Introductory statistics

Cover Page......Page 1
Title Page......Page 4
Copyright Page......Page 5
ABOUT THE AUTHOR......Page 6
DEDICATION......Page 7
PREFACE......Page 18
ACKNOWLEDGMENTS......Page 22
Contents......Page 8
 1.1 Introduction......Page 24
  1.2.1 Data Collection......Page 26
  1.2.2 Inferential Statistics and Probability Models......Page 27
 1.3 Populations and Samples......Page 28
  1.3.1 Stratified Random Sampling......Page 29
 1.4 A Brief History of Statistics......Page 30
 Key Terms......Page 33
 Review Problems......Page 34
Chapter 2 Describing Data Sets......Page 40
 2.2 Frequency Tables and Graphs......Page 41
  2.2.1 Line Graphs, Bar Graphs, and Frequency Polygons......Page 42
  2.2.2 Relative Frequency Graphs......Page 44
  2.2.3 Pie Charts......Page 47
  Problems......Page 48
 2.3 Grouped Data and Histograms......Page 55
  Problems......Page 62
 2.4 Stem-and-Leaf Plots......Page 67
  Problems......Page 70
 2.5 Sets of Paired Data......Page 74
  Problems......Page 77
 2.6 Some Historical Comments......Page 81
 Key Terms......Page 82
 Summary......Page 83
 Review Problems......Page 86
Chapter 3 Using Statistics to Summarize Data Sets......Page 94
 3.1 Introduction......Page 95
 3.2 Sample Mean......Page 96
  3.2.1 Deviations......Page 101
  Problems......Page 102
 3.3 Sample Median......Page 106
  Problems......Page 109
  3.3.1 Sample Percentiles......Page 113
 3.4 Sample Mode......Page 120
  Problems......Page 121
 3.5 Sample Variance and Sample Standard Deviation......Page 122
  Problems......Page 128
 3.6 Normal Data Sets and the Empirical Rule......Page 132
  Problems......Page 137
 3.7 Sample Correlation Coefficient......Page 143
  Problems......Page 151
 Key Terms......Page 157
 Summary......Page 159
 Review Problems......Page 161
Chapter 4 Probability......Page 168
 4.2 Sample Space and Events of an Experiment......Page 169
  Problems......Page 173
 4.3 Properties of Probability......Page 176
  Problems......Page 179
 4.4 Experiments Having Equally Likely Outcomes......Page 184
  Problems......Page 187
 4.5 Conditional Probability and Independence......Page 190
  Problems......Page 200
 4.6 Bayes’ Theorem......Page 208
  Problems......Page 210
 4.7 Counting Principles......Page 212
  Problems......Page 218
 Key Terms......Page 221
 Summary......Page 223
 Review Problems......Page 224
Chapter 5 Discrete Random Variables......Page 232
 5.1 Introduction......Page 233
 5.2 Random Variables......Page 234
  Problems......Page 238
 5.3 Expected Value......Page 241
  5.3.1 Properties of Expected Values......Page 244
  Problems......Page 248
 5.4 Variance of Random Variables......Page 254
  5.4.1 Properties of Variances......Page 256
  Problems......Page 259
 5.5 Binomial Random Variables......Page 261
  5.5.1 Expected Value and Variance of a Binomial Random Variable......Page 266
  Problems......Page 267
 5.6 Hypergeometric Random Variables......Page 271
  Problems......Page 272
 5.7 Poisson Random Variables......Page 273
  Problems......Page 276
 Summary......Page 277
 Review Problems......Page 279
Chapter 6 Normal Random Variables......Page 284
 6.2 Continuous Random Variables......Page 285
  Problems......Page 287
 6.3 Normal Random Variables......Page 289
  Problems......Page 292
 6.4 Probabilities Associated with a Standard Normal Random Variable......Page 294
  Problems......Page 299
 6.5 Finding Normal Probabilities: Conversion to the Standard Normal......Page 300
 6.6 Additive Property of Normal Random Variables......Page 302
  Problems......Page 304
 6.7 Percentiles of Normal Random Variables......Page 307
  Problems......Page 312
 Summary......Page 313
 Review Problems......Page 316
Chapter 7 Distributions of Sampling Statistics......Page 320
 7.2 Introduction......Page 321
 7.3 Sample Mean......Page 322
  Problems......Page 326
 7.4 Central Limit Theorem......Page 327
  7.4.1 Distribution of the Sample Mean......Page 329
  7.4.2 How Large a Sample Is Needed?......Page 333
  Problems......Page 334
 7.5 Sampling Proportions from a Finite Population......Page 336
  7.5.1 Probabilities Associated with Sample Proportions: The Normal Approximation to the Binomial Distribution......Page 340
  Problems......Page 342
 7.6 Distribution of the Sample Variance of a Normal Population......Page 346
 Key Terms......Page 348
 Summary......Page 349
 Review Problems......Page 350
Chapter 8 Estimation......Page 354
 8.1 Introduction......Page 355
 8.2 Point Estimator of a Population Mean......Page 356
  Problems......Page 357
 8.3 Point Estimator of a Population Proportion......Page 359
  Problems......Page 361
  8.3.1 Estimating the Probability of a Sensitive Event......Page 364
 8.4 Estimating a Population Variance......Page 365
  Problems......Page 367
 8.5 Interval Estimators of the Mean of a Normal Population with Known Population Variance......Page 370
  8.5.1 Lower and Upper Confidence Bounds......Page 378
  Problems......Page 380
 8.6 Interval Estimators of the Mean of a Normal Population with Unknown Population Variance......Page 382
  8.6.1 Lower and Upper Confidence Bounds......Page 387
  Problems......Page 389
 8.7 Interval Estimators of a Population Proportion......Page 394
  8.7.1 Length of the Confidence Interval......Page 396
  8.7.2 Lower and Upper Confidence Bounds......Page 398
  Problems......Page 400
 Key Terms......Page 403
 Summary......Page 404
 Review Problems......Page 406
Chapter 9 Testing Statistical Hypotheses......Page 410
 9.2 Hypothesis Tests and Significance Levels......Page 411
  Problems......Page 415
 9.3 Tests Concerning the Mean of a Normal Population: Case of Known Variance......Page 417
  Problems......Page 423
  9.3.1 One-Sided Tests......Page 426
 9.4 The t Test for the Mean of a Normal Population: Case of Unknown Variance......Page 432
  Problems......Page 440
 9.5 Hypothesis Tests Concerning Population Proportions......Page 444
 9.5.1 Two-Sided Tests of p......Page 448
  Problems......Page 452
 Summary......Page 456
 Review Problems and Proposed Case Studies......Page 460
Chapter 10 Hypothesis Tests Concerning Two Populations......Page 466
 10.1 Introduction......Page 467
 10.2 Testing Equality of Means of Two Normal Populations: Case of Known Variance......Page 469
  Problems......Page 473
 10.3 Testing Equality of Means: Unknown Variances and Large Sample Sizes......Page 476
  Problems......Page 482
 10.4 Testing Equality of Means: Small-Sample Tests When the Unknown Population Variances Are Equal......Page 486
  Problems......Page 491
 10.5 Paired-Sample t Test......Page 494
  Problems......Page 499
 10.6 Testing Equality of Population Proportions......Page 504
  Problems......Page 513
 Summary......Page 516
 Review Problems......Page 521
Chapter 11 Analysis of Variance......Page 526
 11.1 Introduction......Page 527
 11.2 One-Factor Analysis of Variance......Page 528
  A Remark on the Degrees of Freedom......Page 530
  Problems......Page 533
 11.3 Two-Factor Analysis of Variance: Introduction and Parameter Estimation......Page 537
  Problems......Page 541
 11.4 Two-Factor Analysis of Variance: Testing Hypotheses......Page 543
  Problems......Page 550
 11.5 Final Comments......Page 552
 Summary......Page 553
 Review Problems......Page 556
Chapter 12 Linear Regression......Page 560
 12.1 Introduction......Page 562
 12.2 Simple Linear Regression Model......Page 563
  Problems......Page 565
 12.3 Estimating the Regression Parameters......Page 567
  Problems......Page 571
 12.4 Error Random Variable......Page 576
  Problems......Page 579
 12.5 Testing the Hypothesis that ß = 0......Page 580
  Problems......Page 583
 12.6 Regression to the Mean......Page 587
  12.6.1 Why Biological Data Sets Are Often Normally Distributed......Page 592
  Problems......Page 593
 12.7 Prediction Intervals for Future Responses......Page 596
  Problems......Page 598
 12.8 Coefficient of Determination......Page 601
  Problems......Page 603
 12.9 Sample Correlation Coefficient......Page 605
  Problems......Page 606
 12.10 Analysis of Residuals: Assessing the Model......Page 607
 12.11 Multiple Linear Regression Model......Page 609
  12.11.1 Dummy Variables for Categorical Data......Page 613
  Problems......Page 615
 Summary......Page 618
 Review Problems......Page 622
Chapter 13 Chi-Squared Goodness-of-Fit Tests......Page 628
 13.1 Introduction......Page 629
 13.2 Chi-Squared Goodness-of-Fit Tests......Page 632
  Problems......Page 638
 13.3 Testing for in Dependence in Populations Classified According to Two Characteristics......Page 643
  Problems......Page 649
 13.4 Testing for Independence in Contingency Tables with Fixed Marginal Totals......Page 654
  Problems......Page 657
 Key Terms......Page 660
 Summary......Page 661
 Review Problems......Page 663
Chapter 14 Nonparametric Hypotheses Tests......Page 670
 14.2 Sign Test......Page 671
  14.2.1 Testing the Equality of Population Distributions when Samples Are Paired......Page 675
  14.2.2 One-Sided Tests......Page 676
   Problems......Page 678
 14.3 Signed-Rank Test......Page 680
  14.3.1 Zero Differences and Ties......Page 685
  Problems......Page 687
 14.4 Rank-Sum Test for Comparing Two Populations......Page 690
  14.4.1 Comparing Nonparametric Tests with Tests that Assume Normal Distributions......Page 695
  Problems......Page 696
 14.5 Runs Test for Randomness......Page 699
  Problems......Page 704
 14.6 Testing the Equality of Multiple Probability Distributions......Page 706
  14.6.1 When the Data Are a Set of Comparison Rankings......Page 708
  Problems......Page 711
 14.7 Permutation Tests......Page 712
  Problems......Page 715
 Summary......Page 716
 Review Problems......Page 719
Chapter 15 Quality Control......Page 722
 15.2 The X Control Chart for Detecting a Shift in the Mean......Page 723
  Problems......Page 728
  15.2.1 When the Mean and Variance Are Unknown......Page 730
  15.2.2 S Control Charts......Page 733
  Problems......Page 736
 15.3 Control Charts for Fraction Defective......Page 738
 15.4 Exponentially Weighted Moving-Average Control Charts......Page 740
  Problems......Page 744
 15.5 Cumulative-Sum Control Charts......Page 745
 Summary......Page 748
 Review Problems......Page 749
Appendices......Page 750
 Appendix A. Data Set......Page 752
  B.2 Absolute Value......Page 756
  B.3 Set Notation......Page 757
Appendix C How to Choose a Random Sample......Page 758
 Table D.1 Standard Normal Probabilities......Page 762
 Table D.2 Percentiles tn,α of t Distributions......Page 763
 Table D.3 Percentiles χ²n,α of the Chi-Squared Distributions......Page 764
 Table D.4 Percentiles of F Distributions......Page 766
 Table D.5 Binomial Distribution Function......Page 772
Appendix E. Programs......Page 778
Answers to Odd-Numbered Problems......Page 780
Index......Page 830