# Introduction to Probability and Statistics, Metric Version, 15th Edition PDF by William Mendenhall, Robert J. Beaver and Barbara M. Beaver

Introduction to Probability and Statistics, 15th Edition
By William Mendenhall, Robert J. Beaver and Barbara M. Beaver Contents

Introduction: What is Statistics? 1
The Population and the Sample 3
Descriptive and Inferential Statistics 4
Achieving the Objective of Inferential Statistics: The Necessary Steps 4
Keys for Successful Learning 5
DESCRIBING DATA WITH GRAPHS 7
1.1 Variables and Data 8
1.2 Types of Variables 9
1.3 Graphs for Categorical Data 11
Exercises 14
1.4 Graphs for Quantitative Data 17
Pie Charts and Bar Charts 17
Line Charts 19
Dotplots 20
Stem and Leaf Plots 20
Interpreting Graphs with a Critical Eye 22
1.5 Relative Frequency Histograms 24
Exercises 28
Chapter Review 33
Technology Today 33
Supplementary Exercises 42
CASE STUDY: How Is Your Blood Pressure? 49
DESCRIBING DATA WITH NUMERICAL MEASURES 50
2.1 Describing a Set of Data with Numerical Measures 51
2.2 Measures of Center 51
Exercises 55
2.3 Measures of Variability 57
Exercises 62
2.4 On the Practical Significance of the Standard Deviation 63
2.5 A Check on the Calculation of s 67
Exercises 69
2.6 Measures of Relative Standing 72
2.7 The Five-Number Summary and the Box Plot 77
Exercises 80
Chapter Review 83
Technology Today 84
Supplementary Exercises 87
CASE STUDY: The Boys of Summer 93
DESCRIBING BIVARIATE DATA 94
3.1 Bivariate Data 95
3.2 Graphs for Categorical Variables 95
Exercises 98
3.3 Scatterplots for Two Quantitative Variables 99
3.4 Numerical Measures for Quantitative Bivariate Data 101
Exercises 107
Chapter Review 109
Technology Today 109
Supplementary Exercises 114
CASE STUDY: Are Your Dishes Really Clean? 121
PROBABILITY AND PROBABILITY DISTRIBUTIONS 123
4.1 The Role of Probability in Statistics 124
4.2 Events and the Sample Space 124
4.3 Calculating Probabilities Using Simple Events 127
Exercises 130
4.4 Useful Counting Rules (Optional) 133
Exercises 137
4.5 Event Relations and Probability Rules 139
Calculating Probabilities for Unions and Complements 141
4.6 Independence, Conditional Probability, and
the Multiplication Rule 144
Exercises 149
4.7 Bayes’ Rule (Optional) 152
Exercises 156
4.8 Discrete Random Variables and Their Probability Distributions 158
Random Variables 158
Probability Distributions 158
The Mean and Standard Deviation for a Discrete Random Variable 160
Exercises 163
Chapter Review 166
Technology Today 167
Supplementary Exercises 169
CASE STUDY: Probability and Decision Making in the Congo 174
SEVERAL USEFUL DISCRETE DISTRIBUTIONS 175
5.1 Introduction 176
5.2 The Binomial Probability Distribution 176
Exercises 185
5.3 The Poisson Probability Distribution 188
Exercises 193
5.4 The Hypergeometric Probability Distribution 194
Exercises 196
Chapter Review 197
Technology Today 198
Supplementary Exercises 202
CASE STUDY: A Mystery: Cancers Near a Reactor 208
THE NORMAL PROBABILITY DISTRIBUTION 209
6.1 Probability Distributions for Continuous Random Variables 210
6.2 The Normal Probability Distribution 213
6.3 Tabulated Areas of the Normal Probability Distribution 214
The Standard Normal Random Variable 214
Calculating Probabilities for a General Normal Random Variable 218
Exercises 221
6.4 The Normal Approximation to the Binomial Probability
Distribution (Optional) 224
Exercises 229
Chapter Review 231
Technology Today 232
Supplementary Exercises 236
CASE STUDY: “Are You Going to Curve the Grades?” 241
SAMPLING DISTRIBUTIONS 242
7.1 Introduction 243
7.2 Sampling Plans and Experimental Designs 243
Exercises 246
7.3 Statistics and Sampling Distributions 248
7.4 The Central Limit Theorem 251
7.5 The Sampling Distribution of the Sample Mean 254
Standard Error 255
Exercises 258
7.6 The Sampling Distribution of the Sample Proportion 260
Exercises 264
7.7 A Sampling Application: Statistical Process Control (Optional) 266
A Control Chart for the Process Mean: The x_ Chart 267
A Control Chart for the Proportion Defective: The p Chart 269
Exercises 271
Chapter Review 272
Technology Today 273
Supplementary Exercises 276
CASE STUDY: Sampling the Roulette at Monte Carlo 279
LARGE-SAMPLE ESTIMATION 281
8.1 Where We’ve Been 282
8.2 Where We’re Going—Statistical Inference 282
8.3 Types of Estimators 283
8.4 Point Estimation 284
Exercises 289
8.5 Interval Estimation 291
Constructing a Confidence Interval 292
Large-Sample Confidence Interval for a Population Mean m 294
Interpreting the Confidence Interval 295
Large-Sample Confidence Interval for a Population Proportion p 297
Exercises 299
8.6 Estimating the Difference between Two Population Means 301
Exercises 304
8.7 Estimating the Difference between Two Binomial Proportions 307
Exercises 309
8.8 One-Sided Confidence Bounds 311
8.9 Choosing the Sample Size 312
Exercises 316
Chapter Review 318
Supplementary Exercises 318
CASE STUDY: How Reliable Is That Poll?
CBS News: How and Where America Eats 322
LARGE-SAMPLE TESTS OF HYPOTHESES 324
9.1 Testing Hypotheses about Population Parameters 325
9.2 A Statistical Test of Hypothesis 325
9.3 A Large-Sample Test about a Population Mean 328
The Essentials of the Test 329
Calculating the p-Value 332
Two Types of Errors 335
The Power of a Statistical Test 336
Exercises 339
9.4 A Large-Sample Test of Hypothesis for the Difference
between Two Population Means 341
Hypothesis Testing and Confidence Intervals 343
Exercises 344
9.5 A Large-Sample Test of Hypothesis for a Binomial Proportion 347
Statistical Significance and Practical Importance 349
Exercises 350
9.6 A Large-Sample Test of Hypothesis for the Difference between
Two Binomial Proportions 351
Exercises 354
9.7 Some Comments on Testing Hypotheses 356
Chapter Review 357
Supplementary Exercises 358
CASE STUDY: An Aspirin a Day . . . ? 362
INFERENCE FROM SMALL SAMPLES 364
10.1 Introduction 365
10.2 Student’s t Distribution 365
Assumptions behind Student’s t Distribution 368
10.3 Small-Sample Inferences Concerning a Population Mean 369
Exercises 373
10.4 Small-Sample Inferences for the Difference between
Two Population Means: Independent Random Samples 376
Exercises 382
10.5 Small-Sample Inferences for the Difference between
Two Means: A Paired-Difference Test 386
Exercises 391
10.6 Inferences Concerning a Population Variance 394
Exercises 400
10.7 Comparing Two Population Variances 401
Exercises 407
10.8 Revisiting the Small-Sample Assumptions 409
Chapter Review 410
Technology Today 410
Supplementary Exercises 416
CASE STUDY: School Accountability Study—
How Is Your School Doing? 424
THE ANALYSIS OF VARIANCE 425
11.1 The Design of an Experiment 426
11.2 What Is an Analysis of Variance? 427
11.3 The Assumptions for an Analysis of Variance 427
11.4 The Completely Randomized Design: A One-Way Classification 428
11.5 The Analysis of Variance for a Completely Randomized Design 429
Partitioning the Total Variation in an Experiment 429
Testing the Equality of the Treatment Means 432
Estimating Differences in the Treatment Means 434
Exercises 437
11.6 Ranking Population Means 440
Exercises 443
11.7 The Randomized Block Design: A Two-Way Classification 444
11.8 The Analysis of Variance for a Randomized Block Design 445
Partitioning the Total Variation in the Experiment 445
Testing the Equality of the Treatment and Block Means 448
Identifying Differences in the Treatment and Block Means 450
Some Cautionary Comments on Blocking 451
Exercises 452
11.9 The a _ b Factorial Experiment: A Two-Way Classification 456
11.10 The Analysis of Variance for an a _ b Factorial Experiment 458
Exercises 462
11.11 Revisiting the Analysis of Variance Assumptions 466
Residual Plots 467
11.12 A Brief Summary 469
Chapter Review 469
Technology Today 470
Supplementary Exercises 475
CASE STUDY: How to Save Money on Groceries! 481
LINEAR REGRESSION AND CORRELATION 482
12.1 Introduction 483
12.2 A Simple Linear Probabilistic Model 483
12.3 The Method of Least Squares 486
12.4 An Analysis of Variance for Linear Regression 488
Exercises 491
12.5 Testing the Usefulness of the Linear Regression Model 494
Inferences Concerning b, the Slope of the Line of Means 495
The Analysis of Variance F-Test 498
Measuring the Strength of the Relationship:
The Coefficient of Determination 498
Interpreting the Results of a Significant Regression 499
Exercises 500
12.6 Diagnostic Tools for Checking the Regression Assumptions 503
Dependent Error Terms 503
Residual Plots 503
Exercises 504
12.7 Estimation and Prediction Using the Fitted Line 507
Exercises 511
12.8 Correlation Analysis 513
Exercises 517
Chapter Review 519
Technology Today 520
Supplementary Exercises 523
CASE STUDY: Is Your Car “Made in the U.S.A.”? 528
MULTIPLE REGRESSION ANALYSIS 530
13.1 Introduction 531
13.2 The Multiple Regression Model 531
13.3 A Multiple Regression Analysis 532
The Method of Least Squares 533
The Analysis of Variance for Multiple Regression 534
Testing the Usefulness of the Regression Model 535
Interpreting the Results of a Significant Regression 536
Checking the Regression Assumptions 538
Using the Regression Model for Estimation and Prediction 538
13.4 A Polynomial Regression Model 539
Exercises 542
13.5 Using Quantitative and Qualitative Predictor Variables
in a Regression Model 546
Exercises 552
13.6 Testing Sets of Regression Coefficients 555
13.7 Interpreting Residual Plots 558
13.8 Stepwise Regression Analysis 559
13.9 Misinterpreting a Regression Analysis 560
Causality 560
Multicollinearity 560
13.10 Steps to Follow When Building a Multiple Regression Model 562
Chapter Review 562
Technology Today 563
Supplementary Exercises 565
CASE STUDY: “Made in the U.S.A.”—Another Look 572
ANALYSIS OF CATEGORICAL DATA 574
14.1 A Description of the Experiment 575
14.2 Pearson’s Chi-Square Statistic 576
14.3 Testing Specified Cell Probabilities: The Goodness-of-Fit Test 577
Exercises 579
14.4 Contingency Tables: A Two-Way Classification 581
The Chi-Square Test of Independence 582
Exercises 586
14.5 Comparing Several Multinomial Populations: A Two-Way
Classification with Fixed Row or Column Totals 588
Exercises 591
14.6 The Equivalence of Statistical Tests 592
14.7 Other Applications of the Chi-Square Test 593
Chapter Review 594
Technology Today 595
Supplementary Exercises 598
CASE STUDY: Who is the Primary Breadwinner in Your Family? 604
NONPARAMETRIC STATISTICS 606
15.1 Introduction 607
15.2 The Wilcoxon Rank Sum Test: Independent Random Samples 607
Normal Approximation for the Wilcoxon Rank Sum Test 611
Exercises 614
15.3 The Sign Test for a Paired Experiment 616
Normal Approximation for the Sign Test 617
Exercises 619
15.4 A Comparison of Statistical Tests 620
15.5 The Wilcoxon Signed-Rank Test for a Paired Experiment 621
Normal Approximation for the Wilcoxon Signed-Rank Test 624
Exercises 625
15.6 The Kruskal–Wallis H-Test for Completely Randomized Designs 627
Exercises 631
15.7 The Friedman Fr-Test for Randomized Block Designs 633
Exercises 636
15.8 Rank Correlation Coefficient 637
Exercises 641
15.9 Summary 643
Chapter Review 644
Technology Today 645
Supplementary Exercises 648
CASE STUDY: How’s Your Cholesterol Level? 653
APPENDIX I 655
Table 1 Cumulative Binomial Probabilities 656
Table 2 Cumulative Poisson Probabilities 662
Table 3 Areas under the Normal Curve 664
Table 4 Critical Values of t 667
Table 5 Critical Values of Chi-Square 668
Table 6 Percentage Points of the F Distribution 670
Table 7 Critical Values of T for the Wilcoxon Rank
Sum Test, n1 _ n2 678
Table 8 Critical Values of T for the Wilcoxon Signed-Rank
Test, n _ 5(1)50 680
Table 9 Critical Values of Spearman’s Rank Correlation Coefficient
for a One-Tailed Test 681
Table 10 Random Numbers 682
Table 11 Percentage Points of the Studentized Range, q.05(k, df ) 684
DATA SOURCES 688
ANSWERS TO SELECTED EXERCISES 700
INDEX 714

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