Introduction to probability and statistics

788 Pages·2020·39.286 MB·English

by  William Mendenhall, Barbara M. Beaver, Robert J. Beaver

■ Table 4 Critical Values of t, pages 692–963
df t.100 t.050 t.025 t.010 t.005 df
a
1 3.078 6.314 12.706 31.821 63.657 1
ta 2 1.886 2.920 4.303 6.965 9.925 2
3 1.638 2.353 3.182 4.541 5.841 3
4 1.533 2.132 2.776 3.747 4.604 4
5 1.476 2.015 2.571 3.365 4.032 5
6 1.440 1.943 2.447 3.143 3.707 6
7 1.415 1.895 2.365 2.998 3.499 7
8 1.397 1.860 2.306 2.896 3.355 8
9 1.383 1.833 2.262 2.821 3.250 9
10 1.372 1.812 2.228 2.764 3.169 10
11 1.363 1.796 2.201 2.718 3.106 11
12 1.356 1.782 2.179 2.681 3.055 12
13 1.350 1.771 2.160 2.650 3.012 13
14 1.345 1.761 2.145 2.624 2.977 14
15 1.341 1.753 2.131 2.602 2.947 15
16 1.337 1.746 2.120 2.583 2.921 16
17 1.333 1.740 2.110 2.567 2.898 17
18 1.330 1.734 2.101 2.552 2.878 18
19 1.328 1.729 2.093 2.539 2.861 19
20 1.325 1.725 2.086 2.528 2.845 20
21 1.323 1.721 2.080 2.518 2.831 21
22 1.321 1.717 2.074 2.508 2.819 22
23 1.319 1.714 2.069 2.500 2.807 23
24 1.318 1.711 2.064 2.492 2.797 24
25 1.316 1.708 2.060 2.485 2.787 25
26 1.315 1.706 2.056 2.479 2.779 26
27 1.314 1.703 2.052 2.473 2.771 27
28 1.313 1.701 2.048 2.467 2.763 28
29 1.311 1.699 2.045 2.462 2.756 29
30 1.310 1.697 2.042 2.457 2.750 30
31 1.309 1.696 2.040 2.453 2.744 31
32 1.309 1.694 2.037 2.449 2.738 32
33 1.308 1.692 2.035 2.445 2.733 33
34 1.307 1.691 2.032 2.441 2.728 34
35 1.306 1.690 2.030 2.438 2.724 35
36 1.306 1.688 2.028 2.434 2.719 36
37 1.305 1.687 2.026 2.431 2.715 37
38 1.304 1.686 2.024 2.429 2.712 38
39 1.304 1.685 2.023 2.426 2.708 39
40 1.303 1.684 2.021 2.423 2.704 40
45 1.301 1.679 2.014 2.412 2.690 45
50 1.299 1.676 2.009 2.403 2.678 50
55 1.297 1.673 2.004 2.396 2.668 55
60 1.296 1.671 2.000 2.390 2.660 60
65 1.295 1.669 1.997 2.385 2.654 65
70 1.294 1.667 1.994 2.381 2.648 70
80 1.292 1.664 1.990 2.374 2.639 80
90 1.291 1.662 1.987 2.368 2.632 90
100 1.290 1.660 1.984 2.364 2.626 100
200 1.286 1.653 1.972 2.345 2.601 200
300 1.284 1.650 1.968 2.339 2.592 300
400 1.284 1.649 1.966 2.336 2.588 400
500 1.283 1.648 1.965 2.334 2.586 500
inf. 1.282 1.645 1.96 2.326 2.576 inf.
Source: Percentage points calculated using Minitab software.
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Body temperature and heart rate 542 Measurement error 263 Social Sciences
Breathing rates 74, 93, 441 Medical diagnostics 162
Achievement scores 581
Bulimia 392 Mercury concentration in dolphins 84, 594
Achievement tests 75, 515, 550
Calcium 440, 460, 464 Metal corrosion and soil acids 572
Adolescents and social stress 376
Calcium content 25 Metabolism and weight gain 552
Alcohol and altitude 442
Cancer survivor rates 12, 187 Monkey business 144
American Presidents-age at death 26
Cerebral blood flow 226, 263, 391, 419 MRIs 164
Animation helps 502
Chemical experiment 306, 515 Nematodes 549
Anxious infants 612
Chemotherapy 642 Omega-3 Fats 250
Back to work 17
Chicago weather 186 Ore samples 74
Books or iPads? 401
Chirping crickets 111, 523, 528 Parasites in foxes 94
Boomers, Xers and Millennial Men 375
Chloroform 92 PCBs 377
Catching a cold 318, 321, 630
Cholesterol 393 Pearl millet 340 Choosing a mate 158
Citrus red mite 325 pH in rainfall 326 Discovery-based teaching 627
Color preferences in mice 210 pH levels in water 660 Drug offenders 156
Cotton versus cucumber 580 Physical fitness 500, 612 Drug testing 156
Cure for insomnia 364 Plant density 208 Eye movement 642
Cure for the common cold 358 Plant genetics 157, 188, 234, 363 Faculty salaries 263, 486, 501
Deep-sea research 617 Plant science 537 Good at math? 460
Diabetes in children 208 Polluted seawater 67, 84 Graduate teaching assistants 628
Digitalis and calcium uptake 475 Pollution 326, 499, 678 Hospital survey 143
Disinfectants 402 Potassium levels 264 Household size 101, 617
Dissolved O2 content 392, 403, 459, 642 Potency of an antibiotic 353 Images and word recall 251, 654
Drugs for hypertension 92 Pulse rates 49, 227 Intensive care 195
Drug potency 420 Purifying organic compounds 392 Jury duty 136
E. coli outbreaks 196 Rain and snow 121 Laptops and learning 51, 524, 528
Early detection of breast cancer 363 Recovery rates 647 Math and art 677
Enzymes 401 Recurring illness 32, 91 Medical bills 189
Excedrin or Tylenol 318 Red blood cell count 25, 393 Memory experiments 412
FDA testing 175 Rh factor 233, 285 Midterm scores 118
Fossils 440 Ring-necked pheasants 440 Music in the workplace 412
Fruit flies 136 Runners and cyclists 402, 428, 443 No pass-no play rule for athletics 162
Geothermal power 542 San Andreas Fault 296 Organized religion 25
Genetic defects 233 Screening tests 162 Political corruption 326
Gestation times 121, 226, 523 Sea urchins 440 Preschool 33
Glucose tolerance 464 Seed treatments 199 Racial bias 250
Good tasting medicine 619, 665 Selenium 311, 326 Reaction times 410, 441, 442,
Ground or air 411 Shade or sun? 440 497, 498
Gulf oil spill 48 Slash pine seedlings 474 Reducing hostility 458
Hazardous waste 26, 123 Sleep deprivation 515, 523 Same-sex marriage 284, 306
Healthy eating 358, 579 Smoking 331, 392 SAT scores 92, 187, 313, 359,
Healthy teeth 401, 411 Sodium hydroxide 439 376, 427
Heart rate and exercise 465, 659 Spraying fruit trees 358 Smoking and cancer 157
Hormone therapy and Alzheimer’s disease 368 Sunflowers 227, 332 Snacking and TV 242
Human body temperatures 50, 95, 242, 264, 307, Survival times 32, 74, 85 Social ambivalence 92
313, 353, 359 Swampy sites 459, 464, 659 Social Security numbers 74
Hungry rats 297 Sweet potato whitefly 363 Social skills training 110, 541, 671
Impurities 428, 439 Tai Chi and fibromyalgia 251, 368 Spending patterns 612
Iodine concentration 331 Taste test for PTC 189 Starting salaries 312, 321, 359
Jigsaw puzzles 654 Tay-Sachs disease 188 Student ratings 671
Lead levels in blood 647 Titanium 402 Teaching biology 312
Lead levels in drinking water 358 Toxic chemicals 664 Test interviews 119, 515
Less red meat 321, 579 Weights of babies 225, 263, 305, 352 Unbiased choices 144, 174, 199
Lobsters 392, 541 Weights of turtles 642 Union Yes! 318
Long stemmed roses 92 Whitefly infestation 210, 499 Violent crime 162
Lung cancer 233 White tailed deer 376 Want to be President? 16
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Introduction
EdItIon
15
to Probability
and Statistics
Metric Version
William Mendenhall, III
1925–2009
Robert J. Beaver
University of California, Riverside, Emeritus
Barbara M. Beaver
University of California, Riverside, Emerita
Australia • Brazil • Mexico • Singapore • United Kingdom • United States
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Introduction to Probability and Statistics, © 2020, 2013, 2009 Cengage Learning, Inc.
Fifteenth Edition, Metric Version WCN: 02-300
William Mendenhall, III, Robert J. ALL RIGHTS RESERVED. No part of this work covered by the copyright
Beaver, Barbara M. Beaver herein may be reproduced or distributed in any form or by any means,
except as permitted by U.S. copyright law, without the prior written
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Brief Contents
introduction: WHAt iS StAtiSticS? 1
1 deScribing dAtA WitH grApHS 7
2 deScribing dAtA WitH numericAl meASureS 54
3 deScribing bivAriAte dAtA 96
4 probAbility 126
5 diScrete probAbility diStributionS 167
6 tHe normAl probAbility diStribution 212
7 SAmpling diStributionS 245
8 lArge-SAmple eStimAtion 288
9 lArge-SAmple teStS of HypotHeSeS 335
10 inference from SmAll SAmpleS 380
11 tHe AnAlySiS of vAriAnce 445
12 Simple lineAr regreSSion And correlAtion 503
13 multiple lineAr regreSSion AnAlySiS 555
14 AnAlySiS of cAtegoricAl dAtA 599
15 nonpArAmetric StAtiSticS 633
Appendix i 681
dAtA SourceS 714
AnSWerS to Selected exerciSeS 727
index 745
iii
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Contents
Introduction: What Is Statistics?  1
The Population and the Sample  3
Descriptive and Inferential Statistics  3
Achieving the Objective of Inferential Statistics: The Necessary Steps  4
Keys for Successful Learning  5
1
describing data with Graphs  7
1.1 Variables and data  8
Types of Variables  9
exercises 11
1.2 Graphs for Categorical data  12
exercises 15
1.3 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
exercises 24
1.4 Relative Frequency Histograms  27
exercises 31
Chapter Review  35
Technology Today  35
Reviewing What You’ve Learned  47
CaSE Study: How Is Your Blood Pressure?  53
2 describing data with numerical Measures  54
Introduction  55
2.1 Measures of Center  55
exercises 59
2.2 Measures of Variability  61
exercises 66
iv
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Contents v
2.3 Understanding and Interpreting the Standard Deviation  67
Tchebysheff’s Theorem  67
The Empirical Rule  69
Approximating s Using the Range  71
Exercises 73
2.4 Measures of Relative Standing  76
z-Scores  76
Percentiles and Quartiles  77
The Five-Number Summary and the Box Plot  80
Exercises 83
Chapter Review   86
Technology Today  87
Reviewing What You’ve Learned  91
CaSe StUDy: The Boys of Summer  95
3 Describing Bivariate Data  96
Introduction  97
3.1 Describing Bivariate Categorical Data  97
Exercises 99
3.2 Describing Bivariate Quantitative Data  101
Scatterplots  101
The Correlation Coefficient  104
The Least-Squares Line  106
Exercises 109
Chapter Review  112
Technology Today  112
Reviewing What You’ve Learned  118
CaSe StUDy: Are Your Clothes Really Clean?  124
4 Probability  126
Introduction  127
4.1 events and the Sample Space  127
Exercises 130
4.2 Calculating Probabilities Using Simple events  131
Exercises 134
4.3 Useful Counting Rules  137
Using the TI-83/84 Plus Calculator  142
Exercises 142
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vi Contents
4.4 Rules for Calculating Probabilities  144
Calculating Probabilities for Unions and Complements  146
Calculating Probabilities for Intersections  148
Exercises 155
4.5 Bayes’ Rule  158
Exercises 161
Chapter Review  163
Reviewing What You’ve Learned  163
CaSe StUDy: Probability and Decision Making in the Congo  166
5 Discrete Probability Distributions  167
5.1 Discrete Random Variables and their Probability Distributions  168
Random Variables  168
Probability Distributions  168
The Mean and Standard Deviation for a Discrete Random Variable  170
Exercises 174
5.2 the Binomial Probability Distribution  176
Exercises 185
5.3 the Poisson Probability Distribution  189
Exercises 194
5.4 the Hypergeometric Probability Distribution  196
Exercises 198
Chapter Review  200
Technology Today  201
Reviewing What You’ve Learned  206
CaSe StUDy: A Mystery: Cancers Near a Reactor  211
6 the Normal Probability Distribution  212
6.1 Probability Distributions for Continuous Random Variables  213
The Continuous Uniform Probability Distribution  215
The Exponential Probability Distribution  216
Exercises 217
6.2 the Normal Probability Distribution  218
The Standard Normal Random Variable  219
Calculating Probabilities for a General Normal Random Variable  222
Exercises 225
6.3 the Normal approximation to the Binomial Probability Distribution  228
Exercises 232
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