Introductory Statistics (eBook)

Front Cover 1
Title Page 4
Copyright Page 5
About the Author 6
Dedication 7
Table of Contents 8
Preface 18
Acknowledgments 22
Chapter 1. Introduction to Statistics 24
1.1 Introduction 24
1.2 The Nature of Statistics 26
1.2.1 Data Collection 26
1.2.2 Inferential Statistics and Probability Models 27
1.3 Populations and Samples 28
*1.3.1 Stratified Random Sampling 29
1.4 A Brief History of Statistics 30
Key Terms 33
The Changing Definition of Statistics 34
Review Problems 34
Chapter 2. Describing Data Sets 40
2.1 Introduction 41
2.2 Frequency Tables and Graphs 41
2.2.1 Line Graphs, Bar Graphs, and Frequency Polygons 42
2.2.2 Relative Frequency Graphs 44
2.2.3 Pie Charts 47
Problems 48
2.3 Grouped Data and Histograms 55
Problems 62
2.4 Stem-and-Leaf Plots 67
Problems 70
2.5 Sets of Paired Data 74
Problems 77
2.6 Some Historical Comments 81
Key Terms 82
Summary 83
Review Problems 86
Chapter 3. Using Statistics to Summarize Data Sets 94
3.1 Introduction 95
3.2 Sample Mean 96
3.2.1 Deviations 101
Problems 102
3.3 Sample Median 106
Problems 109
3.3.1 Sample Percentiles 113
3.4 Sample Mode 120
Problems 121
3.5 Sample Variance and Sample Standard Deviation 122
Problems 128
3.6 Normal Data Sets and the Empirical Rule 132
3.7 Sample Correlation Coefficient 143
Problems 151
Key Terms 157
Summary 159
Review Problems 161
Chapter 4. Probability 168
4.1 Introduction 169
4.2 Sample Space and Events of an Experiment 169
Problems 173
4.3 Properties of Probability 176
Problems 179
4.4 Experiments Having Equally Likely Outcomes 184
Problems 187
4.5 Conditional Probability and Independence 190
Problems 200
*4.6 Bayes’ Theorem 208
Problems 210
*4.7 Counting Principles 212
Problems 218
Key Terms 221
Summary 223
Review Problems 224
Chapter 5. Discrete Random Variables 232
5.1 Introduction 233
5.2 Random Variables 234
Problems 238
5.3 Expected Value 241
5.3.1 Properties of Expected Values 244
Problems 248
5.4 Variance of Random Variables 254
5.4.1 Properties of Variances 256
Problems 259
5.5 Binomial Random Variables 261
5.5.1 Expected Value and Variance of a Binomial Random Variable 266
Problems 267
*5.6 Hypergeometric Random Variables 271
Problems 272
*5.7 Poisson Random Variables 273
Problems 276
Key Terms 277
Summary 277
Review Problems 279
Chapter 6. Normal Random Variables 284
6.1 Introduction 285
6.2 Continuous Random Variables 285
Problems 287
6.3 Normal Random Variables 289
Problems 292
6.4 Probabilities Associated with a Standard Normal Random Variable 294
Problems 299
6.5 Finding Normal Probabilities: Conversion to the Standard Normal 300
6.6 Additive Property of Normal Random Variables 302
Problems 304
6.7 Percentiles of Normal Random Variables 307
Problems 312
Key Terms 313
Summary 313
Review Problems 316
Chapter 7. Distributions of Sampling Statistics 320
7.1 A Preview 321
7.2 Introduction 321
7.3 Sample Mean 322
Problems 326
7.4 Central Limit Theorem 327
7.4.1 Distribution of the Sample Mean 329
7.4.2 How Large a Sample Is Needed? 333
Problems 334
7.5 Sampling Proportions from a Finite Population 336
7.5.1 Probabilities Associated with Sample Proportions: The Normal Approximation to the Binomial Distribution 340
Problems 342
7.6 Distribution of the Sample Variance of a Normal Population 346
Problems 348
Key Terms 348
Summary 349
Review Problems 350
Chapter 8. Estimation 354
8.1 Introduction 355
8.2 Point Estimator of a Population Mean 356
Problems 357
8.3 Point Estimator of a Population Proportion 359
Problems 361
*8.3.1 Estimating the Probability of a Sensitive Event 364
Problems 365
8.4 Estimating a Population Variance 365
Problems 367
8.5 Interval Estimators of the Mean of a Normal Population with Known Population Variance 370
8.5.1 Lower and Upper Confidence Bounds 378
Problems 380
8.6 Interval Estimators of the Mean of a Normal Population with Unknown Population Variance 382
8.6.1 Lower and Upper Confidence Bounds 387
Problems 389
8.7 Interval Estimators of a Population Proportion 394
8.7.1 Length of the Confidence Interval 396
8.7.2 Lower and Upper Confidence Bounds 398
Problems 400
Key Terms 403
Summary 404
Review Problems 406
Chapter 9. Testing Statistical Hypotheses 410
9.1 Introduction 411
9.2 Hypothesis Tests and Significance Levels 411
Problems 415
9.3 Tests Concerning the Mean of a Normal Population: Case of Known Variance 417
Problems 423
9.3.1 One-Sided Tests 426
9.4 The t Test for the Mean of a Normal Population: Case of Unknown Variance 432
Problems 440
9.5 Hypothesis Tests Concerning Population Proportions 444
9.5.1 Two-Sided Tests of p 448
Problems 452
Key Terms 456
Summary 456
Review Problems and Proposed Case Studies 460
Chapter 10. Hypothesis Tests Concerning Two Populations 466
10.1 Introduction 467
10.2 Testing Equality of Means of Two Normal Populations: Case of Known Variance 469
Problems 473
10.3 Testing Equality of Means: Unknown Variances and Large Sample Sizes 476
Problems 482
10.4 Testing Equality of Means: Small-Sample Tests When the Unknown Population Variances Are Equal 486
Problems 491
10.5 Paired-Sample t Test 494
Problems 499
10.6 Testing Equality of Population Proportions 504
Problems 513
Key Terms 516
Summary 516
Review Problems 521
Chapter 11. Analysis of Variance 526
11.1 Introduction 527
11.2 One-Factor Analysis of Variance 528
A Remark on the Degrees of Freedom 530
Problems 533
11.3 Two-Factor Analysis of Variance: Introduction and Parameter Estimation 537
Problems 541
11.4 Two-Factor Analysis of Variance: Testing Hypotheses 543
Problems 550
11.5 Final Comments 552
Key Terms 553
Summary 553
Review Problems 556
Chapter 12.Linear Regression 560
12.1 Introduction 562
12.2 Simple Linear Regression Model 563
Problems 565
12.3 Estimating the Regression Parameters 567
Problems 571
12.4 Error Random Variable 576
Problems 579
12.5 Testing the Hypothesis that ß = 0 580
Problems 583
12.6 Regression to the Mean 587
*12.6.1 Why Biological Data Sets Are Often Normally Distributed 592
Problems 593
12.7 Prediction Intervals for Future Responses 596
Problems 598
12.8 Coefficient of Determination 601
Problems 603
12.9 Sample Correlation Coefficient 605
Problems 606
12.10 Analysis of Residuals: Assessing the Model 607
Problems 609
12.11 Multiple Linear Regression Model 609
12.11.1 Dummy Variables for Categorical Data 613
Problems 615
Key Terms 618
Summary 618
Review Problems 622
Chapter 13. Chi-Squared Goodness-of-Fit Tests 628
13.1 Introduction 629
13.2 Chi-Squared Goodness-of-Fit Tests 632
Problems 638
13.3 Testing for in Dependence in Populations Classified According to Two Characteristics 643
Problems 649
13.4 Testing for Independence in Contingency Tables with Fixed Marginal Totals 654
Problems 657
Key Terms 660
Summary 661
Review Problems 663
Chapter 14. Nonparametric Hypotheses Tests 670
14.1 Introduction 671
14.2 Sign Test 671
14.2.1 Testing the Equality of Population Distributions when Samples Are Paired 675
14.2.2 One-Sided Tests 676
Problems 678
14.3 Signed-Rank Test 680
14.3.1 Zero Differences and Ties 685
Problems 687
14.4 Rank-Sum Test for Comparing Two Populations 690
14.4.1 Comparing Nonparametric Tests with Tests that Assume Normal Distributions 695
Problems 696
14.5 Runs Test for Randomness 699
Problems 704
14.6 Testing the Equality of Multiple Probability Distributions 706
14.6.1 When the Data Are a Set of Comparison Rankings 708
Problems 711
14.7 Permutation Tests 712
Problems 715
Key Terms 716
Summary 716
Review Problems 719
Chapter 15. Quality Control 722
15.1 Introduction 723
15.2 The X Control Chart for Detecting a Shift in the Mean 723
Problems 728
15.2.1 When the Mean and Variance Are Unknown 730
15.2.2 S Control Charts 733
Problems 736
15.3 Control Charts for Fraction Defective 738
Problems 740
15.4 Exponentially Weighted Moving-Average Control Charts 740
Problems 744
15.5 Cumulative-Sum Control Charts 745
Problems 748
Key Terms 748
Summary 748
Review Problems 749
Appendices 750
Appendix A. Data Set 752
Appendix B. Mathematical Preliminaries 756
B.1 Summation 756
B.2 Absolute Value 756
B.3 Set Notation 757
Appendix C. How to Choose a Random Sample 758
Appendix D. Tables 762
Table D.1 Standard Normal Probabilities 762
Table D.2 Percentiles tn,a of t Distributions 763
Table D.3 Percentiles .2n,a of the Chi-Squared Distributions 764
Table D.4 Percentiles of F Distributions 766
Table D.5 Binomial Distribution Function 772
Appendix E. Programs 778
Answers to Odd-Numbered Problems 780
Index 830