Probability and Statistics (Asia Adaptation)

Erscheinungsjahr 2012
ISBN: 978-0-07-108785-8
Verlag: McGraw-Hill Education

Buch, Englisch, 450 Seiten, Format (B × H): 202 mm x 255 mm, Gewicht: 794 g

This textbook helps students to understand statistical methods and reasoning as well as practice in using them. The examples and exercises are specially chosen for those looking for careers in the engineering and computing sciences. The text is intended as a first course in probability and applied statistics for students.A set of exercises is provided throughout the text, in a section for every chapter. In addition, each chapter has a set of review exercises in which the problems are presented in random order. It is hoped that this will help the student develop the ability to recognise the appropriate analysis. Many exercises are left open-ended in hopes of stimulating some classroom discussion. The use of electronic calculators with some built-in statistical capability is encouraged, for it allows the student to concentrate on the interpretation of the analysis rather than on the arithmetic computations.The contents of this edition focus on the applications of Statistics, rather than the mathematical details. Bearing this in mind, a section titled Real World Application has been added to three topics–Comparing Two Means and Two Variances, Analysis of Variance, and Categorical Data, for students to better relate the key concepts learned, to real cases. Another significant addition to this edition is the easy presentation of hypothesis testing. The conclusion of hypothesis testing is drawn by comparing the value of test statistic and the critical value(s), rather than the estimated P value. Moreover, hypothesis testing is presented in a “4-step format”: 1) [Hypotheses]. 2) [Test statistic]. 3) [Critical value]. 4) [Conclusion]. Nevertheless, P value is still estimated. Since the authors view statistics as an art as well as science, it is anticipated and welcomed that students disagree with the conclusion at a particular level of significance. Some large data sets to this edition have been added to better reflect the reality students will encounter after graduation, and for students to learn to manipulate such data analysis via computer. Hence, additional essential instruction has been included, in the interpretation of statistical packages. The packages chosen for illustrative purposes are SAS and MINITAB. This was done because of their widespread availability and ease of use. Most data sets are simulated with care, so that the results of the analysis are consistent with recently reported research. This allows students to gain more insight into the type of real-world engineering problems.In addition, more discussion of the interpretation of computer output is now included in the text. Some of the more difficult derivations have been placed in an Appendix. This gives the text a more applied flavor while preserving the material for those who are particularly interested in the mathematical foundations of the statistical concepts presented.

Autoren/Hrsg.

Milton, J. Susan

Liu, Kwong Ip

Arnold, Jesse

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker

Inhaltsverzeichnis

Probability and Statisticsbody,td,th {font-family: Arial, Helvetica, sans-serif;}Table of Contents

Preface xi
Acknowledgements xvChapter 1
Introduction to Probability and Counting 1
1.1 Interpreting Probabilities 3
1.2 Sample Spaces and Events 4
Mutually Exclusive Events 8
Chapter Summary 8
Exercises 9
Review Exercises 11Chapter 2
Some Probability Laws 13
2.1 Axioms of Probability 13
The General Addition Rule 14
2.2 Conditional Probability 16
2.3 Independence and the Multiplication Rule 17
The Multiplication Rule 21
2.4 Bayes’ Theorem 22
Chapter Summary 24
Exercises 25
Review Exercises 29Chapter 3
Discrete Distributions 31
3.1 Random Variables 31
3.2 Discrete Probability Densities 32
Cumulative Distribution 34
3.3 Expectation and Distribution Parameters 35
Variance and Standard Deviation 38
3.4 Binomial Distribution 42
3.5 Poisson Distribution 45
3.6 Simulating a Discrete Distribution 47
Chapter Summary 49
Exercises 50
Review Exercises 58Chapter 4
Continuous Distributions 60
4.1 Continuous Densities 60
Cumulative Distribution 63
Uniform Distribution 65
4.2 Expectation and Distribution Parameters 65
4.3 Normal Distribution 67
Standard Normal Distribution 69
4.4 Normal Probability Rule and Chebyshev’s Inequality 71
Chebyshev’s Inequality 73
4.5 Normal Approximation to the Binomial Distribution 74
4.6 Simulating a Continuous Distribution 76
Chapter Summary 77
Exercises 78
Review Exercises 87Chapter 5
Descriptive Statistics 90
5.1 Random Sampling 90
5.2 Picturing the Distribution 93
Stem-and-Leaf Diagram 93
Histograms and Ogives 95
Cumulative Distribution Plots (Ogives) 98
5.3 Sample Statistics 100
Location Statistics 100
Measures of Variability 101
5.4 Boxplots 104
Finding the Sample Interquartile Range 104
Constructing a Boxplot 106
Chapter Summary 108
Exercises 109
Review Exercises 116Chapter 6
Estimation 120
6.1 Point Estimation 120
6.2 Functions of Random Variables—Distribution of 123
6.3 Interval Estimation and the Central Limit Theorem 124
Confidence Interval on the Mean: Variance Known 124
Central Limit Theorem 128
Chapter Summary 129
Exercises 130
Review Exercises 134Chapter 7
Inferences on the Mean and Variance of a Distribution 137
7.1 Interval Estimation of Variability 137
7.2 Estimating the Mean and the Student-t Distribution 140
The T Distribution 141
Confidence Interval on the Mean: Variance Estimated 143
7.3 Hypothesis Testing 144
7.4 Significance Testing 149
7.5 Hypothesis and Significance Tests on the Mean 151
7.6 Hypothesis Tests on the Variance 157
7.7 Alternative Nonparametric Methods 158
Sign Test for Median 159
Wilcoxon Signed-Rank Test 161
Chapter Summary 163
Exercises 164
Review Exercises 180Chapter 8
Inferences on Proportions 185
8.1 Estimating Proportions 185
Confidence Interval on p 186
Sample Size for Estimating p 188
8.2 Testing Hypotheses on a Proportion 189
8.3 Comparing Two Proportions: Estimation 191
Confidence Interval on p1 - p2 192
8.4 Comparing Two Proportions: Hypothesis Testing 194
Pooled Proportions 195
Chapter Summary 197
Exercises 198
Review Exercises 204Chapter 9
Comparing Two Means and Two Variances 207
9.1 Point Estimation: Independent Samples 207
9.2 Comparing Variances: The F Distribution 209
9.3 Comparing Means: Variances Equal (Pooled Test) 212
Confidence Interval on µ1 - µ2: Pooled 212
Pooled T Test 215
9.4 Comparing Means: Variances Unequal 217
9.5 Comparing Means: Paired Data 219
Paired T Test 220
9.6 Alternative Nonparametric Methods 221
Wilcoxon Rank-Sum Test 221
Wilcoxon Signed-Rank Test for Paired Observations 223
9.7 A Note on Technology 225
Chapter Summary 227
Real World Application of Comparing Two Means 227
Exercises 228
Review Exercises 240Chapter 10
Simple Linear Regression and Correlation 246
10.1 Model and Parameter Estimation 247
Description of Model 247
Least-Squares Estimation 249
10.2 Properties of Least-Squares Estimators 253
Distribution of B1 254
Distribution of B0 257
Estimator of s2 258
Summary of Theoretical Results 258
10.3 Confidence Interval Estimation and Hypothesis Testing 259
Inferences about Slope 260
Inferences about Intercept 263
Inferences about Estimated Mean 264
Inferences about Single Predicted Value 265
10.4 Residual Analysis 269
Residual Plots 269
Checking for Normality: Stem-and-Leaf Plots and Boxplots 272
10.5 Correlation 278
Interval Estimation and Hypothesis Tests on r 281
Coefficient of Determination 284
Chapter Summary 285
Exercises 286
Review Exercises 294Chapter 11
Analysis of Variance 298
11.1 One-Way Classification Fixed-Effects Model 299
The Model 301
Testing H0 303
11.2 Comparing Variances 308
11.3 Pairwise Comparisons 310
Bonferroni T Tests 310
Duncan’s Multiple Range Test 312
Tukey’s Test 315
11.4 Alternative Nonparametric Methods 315
Kruskal-Wallis Test 316
Chapter Summary 317
Real World Application of Analysis of Variance 317
Exercises 318
Review Exercises 323
Chapter 12 Categorical Data 327
12.1 Multinomial Distribution 327
12.2 Chi-Squared Goodness of Fit Tests 329
12.3 Testing for Independence 330
r × c Test for Independence 335
12.4 Comparing Proportions 336
r × c Test for Homogeneity 339
Comparing Proportions with Paired Data: McNemar’s Test 341
Chapter Summary 342
Real World Application of Comparing Proportions 343
Exercises 343
Review Exercises 348Appendixes
A Statistical Tables 354
B Answers to Selected Problems 389
C Selected Derivations 417
Index 421

Über Autor(innen)

Liu, Kwong Ip
Liu, Kwong Ip is a Lecturer in the Department of Mathematics at Hong Kong Baptist University. Dr.Liu received the BSc. degree from the City Polytechnic of Hong Kong, the MSc. degree from the University of Hong Kong, and Ph.D. degree from Hong Kong Baptist University.

Milton, J. Susan
J.Susan Milton is professor Emeritus of Satatics at Radford University. Dr. Milton recieved the B.S. degree from Western Carolina University, the M.A. degree from the University of North Carolina at Chapel Hill, and the Ph.D degree in Statistics from Virginia Polytechnic Institute and State university. She is a Danforth Associate and is a recipient of the Radford University Foundation Award for Excellence in Teaching. Dr. Milton is the author of Statistical Methods in the Biological and Health Sciences as well as Introduction to statistics, Probability with the Essential Analysis, and a first Course in the Theory of Linear Statistical Models.

Arnold, Jesse
Jesse C. arnold is a Professor of Statistics at Virginia Polytechnic Insitute and state University. Dr. arnold received the B.S. Degree from Southeastern state University, and the M.A and Ph. D degrees in statistics from Florida state university. He served as head of Statistics department for ten years, is a fellow of the American Statistical Association, and elected member of the International Statistics Institute. Ha has served as President of the International Biometric Society (Eastern North American Region) and Chairman of the statistical Educational Section of the American Statistical Association.