Statistics for management and economics

STATISTICS

FOR MANAGEMENT A N D ‘ECONOMICS t

S E V E N T H E D IT IO N

KELLER

DATA TYPES

A GUIDE TO STATISTICAL TECHNIQUES

I Problem O bjective s~

Describe a

P opulation

C om pare Two

P opulations

Com pare Tw o or

M o re Populations

Analyze R elationship

Between Two

Variables

Am ong Two

V a r i e s

Histogram

Section 2.3

Ogive

Section 2.3

Stem -and-leaf

Section 2.3

Box plot

Section 4.3

M ean, m edian, and m ode

Section 4.1

Range, variance, and

standard deviation

Section 4.2

Percentiles and quartiles

Section 4.3

r test and estim ator of a mean

Section 12.1

Chi-squared test and

estim ator o f a variance

Section 12.2

Equal-variances f-test and estim ator of

the difference between two means:

independent samples

Section 13.1

Unequal-variances f-test and

estim ator o f the difference between

two means: independent samples

Section 13.1

r-test and estim ator o f m ean difference

Section 13.3

F-test and estim ator o f ratio o f two

variances

Section 13.4

W ilcoxon rank sum test

Section 21.1

W ilcoxon signed rank sum test

Section 21.2

O ne-way analysis o f variance

Section 15.1

Random ized block design of

analysis of variance

Section 15.3

Tw o-lactor analysis o f variance

Section 15.4

LSD m ultiple com parison m ethod

Section 15.6

Tukey's multiple com parison

m ethod

Section 15.6

Kruskal-VVallis test

Section 21.3

Friedm an test

Section 21.4

Scatter diagram

Section 2.4

Covariance

Section 4.4

Correlation

Section 4.4

Least squares line

Section 4.4

Simple linear regression

C hapter 17

Spearman rank correlation

Section 21.5

M ultiple regression

C hapters 18 » 19

Frequency distribution

Section 2.2

Bar chart

Section 2.2

Pie chart

Section 2.2

Line chart

Section 2.5

z test and estim ator o f a

proportion

Section 12.3

C hi-squared goodness-of-fit

test

Section 16.1

z-test and estim ator o f the difference

between two proportions

Section 13.5

Chi-squared test o f a contingency

table

Section 16.2

C hi-squared test o f a contingency

table

Section 16.2

Contingency table

Section 2.4

Chi-squared test o f a contingency

table

Section 16.2

Box plot

Section 4.3

M edian

Section 4.1

Percentiles and quartiles

Section 4.3

W ilcoxon rank sum test

Section 21.1

Sign test

Section 21.2

Kruskal-W allis test

Section 21.3

Friedm an test

Section 21.4

Spearman rank correlation

Section 21.5

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APPLICATION BOXES

I Banking~

Credit scorecards

[

Finance and Economics

Stock and bond valuation

Return on investment

Geometric mean

Mutual funds

Measuring risk

Demand curve

Histograms to compare credit scores of borrowers who repay and those who default 52

Introduction 40

Histograms of two sets of returns to assess expected returns and risk 41

Calculating average returns on an investment over time 96

Marginal and conditional probability relating mutual fund performance

with manager’s education 161

Normal distribution to show why the standard deviation is a measure of risk 245

Polynomial model to relate price and demand 669

I Human Resource Management

Employee retention

Job applicant testing

Severance pay

Performance measure

I Managerial Accounting

Fixed and variable costs

Pricing

Advertising

Consumer survey

Test marketing

Market segmentation

Market segmentation

Test marketing

Test marketing

Market segmentation

Market segmentation

Market segmentation

Regression analysis to predict which workers will stay on the job 589

Regression analysis to determine whether testing job applicants is effective 590

Multiple regression to judge consistency of severance packages to laid-off worker 643

Multiple regression to predict absenteeism 678

Least squares line to estimate fixed and variable costs 127

Histogram of telephone use 34

Estimating mean exposure to advertising 320

Inference about market share (p) 393

Inference about the difference between two proportions of product purchases 456

Inference about two proportions to determine whether market segments differ 466

Inference about the difference between two means to determine whether two market

segments differ 471

Analysis of variance to determine differences between marketing strategies 493

Analysis of variance to determine differences between pricing strategies 507

Analysis of variance to determine differences between several segments 507

Chi-squared goodness-of-fit test to determine relative sizes of market segments 556

Chi-squared test of a contingency table to determine whether several market

segments differ 574

I Operations Management

PERT/CPM

Waiting lines

Inventory management

PERT/CPM

Waiting lines

Inventory management

Assembly line balancing

Aggregate production plan

Quality

Production design

Pharmaceutical experiments

Location analysis

Learning curve

Expected value of the completion time of a project 209

Poisson distribution to compute probabilities of arrivals 228

Normal distribution to determine the reorder point 252

Normal distribution to determine the probability of completing a project on time 255

Exponential distribution to calculate probabilities of service completions 258

Estimating mean demand during lead time 308

Estimating the mean time to complete a task on an assembly line 316

Inference about mean productivity 363

Inference about a variance 376

Inference about the difference between the means of assembly times 422

Inference about the difference between two drugs 464

Multiple regression to predict profitability of new locations 629

Polynomial model to analyze productivity and job tenure 670

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Section 4.5 (Optional) Application in Professional Sports Management: Determinants of the Number of Wins

in a Baseball Season (illustrating an application of the least squares method and correlation) 128

Section 7.3 (Optional) Application in Finance: Portfolio Diversification and Asset Allocation (illustrating the laws

of expected value and variance, and covariance) 210

Section 12.4 (Optional) Application in Marketing: Market Segmentation (using inference about a proportion

to estimate the size of a market segment) 393

Section 12.5 (Optional) Application in Accounting: Auditing (using inference about the mean and inference about

a proportion to estimate parameters) 397

Section 15.5 (Optional) Application in Operations Management: Finding and Reducing Variation (using analysis

of variance to actively experiment to find sources of variation) 531

Section 17.5 (Optional) Application in Finance: Market Model (illustrating simple linear regression to estimate

a stock’s market-related risk and its firm-specific risk) 606

Section 19.3 (Optional) Human Resources Management: Pay Equity (using multiple regression to determine cases

of discrimination) 678

APPLICATION SUBSECTIONS

Section 6.4 (Optional) Application in Medicine and Medical Insurance: Medical Screening (using Bayes’ Law

to calculate probabilities after a screening test) 177

Section 19.4 (Optional) Application in Banking: Credit Scorecards (using logistic regression to determine

probabilities of consumers’ repaying loans) 684

APPLETS

A PPLICATION SECTIONS

Applet 1 Scatter Diagrams and Correlation 118

Applet 2 Scatter Patterns and Correlation 119

Applet 3 Sampling 153

Applet 4 Normal Distribution Parameters 240

Applet 5 Normal Distribution Areas 244

Applet 6 Student t Distribution 265

Applet 7 Chi-Squared Distribution 269

Applet 8 F Distribution 274

Applet 9 Fair Dice—I 284

Applet 10 Fair Dice— II 284

Applet 11 Loaded Dice 285

Applet 12 Skewed Dice 285

Applet 13 Normal Approximation to Binomial Probabilities 293

Applet 14 Distribution of Difference Between Means 298

Applet 15 Confidence Interval Estimates of a Mean 313

Applet 16 Power of z Test 353

Applet 17 Plots of Two-Way ANOVA Effects 523

Applet 18 Fitting the Regression 584

Applet 19 Analysis of Regression Deviations 600

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FOR MANAGEMENT AND ECONOMICS

S E V E N T H E D I T I O N

Ï

¡0 ^ Asian Network

for Higher Educatioo.

No. Q026

GERALD KELLER

W ilfrid Laurier University

THOMSON

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B R O O K S /C O L E Australia • Canada • Mexico • Singapore • Spain

United Kingdom • United States

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To m y fa m ily

Statistics for Management and Economics

Seventh Edition

Gerald Keller

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BRIEF CONTENTS

1 W H A T IS STATISTICS? 1

2 GRAPHICAL AND TABULAR DESCRIPTIVE TECHNIQUES 17

3 ART AND SCIENCE OF GRAPHICAL PRESENTATIONS 73

4 NUMERICAL DESCRIPTIVE TECHNIQUES 89

5 DATA COLLECTION AND SAMPLING 141

6 PROBABILITY 155

7 RANDOM VARIABLES AND DISCRETE PROBABILITY DISTRIBUTIONS

8 CONTINUOUS PROBABILITY DISTRIBUTIONS 233

9 SAMPLING DISTRIBUTIONS 277

1 0 INTRODUCTION TO ESTIMATION 302

11 INTRODUCTION TO HYPOTHESIS TESTING 325

12 INFERENCE ABOUT A POPULATION 361

1 3 INFERENCE ABOUT COMPARING TWO POPULATIONS 413

1 4 STATISTICAL INFERENCE: REVIEW OF CHAPTERS 12 AND 13 47 6

15 ANALYSIS OF VARIANCE 492

16 CHI-SQUARED TESTS 550

17 SIMPLE LINEAR REGRESSION AND CORRELATION 577

18 MULTIPLE REGRESSION 626

19 MODEL BUILDING 662

2 0 TIME SERIES ANALYSIS AND FORECASTING 698

21 NONPARAMETRIC STATISTICS 725

2 2 STATISTICAL PROCESS CONTROL 774

23 DECISION ANALYSIS 801

2 4 STATISTICAL INFERENCE: CONCLUSION 820

APPENDIX A Data File Sample S tatistics A-1

A P P E N D IX B T a b le s B-1

A P P E N D IX C A n s w e r s t o S e le c te d E v e n - N u m b e r e d E xe rc is es C-1

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CONTENTS

Preface x

Guided Book Tour xii

1 W H A T IS S T A T IS T IC S ? 1

1.1 Key Statistical Concepts 4

1.2 Statistical Applications in Business 5

1.3 Statistics and the C om puter 6

1.4 W orld Wide W eb and Learning Center 7

Appendix 1.A Instructions fo r the CD-ROM 9

Appendix 1.B Introduction to M icrosoft Excel 10

Appendix 1.C Introduction to M initab 14

O Excel Troubleshooting and Detailed Instructions: Appendix A

M in itab Detailed Instructions: Appendix B

2 G R A P H IC A L A N D T A B U L A R D E S C R IP T IV E T E C H N IQ U E S 17

2.1 Types o f Data and Inform ation 18

2.2 Graphical and Tabular Techniques for Nom inal Data 23

2.3 Graphical Techniques for Interval Data 33

2 .4 Describing the Relationship Between Two Variables 52

2 .5 Describing Tim e-Series Data 64

3 A R T A N D S C IE N C E OF G R A P H IC A L P R E S E N T A T IO N S 7 3

3.1 Graphical Excellence 74

3 .2 Graphical Deception 81

3 .3 Presenting Statistics: W ritten Reports and Oral Presentations 86

4 N U M E R IC A L D E S C R IP T IV E T E C H N IQ U E S 8 9

4.1 Measures o f Central Location 90

4.2 Measures o f Variability 99

4.3 Measures o f Relative Standing and Box Plots 107

4 .4 Measures o f Linear Relationship 115

4.5 (o p tio n a l) APPLICATIONS IN PROFESSIONAL SPORTS: Baseball 128

4 .6 Com paring Graphical and Num erical Techniques 131

4.7 General Guidelines for Exploring Data 134

O A pproxim ating Means and Variances from Grouped Data: Appendix C

O Descriptive Techniques Review Exercises: Appendix D

R E V IE W OF D E S C R IP T IV E T E C H N IQ U E S 1 3 9

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Contents v

D A TA C O LLE C TIO N A N D S A M P L IN G 141

5.1 M ethods o f Collecting Data 142

5.2 Sampling 145

5.3 Sampling Plans 147

5 .4 Sampling and Nonsampling Errors 152

P R O B A B IL IT Y 1 5 5

6.1 Assigning Probability to Events 156

6.2 Joint, M arginal, and Conditional Probability 160

6.3 Probability Rules and Trees 170

6 .4 Bayes'Law 177

6 .5 Identifying the Correct M ethod 185

Counting Formulas: Appendix E

R A N D O M V A R IA B L E S A N D D ISC R ETE

P R O B A B IL IT Y D IS T R IB U T IO N S 1 9 2

7.1 Random Variables and Probability Distributions 193

7.2 Bivariate Distributions 203

7.3 (optional) APPLICATIONS IN FINANCE: Portfolio Diversification and

Asset Allocation 210

7 .4 Binomial Distribution 216

7.5 Poisson Distribution 223

«? Hypergeom etric Distribution: Appendix F

C O N T IN U O U S P R O B A B IL IT Y D IS T R IB U T IO N S 2 3 3

8.1 Probability Density Functions 234

8.2 Normal Distribution 239

8.3 (optional) Exponential Distribution 256

8 .4 Other Continuous Distributions 260

Continuous Probability Distributions: Calculus Approach: Appendix G

S A M P L IN G D IS T R IB U T IO N S 2 7 7

9.1 Sampling Distribution o f the M ean 278

9.2 Sampling Distribution o f a Proportion 290

9.3 Sampling Distribution o f the Difference Between Two Means 296

9 .4 From Here to Inference 299

Using the Laws o f Expected Value and Variance to Derive the Parameters

o f Sampling Distributions: Appendix H

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v i Contents

10 INTRODUCTION TO ESTIMATION 302

10.1 Concepts o f Estimation 303

10.2 Estimating the Population M ean W hen the Population Standard

Deviation Is Known 306

10.3 Selecting the Sample Size 321

© Excel Spreadsheets for Techniques in Chapters 1 0 -1 3 : Appendix I

1 1 IN T R O D U C T IO N TO H Y P O T H E S IS T E S T IN G 3 2 5

11.1 Concepts o f Hypothesis Testing 326

11.2 Testing the Population M ean W hen the Population Standard Deviation

Is Known 329

11.3 Calculating the Probability o f a Type II Error 347

11 .4 The Road Ahead 356

<9 Converting Excel's Probabilities to p-Values: A ppendix K

12 IN F E R E N C E A B O U T A P O P U L A T IO N 3 6 1

12.1 Inference about a Population M ean W hen the Standard Deviation

Is Unknown 362

12.2 Inference about a Population Variance 375

12.3 Inference about a Population Proportion 381

12.4 [optional] APPLICATIONS IN MARKETING: M arket Segmentation 393

1 2.5 (optional) A PPLIC A TIO N S IN A C C O U N T IN G : Auditing 397

«0 Excel and M initab Instructions fo r Missing Data and for Recoding Data:

Appendix J

Probability o f a Type II Error W hen Testing a Proportion: Appendix L

Approxim ating p-Values from th e S tudent t Table: A ppendix M

1 3 IN F E R E N C E A B O U T C O M P A R IN G T W O P O P U L A T IO N S 4 1 3

13.1 Inference about the D ifference Between Two Means:

Independent Samples 414

13.2 Observational and Experim ental Data 432

13.3 Inference about the D ifference Between Two Means:

M atched Pairs Experim ent 434

13 .4 Inference about the Ratio o f Two Variances 446

13.5 Inference about the D ifference Between Two

Population Proportions 452

Appendix 13.A Excel Instructions fo r Stacked and Unstacked Data 4 7 4

Appendix 13.B M initab Instructions fo r Stacked and Unstacked Data 4 7 4

Probability o f a Type II Error W hen Testing the D ifference Between Two

Means: Appendix N

O Probability o f a Type II Error W hen Testing the D ifference Between Two

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