本书深入浅出地介绍统计理论与方法，突出统计思想，为便于读者学习和掌握所介绍的各种统计方法，列举了大量的实际数据例子。主要内容包括：概率、随机变量与概率分布、数学期望、一些离散概率分布、连续型概率分布、基本的抽样分布和数据描述、单样本和两样本的估计问题、单样本和两样本的假设检验、简单线性回归、单因子试验、析因试验等。

本书是数理统计学的优秀入门教材，深入浅出地介绍了统计理论与方法，通过大量的实际数据例子强调概率模型和统计方法的应用，使读者更能洞悉和体会统计思维与统计方法的本质。本书主要内容包括：统计与概率导论，随机变量、分布和数学期望，概率分布，抽样分布和数据描述，单样本和两样本的估计问题，单样本和两样本的假设检验，线性回归，析因试验等。

突出统计思想。本书中的统计方法大多是现代统计学的常用统计理论与方法，在介绍每一种统计方法前都详细叙述统计方法的思想。
注重实际应用。把抽象的统计理论与方法进行直观描述与总结，不偏重理论的推导，而是注重具体应用。
内容丰富，实用性强。书中含有大量的例子和习题，通过真实、科学的模型方案和数据使读者掌握统计方法。这些例子和习题不局限于工程领域，还包括一些社会学、经济学、生物学、物理学和计算机科学领域的应用。
要求数学知识少。只要读者掌握基本的微积分和非常简单的矩阵运算知识，就可以畅通无阻地阅读全书，并能应用所介绍的统计方法。

Preface
General Approach and Mathematical Level
This text was designed for a one-semester course that covers the essential
topics needed for a fundamental understanding of basic statistics and its
applications in the fields of engineering and the sciences. A balance
between theory and application is maintained throughout the text.　Coverage of analytical tools in statistics is enhanced with the use of calculus when discussion centers on rules and concepts in probability. Students using this text should have the equivalent of the completion of one semester of differential and integral calculus. Linear algebra would be helpful but not necessary if the instructor chooses not to include Section 7.11 on multiple linear regression using matrix algebra.
Class projects and case studies are presented throughout the text to give the student a deeper understanding of real-world usage of statistics.　Class projects provide the opportunity for students to work alone or in groups to gather their own experimental data and draw inferences using the data.　In some cases, the work conducted by the student involves a problem whose solution will illustrate the meaning of a concept and/or will provide an empirical understanding of an important statistical result. Case studies provide commentary to give the student a clear understanding in the context of a practical situation.　The comments we affectionately call “Pot Holes” at the end of each chapter present the big pic- ture and show how the chapters relate to one another.　
They also provide warn- ings about the possible misuse of statistical techniques presented in the chapter.A large number of exercises are available to challenge the student.　These exer- cises deal with real-life scientific and engineering applications.　The many data sets associated with the exercises are available for download from the website http://www.pearsonhighered.com/mathstatsresources.
Content and Course Planning
This textbook contains nine chapters. The first two chapters introduce the notion of random variables and their properties, including their role in characterizing data sets. Fundamental to this discussion is the distinction, in a practical sense, between populations and samples.
In Chapter 3, both discrete and continuous random variables are illustrated with examples.　The binomial, Poisson, hypergeometric, and other useful discrete distributions are discussed. In addition, continuous distributions include the nor-mal, gamma, and exponential.　In all cases, real-life scenarios are given to reveal how these distributions are used in practical engineering problems.
The material on specific distributions in Chapter 3 is followed in Chapter 4 bypractical topics such as random sampling and the types of descriptive statistics that convey the center of location and variability of a sample.　Examples involv- ing the sample mean and sample variance are included.　Following the introduc- tion of central tendency and variability is a substantial amount of material dealing with the importance of sampling distributions. Real-life illustrations highlight how sampling distributions are used in basic statistical inference.　Central Limit type methodology is accompanied by the mechanics and purpose behind the use of the normal, Student t, χ2 , and f　distributions, as well as examples that illustrate their use. Students are exposed to methodology that will be brought out again in later chapters in the discussions of estimation and hypothesis testing. This fundamental methodology is accompanied by illustration of certain important graphical meth- ods, such as stem-and-leaf and box-and-whisker plots. Chapter 4 presents the first of several case studies involving real data.
Chapters 5 and 6 complement each other, providing a foundation for the solu- tion of practical problems in which estimation and hypothesis testing
are employed. Statistical inference involving a single mean and two means, as well as one and two proportions, is covered.　Confidence intervals are
displayed and thoroughly dis- cussed; prediction intervals and tolerance intervals are touched upon.　Problems with paired observations are covered
in detail.
In Chapter 7, the basics of simple linear regression (SLR) and multiple linear regression (MLR) are covered in a depth suitable for a one-semester course. Chap- ters 8 and 9 use a similar approach to expose students to the standard methodology associated with analysis of variance (ANOVA). Although
regression and ANOVA are challenging topics, the clarity of presentation, along with case studies, class projects, examples, and exercises, allows
students to gain an understanding of the essentials of both.
In the discussion of rules and concepts in probability, the coverage of analytical tools is enhanced through the use of calculus.　Though the material on multiple linear regression in Chapter 7 covers the essential methodology, students are not burdened with the level of matrix algebra and relevant manipulations that they would confront in a text designed for a two-semester course.
Computer Software
Case studies, beginning in Chapter 4, feature computer printout and graphical material generated using both SASR　　and MINITABR　. The inclusion of the com-puter reflects our belief that students should have the experience of reading and interpreting computer printout and graphics, even if the software in the text is not that which is used by the instructor. Exposure to more than one type of software can broaden the experience base for the student. There is no reason to believe that the software used in the course will be that which the student will be called upon to use in a professional setting.
Supplements Instructor’s Solutions Manual. This resource contains worked-out solutions to all text exercises and is available for download from Pearson’s Instructor Resource Center at www.pearsonhighered.com/irc.
Student’s Solutions Manual. ISBN-10: 0-321-78399-9; ISBN-13: 978-0-321-78399-8.　This resource contains complete solutions to selected exercises.　It is available for purchase from MyPearsonStore at www.mypearsonstore.com, or ask your local representative for value pack options.
PowerPointR　　Lecture　Slides.　These slides include most of the figures and tables from the text. Slides are available for download from Pearson’s
Instructor Resource Center at www.pearsonhighered.com/irc.
Looking for more comprehensive coverage for a two-semester course See the more comprehensive book Probability　and　Statistics　for　Engineers　and　
Scientists, 9th edition, by Walpole, Myers, Myers, and Ye (ISBN-10:　0-321-62911-6; ISBN-13:978-0-321-62911-1).
Acknowledgments
We are indebted to those colleagues who provided many helpful suggestions for this text.　They are David Groggel, Miami University; Lance Hemlow, Raritan Valley Community College; Ying Ji, University of Texas at San Antonio; Thomas Kline, University　of　Northern　Iowa; Sheila Lawrence, Rutgers　University; Luis Moreno, Broome County Community College; Donald Waldman, University of Colorado— Boulder;　and Marlene Will, Spalding　University.　 We would also like to thank Delray Schultz, Millersville　University, and Keith Friedman, University　of　Texas— Austin, for ensuring the accuracy of this text.
We would like to thank the editorial and production services provided by nu- merous people from Pearson/Prentice Hall, especially the editor in chief Deirdre Lynch, acquisitions editor Chris Cummings, sponsoring editor Christina Lepre, as- sociate content editor Dana Bettez, editorial assistant Sonia Ashraf, production project manager Tracy Patruno, and copyeditor Sally Lifland. We thank the Vir- ginia Tech Statistical Consulting Center, which was the source of many real-life data sets.

R.H.M.
S.L.M.
K.Y.

数学

本书是数理统计学的优秀入门教材，深入浅出地介绍了统计理论与方法，通过大量的实际数据例子强调概率模型和统计方法的应用，使读者更能洞悉和体会统计思维与统计方法的本质。本书主要内容包括：统计与概率导论，随机变量、分布和数学期望，概率分布，抽样分布和数据描述，单样本和两样本的估计问题，单样本和两样本的假设检验，线性回归，析因试验等。

　　 本书特色
　　 突出统计思想。本书中的统计方法大多是现代统计学的常用统计理论与方法，在介绍每一种统计方法前都详细叙述统计方法的思想。
　　 注重实际应用。把抽象的统计理论与方法进行直观描述与总结，不偏重理论的推导，而是注重具体应用。
　　 内容丰富，实用性强。书中含有大量的例子和习题，通过真实、科学的模型方案和数据使读者掌握统计方法。这些例子和习题不局限于工程领域，还包括一些社会学、经济学、生物学、物理学和计算机科学领域的应用。
　　 要求数学知识少。只要读者掌握基本的微积分和非常简单的矩阵运算知识，就可以畅通无阻地阅读全书，并能应用所介绍的统计方法

Preface. . . . . . . . . . . . . . . . . . . iii
1 Introduction to Statistics and Probability. . . . . . 1
1.1 Overview:　Statistical Inference, Samples, Populations, and the
Role of Probability . . . . . . . . 1
1.2 Sampling Procedures; Collection of Data . . . .. . . . . . . . 7
1.3 Discrete and Continuous Data . . . . . . . . . .. . . . . . 11
1.4 Probability: Sample Space and Events . . . . . . . . . . 11
Exercises . . . . . . . . . . . . . . . . . . . . . . . 18
1.5 Counting Sample Points . . . . . . . . . . . . . . . 20
Exercises . . . . . . . . . . . . . 24
1.6 Probability of an Event . . . . . . . . . . . . . . . 25
1.7 Additive Rules . . . . . . . .. . . . 27
Exercises . . . . . . . . . . . . . 31
1.8 Conditional Probability, Independence, and the Product Rule . . . 33
Exercises . . . . . . . . . . . . . . .　. . . . . . . . 39
1.9 Bayes’ Rule . . . .　. . . . . . . . . 41
Exercises . . . . . . . . .　. . . . 46
Review Exercises . . . . . . . . 47
2 Random Variables, Distributions,
and Expectations . . . . . . . .. . . . . . . . 49
2.1 Concept of a Random Variable . . . .　. . . . . . . . . . 49
2.2 Discrete Probability Distributions . . . . . . . . .. . . . . . . 52
2.3 Continuous Probability Distributions . . . . . .. . . . . . . . 55
Exercises . . . . . . . .. . . . . . . . 59
2.4 Joint Probability Distributions . . . . . . . . . . . . . . 62
Exercises . . . . . . . . . . . . . . . .　. . . . . . . . . 72
2.5 Mean of a Random Variable . . . .. . . . . . . . . . . . . . 74
Exercises . . . . . . . . . . . . . .　. . . . . . . . 79
2.6 Variance and Covariance of Random Variables. . . . . . . 81
Exercises . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 88
2.7 Means and Variances of Linear Combinations of Random Variables 89
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 94
Review Exercises . . . . . . . . . . . . . . . .. . . . . . . 95
2.8 Potential Misconceptions and Hazards;
Relationship to Material in Other Chapters . . . . . . . . . . . . 99
3 Some Probability Distributions . . . . . . . . 101
3.1 Introduction and Motivation . . . . . . . . .. . . . . . 101
3.2 Binomial and Multinomial Distributions . . .. 101
Exercises . . . . . . . . . . . . . . . . . . . . . . . . 108
3.3 Hypergeometric Distribution . . . . . . . . .. . . . . . 109
Exercises . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 113
3.4 Negative Binomial and Geometric Distributions . . . . . . . . . 114
3.5 Poisson Distribution and the Poisson Process . . . . . . . . . . 117
Exercises . . . . . . . . . . . . . . . . . . 120
3.6 Continuous Uniform Distribution . . . . . . .. . . . 122
3.7 Normal Distribution . . . . . . . . . . . . . . 123
3.8 Areas under the Normal Curve . . . . . . . .. . . . . 126
3.9 Applications of the Normal Distribution . . .. 132
Exercises . . . . . . . . . . . . . . .　. . . 135
3.10 Normal Approximation to the Binomial . . . . . .. . . . . . 137
Exercises . . . . . . . . . . . . . .. . . . . . 142
3.11 Gamma and Exponential Distributions . . . .. 143
3.12 Chi-Squared Distribution . . . . . . . .　. . . 149
Exercises . . . . . . . . . . . . . . . . . . . . . . . 150
Review Exercises . . . . . . . . . . . . . . . .. . . . 151
3.13 Potential Misconceptions and Hazards;
Relationship to Material in Other Chapters . . . . . . . . . . 155
4 Sampling Distributions and Data Descriptions 157
4.1 Random Sampling . . . . . . . . . . . . . . . . 157
4.2 Some Important Statistics . . . . . . . . . . . . . 159
Exercises . . . . . . . . . . . . . . . . . . . . . . 162
4.3 Sampling Distributions . . . . . . . . . . . . . . . 164
4.4 Sampling Distribution of Means and the Central Limit Theorem . 165
Exercises . . . . . . . . . . . . . . .　. . . . . . . 172
4.5 Sampling Distribution of S2 . . . . . . . . . . . 174
4.6 t-Distribution . . . . . . . . . . . . . . 176
4.7 F -Distribution . . . . . . . . . . . . . . . 180
4.8 Graphical Presentation . . . . . . . . . . . . . 183
Exercises . . . . . . . . . . . . . . . . . . . 190
Review Exercises . . . . . . . . . . . .. . . . 192
4.9 Potential Misconceptions and Hazards;
Relationship to Material in Other Chapters . . . . . . . . . . . . . 194
5 One- and Two-Sample Estimation Problems 195
5.1 Introduction . . . . . . . . . . . . . . . . . . 195
5.2 Statistical Inference . . . . . . . . . . . . . 195
5.3 Classical Methods of Estimation . . . . . . .. . . . . 196
5.4 Single Sample: Estimating the Mean . . . . .. . 199
5.5 Standard Error of a Point Estimate . . . . .. . . 206
5.6 Prediction Intervals . . . . . . . . . . . . . 207
5.7 Tolerance Limits . . . . . . . . . . . . . . . 210
Exercises . . . . . . . . . . . . . . . . . . . . . . . . 212
5.8 Two Samples: Estimating the Difference between Two Means . . . 214
5.9 Paired Observations . . . . . . . . . . . . . . . . 219
Exercises . . . . . . . . . . . . . .. . . . . . . . 221
5.10 Single Sample: Estimating a Proportion . . .. 223
5.11 Two Samples: Estimating the Difference between Two Proportions　 226
Exercises . . . . . . . . . . . . . . . . .. . . . 227
5.12 Single Sample: Estimating the Variance . . .. 228
Exercises . . . . . . . . . . . . . . . . . . . . . . . . 230
Review Exercises . . . . . . . . . . . . . . . .. . . 230
5.13 Potential Misconceptions and Hazards;
Relationship to Material in Other Chapters . . . . . . . . . . . . 233
6 One- and Two-Sample Tests of Hypotheses . . .　235
6.1 Statistical Hypotheses: General Concepts . . . . . . . . . . . . 235
6.2 Testing a Statistical Hypothesis . . . . . .. . . . . . 237
6.3 The Use of P -Values for Decision Making in Testing Hypotheses . 247
Exercises . . . . . . . . . . . . . . . . . . . .. . . . . . . . 250
6.4 Single Sample: Tests Concerning a Single Mean . . . . . . . 251
6.5 Two Samples: Tests on Two Means . . . . . . .. 258
6.6 Choice of Sample Size for Testing Means . . . . . . . . . . . . . 264
6.7 Graphical Methods for Comparing Means . . . . . . .. . . . . . 266
Exercises . . . . . . . . . .　. . . . . . . . 268
6.8 One Sample: Test on a Single Proportion. . . . .. . . . . . . . 272
6.9 Two Samples: Tests on Two Proportions . . . . . . . . . . . . . . 274
Exercises . . . . . . . . . . . . . . . . . . . . . . . 276
6.10 Goodness-of-Fit Test . . . . . . . . . . . ... . . . . 277
6.11 Test for Independence (Categorical Data) . .　. . . . . . . . . 280
6.12 Test for Homogeneity . . . . . . . . . . .　. . . 283
6.13 Two-Sample Case Study . . . . . . . . . . . . 286
Exercises . . . . . . . . . . . . . . . . . . . .. . .　. . 288
Review Exercises . . . . . . . . . . . . . . . .. . . . . . . 290
6.14 Potential Misconceptions and Hazards;
Relationship to Material in Other Chapters . . . . . . . . . . . 292
7 Linear Regression . . . . . . . . . . . . . . .. .　 295
7.1 Introduction to Linear Regression . . . . . .. . . . 295
7.2 The Simple Linear Regression (SLR) Model and the
Least Squares Method. . . . . . . . . . . . . . . . . . 296
Exercises . . . . . . . . . . . . . . . . . . . . . 303
7.3 Inferences Concerning the Regression Coeffcients. . . .. . . . 306
7.4 Prediction . . . . .　. . . . . . . . . . 314
Exercises . . . . . . . . . . . . . . . . . . . . . . . . 318
7.5 Analysis-of-Variance Approach . . . . . . . .. . . . . 319
7.6 Test for Linearity of Regression: Data with Repeated Observations　 324
Exercises . . . . . . . . . . . . . . . . . . . .. . . . 327
7.7 Diagnostic Plots of Residuals: Graphical Detection of Violation of Assumptions . . . . . . . . . . . . . .. . . 330
7.8 Correlation . . . . . . . . . . . . . 331
7.9 Simple Linear Regression Case Study . . . . .. . 333
Exercises . . . . . . . . . . . . . . . 335
7.10 Multiple Linear Regression and Estimation of the Coeffcients . . . 335
Exercises . . . . . . . . . . . . . . . . . . 340
7.11 Inferences in Multiple Linear Regression . .. . 343
Exercises . . . . . . . . . . . . . . . . . 346
Review Exercises . . . . . .　. . . . . . 346
8 One-Factor Experiments: General . . . . . . . . . . . .　 355
8.1 Analysis-of-Variance Technique and the Strategy of Experimental Design . . . . . . . . . . . . 355
8.2 One-Way Analysis of Variance (One-Way ANOVA):
Completely Randomized Design . . . . . . . . . .. . 357
8.3 Tests for the Equality of Several Variances . . . . . . . . . 364
Exercises . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 366
8.4 Multiple Comparisons . . . . . . . . . . . .. . . . . . . . . . 368
Exercises . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 371
8.5 Concept of Blocks and the Randomized Complete Block Design . 372
Exercises . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 380
8.6 Random Effects Models . . . . . . . . . . . .. . . . . . . . 383
8.7 Case Study for One-Way Experiment . . . . . .. 385
Exercises . . . . . . . . . . . . . . . . . . . . . . . 387
Review Exercises . . . . . . . . . . . . . . . .. . . . . . . 389
8.8 Potential Misconceptions and Hazards;
Relationship to Material in Other Chapters . . . . . . .. . . . . 392
9 Factorial Experiments (Two or More Factors) 393
9.1 Introduction . . . . . . . . . . . . .　. . . 393
9.2 Interaction in the Two-Factor Experiment . . . . . . . . . . . . 394
9.3 Two-Factor Analysis of Variance . . . . . . .. . . . 397
Exercises . . . . . . . . . . . . . . . . . .　. . . . 406
9.4 Three-Factor Experiments . . . . . . . .. . . . 409
Exercises . . . . . . . . . . . . . . . . . . 416
Review Exercises . . . . . . . . . . . .　. . 419
9.5 Potential Misconceptions and Hazards;
Relationship to Material in Other Chapters . . . . . . . . . . 421
Bibliography . . . . . . . . . . . . . . . . . . . . . .　 423
Appendix A: Statistical Tables and Proofs . . . . . . . .　427
Appendix B: Answers to Odd-Numbered
Non-Review Exercises . . . . . . .. . .　 455
Index . . . . . . . . . . . . . . . . . . . . . .　 463