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Introductory Statistics
Sheldon M. Ross
Verlag Elsevier Textbooks, 2010
ISBN 9780080922102 , 841 Seiten
3. Auflage
Format PDF, ePUB, OL
Kopierschutz DRM
Geräte
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
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