Elementary Statistics For Business And Economics – Carin Lombard

Hypothesis Testing that H 0 were true, whereas a “large” X-value would indicate that H t might be true. Hence, for some number X*, calculated beforehand, we would reject H 0 if X > X*, but accept H0if X ^ X*. We say that X is the test statistic and X* the critical value. Thus we have the decision rule: If X > X*, reject H 0 (i.e. accept H J . If X ^ X*, accept H 0 (i.e.

reject H^. If H 0 is rejected, we say that the result is statistically significant. Because the rejection region is in the upper (right-hand) tail of the distribution, we say that we use an upper-tail (or right-tail) test. How should we determine the critical value X*? There is always the risk of making the wrong decision, i. e. rejecting a true H0, or accepting a false H0. The first error, rejecting H 0 if it is true, is called a Type I error; the other error, accepting H 0 if it is false, is called a Type II error.

The probabilities of making these errors can of course be calculated, with X* given and the probability distribution of X known. Definition: P (Type I error) = P (Reject H 0|H 0 true) = a P (Type II error) = P (Accept H 0|H 0 false) = /} a is the significance level and 1 — /? the power of the test (see Figs. 9/2 and 9/3 on the next page).

The significance level a is usually predetermined (e.g. a = 0.05, 0.01, 0.001). How do we find X* if a is given? Solution: Referring to Example 9.2 we obtain: 9.1 Introduction and Basic Concepts Fig, 9/2: «, the probability of a Type I error, X* — fin „ ff In other words, = z„.

Elementary statistics for business and economics. Includes bibliographies and index. 1. Social sciences – Statistical methods. 2. Statis- tics. 3. Commercial statistics. 4. Economics – Statistical methods. I. Title. HA29.S249 1983 519.5 83-11627 ISBN 3-11-008302-7 © Copyright 1983 by Walter de Gruyter & Co., Berlin. – All rights reserved, including those of translation into foreign languages. No part of this book may be reproduced in any form – by photoprint, microfilm, or any other means – nor transmitted nor translated into a machine lan- guage without written permission from the publisher.

Printed in Germany. Printing: Tutte Druckerei GmbH, Salzweg. Binding: Luderitz & Bauer, Berlin. Preface A striking feature of this book is its size. By careful attention to the language, by appropriately using examples to illustrate concepts and methods and by omitt- ing any unnecessary material, I have managed to keep the size to about half of most other similar books, and by so doing I hope to have combined brevity with clarity. Comments from many students have convinced me that the brief appro- ach is pedagogically superior; the short treatment makes it easier for the stu- dents to grasp the main points and to follow the logical development of the material covered.

The contents are intended for basic statistics courses (undergraduate as well as graduate) in business administration, public administration, and economics. The book would be appropriate for a two-semester course but could also be used in a more intensive one-semester course. No previous exposure to statistics is assumed and no university level mathematics is required; however, some analytical capacity of the reader would of course be useful.

The exercises at the end of each chapter form an integral part of the book and the student is urged to solve as many of them that he or she feels are necessary for a thorough understanding of the chapter. This problem-solving aspect is absolutely essential; its importance can hardly be overemphasized. Partial answers to some of the exercises are given at the end of the book. Starred (*) or double-starred (**) problems are mathematically more challenging. Some chapter sections are also marked by a star; these can be left out without disrupt- ing continuity.

All diagrams in the text are drawn to scale, using a Hewlett-Packard micro- computer and plotter. I am grateful to several persons, first of all to the editor, Werner Schuder of Walter de Gruyter & Co. for encouragement, patience and understanding. My assistants, Richard Germain and Kathie Brown and my wife Ulrika helped by reviewing the entire manuscript, pointing out errors and making many helpful suggestions for improvement.

In addition, Kathie Brown produced the dia- grams. Thanks are also due to Antoinette Gerritse and Anita Beauchamp for efficient and meticulous typing. I am also grateful to the Literary Executor of the late Sir Ronald A. Fisher, 6 Preface F. R. S. to Dr. Frank Yates, F. R. S. and to Longman Group Ltd.

This is a short excerpt from the opening of “” by Unknown, quoted for review and introduction purposes. All rights belong to the copyright holders.

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