DeCoursey-EXCEL-Statistics-and-Probability-for-Engineering PDF

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Statistics and Probability

for Engineering Applications

With Microsoft

Excel [This is a blank page.]

Statistics and Probability

for Engineering Applications

With Microsoft

Excel by

W.J. DeCoursey

College of Engineering,

University of Saskatchewan

Saskatoon

Amster dam Boston London New York Oxfor d Paris San Diego San Francisco Singapor e Sydney Tokyo

Newnes is an imprint of Elsevier Science.

Copyright © 2003, Elsevier Science (USA). 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, photocopy ing, recording, or otherwise, without the prior written permission of the publisher. Recognizing the importance of preserving what has been written, Elsevier Science prints its books on acid-free paper whenever possible. Library of Congress Cataloging-in-Publication Data

ISBN: 0-7506-7618-3

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library. The publisher offers special discounts on bulk orders of this book.

For information, please contact:

Manager of Special Sales

Elsevier Science

225 Wildwood Avenue

Woburn, MA 01801-2041

Tel: 781-904-2500

Fax: 781-904-2620

For information on all Newnes publications available, contact our World Wide

Web home page at: http://www.newnespress.com

10 9 8 7 6 5 4 3 2 1

Printed in the United States of America

Preface ........................................................................ ........................ xi What's on the CD-ROM? ................................................................. xiii List of Symbols ........................................................................ .......... xv

1. Introduction: Probability and Statistics......................................... 1

1.1 Some Important Terms ................................................................... 1

1.2 What does this book contain? ....................................................... 2

2. Basic Probability........................................................................

..... 6

2.1 Fundamental Concepts .................................................................. 6

2.2 Basic Rules of Combining Probabilities ......................................... 11

2.2.1 Addition Rule .................................................................... 11

2.2.2 Multiplication Rule ............................................................ 16

2.3 Permutations and Combinations .................................................. 29

2.4 More Complex Problems: Bayes' Rule .......................................... 34

3. Descriptive Statistics: Summary Numbers ................................... 41

3.1 Central Location ........................................................................

.. 41

3.2 Variability or Spread of the Data ................................................... 44

3.3 Quartiles, Deciles, Percentiles, and Quantiles ................................ 51

3.4 Using a Computer to Calculate Summary Numbers ...................... 55

4. Grouped Frequencies and Graphical Descriptions..................... 63

4.1 Stem-and-Leaf Displays ................................................................ 63

4.2 Box Plots ........................................................................

.............. 65

4.3 Frequency Graphs of Discrete Data .............................................. 66

4.4 Continuous Data: Grouped Frequency ......................................... 66

4.5 Use of Computers ........................................................................

75
v

5. Probability Distributions of Discrete Variables ........................... 84

5.1 Probability Functions and Distribution Functions .......................... 85

(a) Probability Functions ............................................................... 85 (b) Cumulative Distribution Functions .......................................... 86

5.2 Expectation and Variance ............................................................. 88

(a) Expectation of a Random Variable .......................................... 88 (b) Variance of a Discrete Random Variable .................................. 89 (c) More Complex Problems ......................................................... 94

5.3Binomial Distribution ................................................................. 101

(a) Illustration of the Binomial Distribution ................................. 101 (b) Generalization of Results ...................................................... 102 (c) Application of the Binomial Distribution ............................... 102 (d) Shape of the Binomial Distribution ....................................... 104 (e) Expected Mean and Standard Deviation ................................ 105 (f) Use of Computers ................................................................ 107 (g) Relation of Proportion to the Binomial Distribution ............... 108 (h) Nested Binomial Distributions ............................................... 110 (i) Extension: Multinomial Distributions ..................................... 111

5.4Poisson Distribution ................................................................... 117

(a) Calculation of Poisson Probabilities ....................................... 118 (b) Mean and Variance for the Poisson Distribution .................... 123 (c) Approximation to the Binomial Distribution .......................... 123 (d) Use of Computers ................................................................ 125

5.5Extension: Other Discrete Distributions ....................................... 131

5.6Relation Between Probability Distributions and

Frequency Distributions

............................................................... 133 (a) Comparisons of a Probability Distribution with

Corresponding Simulated Frequency Distributions

................ 133 (b) Fitting a Binomial Distribution ............................................... 135 (c) Fitting a Poisson Distribution ................................................. 136

6. Probability Distributions of Continuous Variables ................... 141

6.1 Probability from the Probability Density Function ........................ 141

6.2Expected Value and Variance ..................................................... 149

6.3Extension: Useful Continuous Distributions ................................ 155

6.4Extension: Reliability ................................................................... 156

7. The Normal Distribution............................................................. 157

7.1Characteristics ........................................................................

.... 157

7.2Probability from the Probability Density Function ........................ 158

7.3Using Tables for the Normal Distribution .................................... 161

7.4Using the Computer .................................................................. 173

7.5Fitting the Normal Distribution to Frequency Data ...................... 175

7.6Normal Approximation to a Binomial Distribution ...................... 178

7.7Fitting the Normal Distribution to Cumulative

Frequency Data

.. 184

7.8Transformation of Variables to Give a Normal Distribution .......... 190

8. Sampling and Combination of Variables .................................. 197

8.1Sampling ........................................................................

........... 197

8.2Linear Combination of Independent Variables ............................ 198

8.3Variance of Sample Means ......................................................... 199

8.4Shape of Distribution of Sample Means:

Central Limit Theorem

................................................................ 205

9. Statistical Inferences for the Mean............................................ 212

9.1Inferences for the Mean when Variance Is Known ...................... 213

9.1.1Test of Hypothesis ........................................................... 213

9.1.2Confidence Interval ......................................................... 221

9.2Inferences for the Mean when Variance Is

Estimated from a Sample

........................................................... 228

9.2.1Confidence Interval Using the t-distribution .................... 232

9.2.2Test of Significance: Comparing a Sample Mean

to a Population Mean ..................................................... 233

9.2.3Comparison of Sample Means Using Unpaired Samples .. 234

9.2.4Comparison of Paired Samples ........................................ 238

10. Statistical Inferences for Variance and Proportion ................. 248

10.1 Inferences for Variance ............................................................... 248

10.1.1 Comparing a Sample Variance with a

Population Variance

........................................................ 248

10.1.2 Comparing Two Sample Variances .................................. 252

10.2 Inferences for Proportion ........................................................... 261

10.2.1 Proportion and the Binomial Distribution ........................ 261

vii

10.2.2 Test of Hypothesis for Proportion .................................... 261

10.2.3 Confidence Interval for Proportion .................................. 266

10.2.4 Extension ........................................................................

269

11. Introduction to Design of Experiments................................... 272

11.1 Experimentation vs. Use of Routine Operating Data ................... 273

11.2 Scale of Experimentation ............................................................ 273

11.3 One-factor-at-a-time vs. Factorial Design .................................... 274

11.4 Replication ........................................................................

......... 279

11.5 Bias Due to Interfering Factors ................................................... 279

(a) Some Examples of Interfering Factors .................................... 279 (b) Preventing Bias by Randomization ........................................ 280 (c) Obtaining Random Numbers Using Excel .............................. 284 (d) Preventing Bias by Blocking .................................................. 285

11.6 Fractional Factorial Designs ........................................................ 288

12. Introduction to Analysis of Variance ....................................... 294

12.1 One-way Analysis of Variance .................................................... 295

12.2 Two-way Analysis of Variance .................................................... 304

12.3 Analysis of Randomized Block Design ........................................ 316

12.4 Concluding Remarks .................................................................. 320

13. Chi-squared Test for Frequency Distributions ........................ 324

13.1 Calculation of the Chi-squared Function .................................... 324

13.2 Case of Equal Probabilities ......................................................... 326

13.3 Goodness of Fit ........................................................................

.. 327

13.4 Contingency Tables .................................................................... 331

14. Regression and Correlation ..................................................... 341

14.1 Simple Linear Regression ............................................................ 342

14.2 Assumptions and Graphical Checks ........................................... 348

14.3 Statistical Inferences ................................................................... 352

14.4 Other Forms with Single Input or Regressor ............................... 361

14.5 Correlation ........................................................................

........ 364

14.6 Extension: Introduction to Multiple Linear Regression ................ 367

viii

15. Sources of Further Information ............................................... 373

15.1 Useful Reference Books ............................................................. 373

15.2 List of Selected References ......................................................... 374

Appendices ........................................................................ .............. 375 Appendix A: Tables ........................................................................ ..... 376

Appendix B: Some Properties of Excel Useful

Appendix C: Functions Useful Once the

During the Learning Process ....................................................... 382 Fundamentals Are Understood................................................... 386 Appendix D: Answers to Some of the Problems .................................. 387 Engineering Problem-Solver Index ............................................... 391 Index ........................................................................ ........................ 393 ix [This is a blank page.]quotesdbs_dbs4.pdfusesText_8

[PDF] DeCoursey-EXCEL-Statistics-and-Probability-for-Engineering

Statistics and Probability

With Microsoft

Statistics and Probability

With Microsoft

W.J. DeCoursey

College of Engineering,

University of Saskatchewan

Saskatoon

Newnes is an imprint of Elsevier Science.

ISBN: 0-7506-7618-3

British Library Cataloguing-in-Publication Data

For information, please contact:

Manager of Special Sales

Elsevier Science

225 Wildwood Avenue

Woburn, MA 01801-2041

Tel: 781-904-2500

Fax: 781-904-2620

Web home page at: http://www.newnespress.com

10 9 8 7 6 5 4 3 2 1

Printed in the United States of America

Contents

1. Introduction: Probability and Statistics......................................... 1

1.1 Some Important Terms ................................................................... 1

1.2 What does this book contain? ....................................................... 2

2. Basic Probability........................................................................

2.1 Fundamental Concepts .................................................................. 6

2.2 Basic Rules of Combining Probabilities ......................................... 11

2.2.1 Addition Rule .................................................................... 11

2.2.2 Multiplication Rule ............................................................ 16

2.3 Permutations and Combinations .................................................. 29

2.4 More Complex Problems: Bayes' Rule .......................................... 34

3. Descriptive Statistics: Summary Numbers ................................... 41

3.1 Central Location ........................................................................

3.2 Variability or Spread of the Data ................................................... 44

3.3 Quartiles, Deciles, Percentiles, and Quantiles ................................ 51

3.4 Using a Computer to Calculate Summary Numbers ...................... 55

4. Grouped Frequencies and Graphical Descriptions..................... 63

4.1 Stem-and-Leaf Displays ................................................................ 63

4.2 Box Plots ........................................................................

4.3 Frequency Graphs of Discrete Data .............................................. 66

4.4 Continuous Data: Grouped Frequency ......................................... 66

4.5 Use of Computers ........................................................................

5. Probability Distributions of Discrete Variables ........................... 84

5.1 Probability Functions and Distribution Functions .......................... 85

5.2 Expectation and Variance ............................................................. 88

5.3Binomial Distribution ................................................................. 101

5.4Poisson Distribution ................................................................... 117

5.5Extension: Other Discrete Distributions ....................................... 131

5.6Relation Between Probability Distributions and

Frequency Distributions

Corresponding Simulated Frequency Distributions

6. Probability Distributions of Continuous Variables ................... 141

6.1 Probability from the Probability Density Function ........................ 141

6.2Expected Value and Variance ..................................................... 149

6.3Extension: Useful Continuous Distributions ................................ 155

6.4Extension: Reliability ................................................................... 156

7. The Normal Distribution............................................................. 157

7.1Characteristics ........................................................................

7.2Probability from the Probability Density Function ........................ 158

7.3Using Tables for the Normal Distribution .................................... 161

7.4Using the Computer .................................................................. 173

7.5Fitting the Normal Distribution to Frequency Data ...................... 175

7.6Normal Approximation to a Binomial Distribution ...................... 178

7.7Fitting the Normal Distribution to Cumulative

Frequency Data

7.8Transformation of Variables to Give a Normal Distribution .......... 190

8. Sampling and Combination of Variables .................................. 197

8.1Sampling ........................................................................

8.2Linear Combination of Independent Variables ............................ 198

8.3Variance of Sample Means ......................................................... 199

8.4Shape of Distribution of Sample Means:

Central Limit Theorem

9. Statistical Inferences for the Mean............................................ 212

9.1Inferences for the Mean when Variance Is Known ...................... 213

9.1.1Test of Hypothesis ........................................................... 213

9.1.2Confidence Interval ......................................................... 221

9.2Inferences for the Mean when Variance Is

Estimated from a Sample