious that there are many connotations to the word statistics. In its infancy, the study of statistics was confined largely to methods of summarizing and describing data, constructing bar or pie charts, and illustrating various graphical techniques. This is known as descriptive statistics, which, after a period of disfavor, has returned in full bloom with the advent of the microcomputer and its sophisticated graphical software. According to the Chinese, a picture is worth more than ten thousand words. Thus, descriptive statistics is a powerful medium for communication. The rebirth of descriptive statistics is exciting, but the heady branch of statistics has to do with the drawing of conclusions or the making of decisions on the basis of sample data. This is known as inferential statistics. Think, for example, of the controversy about cigarette smoking. Inferential statistics began in manufacturing and quality control, where it was usually clear that the decisions made by the use of statistics would enhance profits and be reflected on the bottom line. But the acceptance or interpretation of inferential statistics in matters that touch on the emotions or on public policy is not as clear. And since it is easy for the adroit to deceive with data, it becomes quite easy to fluff or lie with statistics. How to abuse statistics is not the private preserve ofthe politicians and the news media. It is a common practice anywhere when the term statistics shrouds with respectability almost every kind of research and when those who use "canned" statistical programs are unaware of the statistical assumptions and appropriateness of such techniques for the problem at hand. To most, a computer output without any error messages is proof that the correct solution has been found. In summary, we could say that statistics is the science and art of gathering and analyzing data in order to visualize or to make inferences about the characteristics of a group or a population. The data are obtained from a randomly selected sample taken from that population. And there are two broad subdivisions ofthe subject: descriptive statistics and inferential statistics. 1.2. A BRIEF HISTORICAL PERSPECTIVE Thus, statistics may be thought of as a science and an art. It can also be thought of as theory and practice. The great German mathematician, Carl Friedrich Gaus ( 1777-1855) developed the method of least squares in order to improve the accuracy of measurements. This among other advances in statistics