Ebook Business statistics: For contemporary decision making (Sixth edition) - Part 1

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Part 1 of ebook Business statistics: For contemporary decision making provide readers with content about: introduction to statistics; charts and graphs; descriptive statistics; distributions and sampling; discrete distributions; continuous distributions; sampling and sampling distributions; making inferences about population parameters; statistical inference - estimation for single populations;... This online teaching and learning environment integrates the entire digital textbook with the most effective instructor and student resources WRÀWHYHU\OHDUQLQJVW\OH With WileyPLUS: ‡ Students achieve concept mastery in a rich, structured environment that’s available 24/7 ‡ Instructors personalize and manage their course more effectively with assessment, assignments, grade tracking, and more ‡ manage time better ‡study smarter ‡ save money From multiple study paths, to self-assessment, to a wealth of interactive visual and audio resources, WileyPLUS gives you everything you need to personalize the teaching and learning experience » F i n d o u t h ow t o M A K E I T YO U R S » www.wileyplus.com ALL THE HELP, RESOURCES, AND PERSONAL SUPPORT YOU AND YOUR STUDENTS NEED! 2-Minute Tutorials and all of the resources you & your students need to get started www.wileyplus.com/firstday Student support from an experienced student user Ask your local representative for details! Collaborate with your colleagues, find a mentor, attend virtual and live events, and view resources www.WhereFacultyConnect.com Pre-loaded, ready-to-use assignments and presentations www.wiley.com/college/quickstart Technical Support 24/7 FAQs, online chat, and phone support www.wileyplus.com/support Your WileyPLUS Account Manager Training and implementation support www.wileyplus.com/accountmanager MAKE IT YOURS! 6T H E D I T I O N Business Statistics For Contemporary Decision Making 6T H E D I T I O N Business Statistics For Contemporary Decision Making Ken Black University of Houston—Clear Lake John Wiley & Sons, Inc Vice President & Publisher George Hoffman Acquisitions Editor Franny Kelly Assistant Editor Maria Guarascio Executive Marketing Manager Amy Scholz Editorial Assistant Emily McGee Production Manager Dorothy Sinclair Senior Production Editor Sandra Dumas Senior Designer Madelyn Lesure Executive Media Editor Allison Morris Photo Department Manager Hilary Newman Production Management Services Aptara Associate Media Editor Elena Santa Maria This book was typeset in 10/12 Minion at Aptara®, Inc and printed and bound by R R Donnelley/ Jefferson City The cover was printed by R R Donnelley/Jefferson City The paper in this book was manufactured by a mill whose forest management programs include sustained yield harvesting of its timberlands Sustained yield harvesting principles ensure that the number of trees cut each year does not exceed the amount of new growth This book is printed on acid-free paper ϱ Copyright © 2010, 2008, 2006, 2004 by John Wiley & Sons, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600 Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201) 748-6011, fax (201) 748-6008 Evaluation copies are provided to qualified academics and professionals for review purposes only, for use in their courses during the next academic year These copies are licensed and may not be sold or transferred to a third party Upon completion of the review period, please return the evaluation copy to Wiley Return instructions and a free of charge return shipping label are available at www.wiley.com/go/returnlabel Outside of the United States, please contact your local representative Black, Ken Business Statistics: For Contemporary Decision Making, Sixth Edition ISBN 13 978-0470-40901-5 ISBN 13 978-0470-55667-2 Printed in the United States of America 10 For Carolyn, Caycee, and Wendi BRIEF CONTENTS UNIT I INTRODUCTION UNIT II Introduction to Statistics Charts and Graphs 16 Descriptive Statistics 46 Probability 92 DISTRIBUTIONS AND SAMPLING UNIT III Discrete Distributions 136 Continuous Distributions 178 Sampling and Sampling Distributions 216 MAKING INFERENCES ABOUT POPULATION PARAMETERS 10 11 UNIT IV Statistical Inference: Estimation for Single Populations Statistical Inference: Hypothesis Testing for Single Populations 288 Statistical Inferences About Two Populations 342 Analysis of Variance and Design of Experiments 402 REGRESSION ANALYSIS AND FORECASTING 12 13 14 15 UNIT V Simple Regression Analysis and Correlation 464 Multiple Regression Analysis 516 Building Multiple Regression Models 546 Time-Series Forecasting and Index Numbers 588 NONPARAMETRIC STATISTICS AND QUALITY 16 17 18 Analysis of Categorical Data 644 Nonparametric Statistics 670 Statistical Quality Control 720 APPENDICES A B Tables 765 Answers to Selected Odd-Numbered Quantitative Problems 805 GLOSSARY INDEX 815 825 The following materials are available at www.wiley.com/college/black 19 Supplement Supplement Supplement viii Decision Analysis C19-2 Summation Notation S1-1 Derivation of Simple Regression Formulas for Slope and y Intercept S2-1 Advanced Exponential Smoothing S3-1 250 448 Chapter 11 Analysis of Variance and Design of Experiments 11.37 Describe the following factorial design How many independent and dependent variables are there? How many levels are there for each treatment? If the data were known, could interaction be determined from this design? Compute all degrees of freedom Each data value is represented by an x Variable x111 x112 x121 x122 x131 x132 x211 x212 x221 x222 x231 x232 x311 x312 x321 x322 x331 x332 x411 x412 x421 x422 x431 x432 Variable 11.38 Complete the following two-way ANOVA table Determine the critical table F values and reach conclusions about the hypotheses for effects Let a = 05 Source of Variance Row Column Interaction Error Total SS df 126.98 37.49 380.82 733.65 MS F 60 11.39 Complete the following two-way ANOVA table Determine the critical table F values and reach conclusions about the hypotheses for effects Let a = 05 Source of Variance Row Column Interaction Error Total SS df MS 1.047 3.844 0.773 _ 12.632 F 23 11.40 The data gathered from a two-way factorial design follow Use the two-way ANOVA to analyze these data Let a = 01 Treatment A B C A 23 25 21 21 20 22 B 27 28 24 27 26 27 Treatment 11.41 Suppose the following data have been gathered from a study with a two-way factorial design Use a = 05 and a two-way ANOVA to analyze the data State your conclusions Treatment A B C D A 1.2 1.3 1.3 1.5 2.2 2.1 2.0 2.3 1.7 1.8 1.7 1.6 2.4 2.3 2.5 2.4 Treatment B 1.9 1.6 1.7 2.0 2.7 2.5 2.8 2.8 1.9 2.2 1.9 2.0 2.8 2.6 2.4 2.8 Problems 449 11.42 Children are generally believed to have considerable influence over their parents in the purchase of certain items, particularly food and beverage items To study this notion further, a study is conducted in which parents are asked to report how many food and beverage items purchased by the family per week are purchased mainly because of the influence of their children Because the age of the child may have an effect on the study, parents are asked to focus on one particular child in the family for the week, and to report the age of the child Four age categories are selected for the children: 4–5 years, 6–7 years, 8–9 years, and 10–12 years Also, because the number of children in the family might make a difference, three different sizes of families are chosen for the study: families with one child, families with two children, and families with three or more children Suppose the following data represent the reported number of child-influenced buying incidents per week Use the data to compute a two-way ANOVA Let a = 05 Number of Children in Family 4–5 Age of Child (years) 6–7 8–9 10–12 or more 8 5 1 2 11.43 A shoe retailer conducted a study to determine whether there is a difference in the number of pairs of shoes sold per day by stores according to the number of competitors within a 1-mile radius and the location of the store The company researchers selected three types of stores for consideration in the study: stand-alone suburban stores, mall stores, and downtown stores These stores vary in the numbers of competing stores within a 1-mile radius, which have been reduced to four categories: competitors, competitor, competitors, and or more competitors Suppose the following data represent the number of pairs of shoes sold per day for each of these types of stores with the given number of competitors Use a = 05 and a two-way ANOVA to analyze the data Number of Competitors Stand-Alone Store Location Mall Downtown or more 41 30 45 25 31 22 18 29 33 38 31 39 29 35 30 22 17 25 59 48 51 44 48 50 29 28 26 47 40 39 43 42 53 24 27 32 11.44 Study the following analysis of variance table that was produced by using Minitab Describe the design (number of treatments, sample sizes, etc.) Are there any significant effects? Discuss the output 450 Chapter 11 Analysis of Variance and Design of Experiments Two-way ANOVA:DV versus RowEffect, ColEffect Source DF SS MS F RowEffect 92.31 46.156 13.23 ColEffect 998.80 249.700 71.57 Interaction 442.13 55.267 15.84 Error 30 104.67 3.489 Total 44 1637.91 P 0.000 0.000 0.000 11.45 Consider the valve opening data displayed in Table 11.1 Suppose the data represent valves produced on four different machines on three different shifts and that the quality controllers want to know whether there is any difference in the mean measurements of valve openings by shift or by machine The data are given here, organized by machine and shift In addition, Excel has been used to analyze the data with a two-way ANOVA What are the hypotheses for this problem? Study the output in terms of significant differences Discuss the results obtained What conclusions might the quality controllers reach from this analysis? Valve Openings (cm) Shift Shift Shift 6.56 6.40 6.54 6.34 6.58 6.44 6.36 6.50 6.38 6.19 6.26 6.23 6.22 6.27 6.29 6.19 6.29 6.23 6.19 6.33 6.26 6.31 6.21 6.58 Machine ANOVA: Two-Factor with Replication ANOVA Source of Variation Sample Columns Interaction Within Total SS 0.00538 0.19731 0.03036 0.15845 0.39150 df 12 23 MS 0.00179 0.09865 0.00506 0.01320 F 0.14 7.47 0.38 P-value 0.9368 0.0078 0.8760 F crit 3.49 3.89 3.00 11.46 Finish the computations in the Minitab ANOVA table shown below and on the next page and determine the critical table F values Interpret the analysis Examine the associated Minitab graph and interpret the results Discuss this problem, including the structure of the design, the sample sizes, and decisions about the hypotheses Two-way ANOVA: Source Row Column Interaction Error Total depvar versus row, column DF SS MS 0.296 0.148 1.852 0.926 4.370 1.093 18 14.000 0.778 26 20.519 Problems 451 4.4 4.2 Row 4.0 Row 3.8 3.6 3.4 3.2 3.0 2.8 2.6 Column Is there a difference in the job satisfaction ratings of self-initiated expatriates by industry? The data presented in the Decision Dilemma to study this question represent responses on a seven-point Likert scale by 24 self-initiated expatriates from five different industries The Likert scale score is the dependent variable There is only one independent variable, industry, with five classification levels: IT, finance, education, healthcare, and consulting If a series of t tests for the difference of two means from independent populations were used to analyze these data, there would be 5C2 or 10 different t tests on this one problem Using a = 05 for each test, the probability of at least one of the 10 tests being significant by chance when the null hypothesis is true is - (.95)10 = 4013 That is, performing 10 t tests on this problem could result in an overall probability of committing a Type I error equal to 4013, not 05 In order to control the overall error, a one-way ANOVA is used on this completely randomized design to analyze these data by producing a single value of F and holding the probability of committing a Type I error at 05 Both Excel and Minitab have the capability of analyzing these data, and Minitab output for this problem is shown below One-way ANOVA: IT, Finance, Education, Healthcare, Consulting Source DF SS MS F P Factor 43.175 10.794 15.25 0.000 Error 19 13.450 0.708 Total 23 56.625 S = 0.8414 R-Sq = 76.25% R-Sq(adj) = 71.25% Individual 95% CIs For Mean Based on Pooled StDev Level IT Finance Education Healthcare Consulting N Mean 5.7500 4.0000 2.5000 3.4000 6.0000 StDev 0.9574 0.7071 0.5477 ( 1.1402 0.8165 ( * * ( ) ( * ) ( 3.0 With an F value of 15.25 and a p-value of 0.000, the results of the one-way ANOVA show that there is an overall significant difference in job satisfaction between the five industries Examining the Minitab confidence intervals shown graphi- ) * ) 4.5 * 6.0 ) 7.5 cally suggests that there might be a significant difference between some pairs of industries Because there was an overall significant difference in the industries, it is appropriate to use Tukey’s HSD test to determine which of the pairs of 452 Chapter 11 Analysis of Variance and Design of Experiments industries are significantly different Tukey’s test controls for the overall error so that the problem mentioned previously arising from computing ten t tests is avoided The Minitab output for Tukey’s test is: Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons Individual confidence level = 99.27% IT subtracted from: Lower Finance –3.4462 Education –4.8821 Healthcare –4.0462 Consulting –1.5379 Center –1.7500 –3.2500 –2.3500 0.2500 Upper –0.0538 –1.6179 –0.6538 2.0379 ( ( ) * ) * ( ) * ( –3.0 Finance subtracted from: Lower Education –3.0311 Healthcare –2.1991 Consulting 0.3038 Center –1.5000 –0.6000 2.0000 Upper 0.0311 0.9991 3.6962 ( 0.0 ( Upper 2.4311 5.1321 ( 3.0 –3.0 0.0 ) * 0.0 ( 6.0 ) * ( Upper 4.2962 Any confidence interval in which the sign of the value for the lower end of the interval is the same as the sign of the value for the upper end indicates that zero is not in the interval and that there is a significant difference between the pair in that case Examining the Minitab output reveals that IT and Finance, IT and Education, IT and Healthcare, Finance and Consulting, Education and Consulting, and Healthcare and Consulting all are significantly different pairs of industries In analyzing career satisfaction, self-initiated expatriates were sampled from three age categories and four categories of ) * 0.0 –3.0 Healthcare subtracted from: Lower Center Consulting 0.9038 2.6000 6.0 ) * –3.0 Education subtracted from: Lower Center Healthcare –0.6311 0.9000 Consulting 1.8679 3.5000 3.0 ) * ( ) * 3.0 6.0 ) * 3.0 6.0 time in the host country This experimental design is a twoway factorial design with age and time in the host country as independent variables and individual scores on the sevenpoint Likert scale being the dependent variable There are three classification levels under the independent variable Age: 30–39, 40–49, and over 50, and there are four classifications under the independent variable Time in Host Country:
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