vii
To Instructors: About This Bookxv
Media and Supplementsxxi
To Students: What Is Statistics?xxiv
Index of Casesxxviii
Index of Data Tablesxxix
Beyond the Basics Indexxxx
About the Authorsxxxi
CHAPTER 1 Examining Distributions1
Introduction1
1.1Data2
Section 1.1 Summary6
Section 1.1 Exercises6
1.2Displaying Distributions with Graphs7
Categorical variables: Bar graphs and pie charts7
Quantitative variables: Histograms12
Case 1.1 Treasury Bills12
Quantitative variables: Stemplots15
Interpreting histograms and stemplots17
Time plots19
Section 1.2 Summary20
Section 1.2 Exercises21
1.3Describing Distributions with Numbers23
Case 1.2 Time to Start a Business23
Measuring center: The mean24
Measuring center: The median25
Comparing the mean and the median26
Measuring spread: The quartiles27
The five-number summary and boxplots29
Measuring spread: The standard deviation31
Choosing measures of center and spread32
Beyond the Basics: Risk and Return33
Section 1.3 Summary34
Section 1.3 Exercises35
1.4Density Curves and the Normal Distributions38
Density curves38
The median and mean of a density curve39
Normal distributions42
The 68–95–99.7 rule43
The standard Normal distribution45
Normal distribution calculations46
Using the standard Normal table48
Inverse Normal calculations49
Assessing the Normality of data51
BEYOND THE BASICS: Density Estimation54
Section 1.4 Summary56
Section 1.4 Exercises57
Chapter 1 Review Exercises59
CHAPTER 2 Examining Relationships63
Introduction63
2.1Scatterplots65
Case 2.1 Education Expenditures and Population: Benchmarking65
Interpreting scatterplots67
The log transformation68
Adding categorical variables to scatterplots70
Section 2.1 Summary71
Section 2.1 Exercises72
2.2Correlation74
The correlation 75
Facts about correlation76
Section 2.2 Summary78
Section 2.2 Exercises78
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2.3Least-Squares Regression80
The least-squares regression line81
Facts about least-squares regression86
Interpretation of 87
Residuals88
The distribution of the residuals92
Influential observations92
Section 2.3 Summary94
Section 2.3 Exercises95
2.4Cautions about Correlation and Regression98
Extrapolation98
Correlations based on averaged data99
Lurking variables100
Association is not causation101
BEYOND THE BASICS: Data Mining102
Section 2.4 Summary103
Section 2.4 Exercises103
2.5Relations in Categorical Data104
Case 2.2 Does the Right Music Sell the Product?104
Marginal distributions105
Conditional distributions107
Mosaic plots and software output109
Simpson’s paradox110
Section 2.5 Summary112
Section 2.5 Exercises113
Chapter 2 Review Exercises116
CHAPTER 3 Producing Data123
Introduction123
3.1Sources of Data124
Anecdotal data124
Available data124
Sample surveys and experiments126
Section 3.1 Summary127
Section 3.1 Exercises128
3.2Designing Samples129
Simple random samples132
Stratified samples134
Multistage samples135
Cautions about sample surveys136
BEYOND THE BASICS: Capture-Recapture Sampling139
Section 3.2 Summary140
Section 3.2 Exercises140
3.3Designing Experiments142
Comparative experiments145
Randomized comparative experiments146
Completely randomized designs147
How to randomize147
The logic of randomized comparative experiments150
Cautions about experimentation153
Matched pairs designs154
Block designs155
Section 3.3 Summary157
Section 3.3 Exercises157
3.4Data Ethics160
Institutional review boards160
Informed consent161
Confidentiality162
Clinical trials163
Behavioral and social science experiments165
Section 3.4 Summary167
Section 3.4 Exercises167
Chapter 3 Review Exercises169
CHAPTER 4 Probability: The Study of Randomness173
Introduction173
4.1Randomness174
The language of probability175
Thinking about randomness and probability176
Section 4.1 Summary176
Section 4.1 Exercises177
4.2Probability Models179
Sample spaces179
Probability rules182
Assigning probabilities: Finite number of outcomes184
Case 4.1 Uncovering Fraud by Digital Analysis184
Assigning probabilities: Equally likely outcomes186
ix
Independence and the multiplication rule187
Applying the probability rules189
Section 4.2 Summary191
Section 4.2 Exercises191
4.3General Probability Rules194
General addition rules194
Conditional probability197
General multiplication rules200
Tree diagrams201
Bayes’s rule203
Independence again205
Section 4.3 Summary205
Section 4.3 Exercises206
4.4Random Variables209
Discrete random variables210
Case 4.2 Tracking Perishable Demand210
Continuous random variables213
Normal distributions as probability distributions215
Section 4.4 Summary216
Section 4.4 Exercises217
4.5Means and Variances of Random Variables219
The mean of a random variable219
Mean and the law of large numbers222
Thinking about the law of large numbers223
Rules for means224
Case 4.3 Portfolio Analysis225
The variance of a random variable229
Rules for variances and standard deviations230
Section 4.5 Summary235
Section 4.5 Exercises236
Chapter 4 Review Exercises239
CHAPTER 5 Distributions for Counts and Proportions243
Introduction243
5.1The Binomial Distributions244
The binomial distributions for sample counts245
The binomial distributions for statistical sampling247
Case 5.1 Inspecting a Supplier’s Products247
Finding binomial probabilities247
Binomial formula250
Binomial mean and standard deviation253
Sample proportions255
Normal approximation for counts and proportions256
The continuity correction260
Assessing binomial assumption with data261
Section 5.1 Summary263
Section 5.1 Exercises264
5.2The Poisson Distributions267
The Poisson setting267
The Poisson model269
Approximations to the Poisson270
Assessing Poisson assumption with data271
Section 5.2 Summary273
Section 5.2 Exercises273
5.3Toward Statistical Inference275
Sampling distributions276
Bias and variability279
Why randomize?280
Section 5.3 Summary281
Section 5.3 Exercises281
Chapter 5 Review Exercises284
CHAPTER 6 Introduction to Inference287
Introduction287
Overview of inference288
6.1The Sampling Distribution of a Sample Mean288
The mean and standard deviation of 292
The central limit theorem294
Section 6.1 Summary299
Section 6.1 Exercises300
x
6.2Estimating with Confidence302
Statistical confidence302
Confidence intervals304
Confidence interval for a population mean306
How confidence intervals behave309
Some cautions311
Section 6.2 Summary313
Section 6.2 Exercises314
6.3Tests of Significance316
The reasoning of significance tests316
Case 6.1 Fill the Bottles317
Stating hypotheses319
Test statistics321
-values322
Statistical significance324
Tests of one population mean326
Two-sided significance tests and confidence intervals329
-values versus reject-or-not reporting331
Section 6.3 Summary332
Section 6.3 Exercises333
6.4Using Significance Tests336
Choosing a level of significance337
What statistical significance does not mean337
Statistical inference is not valid for all sets of data339
Beware of searching for significance339
Section 6.4 Summary341
Section 6.4 Exercises341
6.5Power and Inference as a Decision343
Power343
Increasing the power345
Inference as decision346
Two types of error346
Error probabilities347
The common practice of testing hypotheses349
Section 6.5 Summary350
Section 6.5 Exercises350
Chapter 6 Review Exercises351
CHAPTER 7 Inference for Means357
Introduction357
7.1Inference for the Mean of a Population358
distributions358
The one-sample confidence interval360
Case 7.1 Time Spent Using a Smartphone361
The one-sample test362
Using software365
Matched pairs procedures368
Robustness of the one-sample procedures371
BEYOND THE BASICS: The Bootstrap372
Section 7.1 Summary373
Section 7.1 Exercises374
7.2Comparing Two Means378
The two-sample statistic379
The two-sample confidence interval381
The two-sample significance test383
Robustness of the two-sample procedures384
Inference for small samples385
The pooled two-sample procedures386
Case 7.2 Active versus Failed Retail Companies389
Section 7.2 Summary392
Section 7.2 Exercises393
7.3Additional Topics on Inference398
Choosing the sample size398
Inference for non-Normal populations406
Section 7.3 Summary408
Section 7.3 Exercises409
Chapter 7 Review Exercises411
CHAPTER 8 Inference for Proportions417
Introduction417
8.1Inference for a Single Proportion418
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Case 8.1 Robotics and Jobs418
Large-sample confidence interval for a single proportion420
Plus four confidence interval for a single proportion421
Significance test for a single proportion423
Choosing a sample size for a confidence interval426
Case 8.2 Marketing Christmas Trees428
Choosing a sample size for a significance test429
Section 8.1 Summary431
Section 8.1 Exercises432
8.2Comparing Two Proportions436
Large-sample confidence intervals for a difference in proportions437
Case 8.3 Social Media in the Supply Chain438
Plus four confidence intervals for a difference in proportions440
Significance tests440
Choosing a sample size for two sample proportions444
BEYOND THE BASICS: Relative Risk447
Section 8.2 Summary448
Section 8.2 Exercises449
Chapter 8 Review Exercises451
CHAPTER 9 Inference for Categorical Data455
9.1Inference for Two-Way Tables455
Two-way tables456
Case 9.1 Are Flexible Companies More Competitive?457
Describing relations in two-way tables458
The hypothesis: No association462
Expected cell counts462
The chi-square test463
The chi-square test and the test465
Models for two-way tables466
BEYOND THE BASICS: Meta-Analysis468
Section 9.1 Summary470
9.2Goodness of Fit470
Section 9.2 Summary475
Chapter 9 Review Exercises475
CHAPTER 10 Inference for Regression483
Introduction483
10.1Inference about the Regression Model484
Statistical model for simple linear regression484
From data analysis to inference485
Case 10.1 The Relationship between Income and Education for Entrepreneurs485
Estimating the regression parameters490
Conditions for regression inference494
Confidence intervals and significance tests495
The word “regression”500
Inference about correlation500
Section 10.1 Summary502
Section 10.1 Exercises503
10.2Using the Regression Line510
BEYOND THE BASICS: Nonlinear Regression515
Section 10.2 Summary515
Section 10.2 Exercises516
10.3Some Details of Regression Inference517
Standard errors518
Analysis of variance for regression520
Section 10.3 Summary524
Section 10.3 Exercises524
Chapter 10 Review Exercises526
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CHAPTER 11 Multiple Regression531
Introduction531
11.1Data Analysis for Multiple Regression534
Case 11.1 Assets, Sales, and Profits534
Data for multiple regression534
Preliminary data analysis for multiple regression535
Estimating the multiple regression coefficients538
Regression residuals541
The regression standard error544
Section 11.1 Summary545
Section 11.1 Exercises546
11.2Inference for Multiple Regression548
Multiple linear regression model549
Case 11.2 Predicting Movie Revenue550
Estimating the parameters of the model550
Inference about the regression coefficients551
Inference about prediction554
ANOVA table for multiple regression555
Squared multiple correlation 558
Inference for a collection of regression coefficients559
Section 11.2 Summary561
Section 11.2 Exercises562
11.3Multiple Regression Model Building566
Case 11.3 Prices of Homes566
Models for curved relationships569
Models with categorical explanatory variables571
More elaborate models575
Variable selection methods577
BEYOND THE BASICS: Multiple Logistic Regression580
Section 11.3 Summary582
Section 11.3 Exercises582
Chapter 11 Review Exercises584
CHAPTER 12 Statistics for Quality: Control and Capability591
Introduction591
Quality overview592
Systematic approach to process improvement593
Process improvement toolkit594
12.1Statistical Process Control597
Section 12.1 Summary599
Section 12.1 Exercises600
12.2Variable Control Charts600
and charts601
Case 12.1 Turnaround Time for Lab Results604
Case 12.2 O-Ring Diameters609
and charts612
Charts for individual observations614
Don’t confuse control with capability!619
Section 12.2 Summary626
Section 12.2 Exercises626
12.3Attribute Control Charts630
Control charts for sample proportions630
Case 12.3 Reducing Absenteeism631
Control charts for counts per unit of measure636
Section 12.3 Summary638
Section 12.3 Exercises638
Chapter 12 Review Exercises639
CHAPTER 13 Time Series Forecasting643
Introduction643
Overview of Time Series Forecasting643
13.1Assessing Time Series Behavior644
Case 13.1 Amazon Sales647
Runs test648
Autocorrelation function651
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Forecasts656
Section 13.1 Summary657
Section 13.1 Exercises657
13.2Random Walks657
Price changes versus returns661
Section 13.2 Summary663
Section 13.2 Exercises663
13.3Modeling Trend and Seasonality Using Regression664
Identifying trends665
Seasonal patterns671
Using indicator variables672
Residual checking677
Section 13.3 Summary679
Section 13.3 Exercises679
13.4Lag Regression Models681
Autoregressive-based models681
Section 13.4 Summary690
Section 13.4 Exercises691
13.5Moving-Average and Smoothing Models691
Moving-average models691
Moving average and seasonal ratios694
Exponential smoothing models699
Section 13.5 Summary706
Section 13.5 Exercises706
Chapter 13 Review Exercises708
CHAPTER 14 One-Way Analysis of Variance711
Introduction711
14.1One-Way Analysis of Variance712
The ANOVA setting712
Comparing means713
The two-sample statistic714
An overview of ANOVA715
Case 14.1 Tip of the Hat and Wag of the Finger?715
The ANOVA model718
Estimates of population parameters720
Testing hypotheses in one-way ANOVA722
The ANOVA table724
The test726
Using software729
BEYOND THE BASICS: Testing the Equality of Spread731
Section 14.1 Summary733
14.2Comparing Group Means733
Contrasts733
Case 14.2 Evaluation of a New Educational Product733
Multiple comparisons740
Simultaneous confidence intervals744
Section 14.2 Summary744
14.3The Power of the ANOVA Test745
Section 14.3 Summary749
Chapter 14 Review Exercises749
Notes and Data SourcesN-1
TablesT-1
Answers to Odd-Numbered ExercisesS-1
IndexI-1
The following optional Companion Chapters can be found online at www.macmillanhighered.com/psbe4e.
CHAPTER 15 Two-Way Analysis of Variance 15-1
Introduction15-1
15.1The Two-Way ANOVA Model15-2
Advantages of two-way ANOVA15-2
The two-way ANOVA model15-5
Main effects and interactions15-7
Section 15.1 Summary15-13
15.2Inference for Two-Way ANOVA15-13
The ANOVA table for two-way ANOVA15-13
Carrying out a two-way ANOVA15-15
Case 15.1 Discounts and Expected Prices15-15
xiv
Case 15.2 Expected Prices15-16
Section 15.2 Summary15-21
Chapter 15 Review Exercises15-21
Notes and Data Sources15-28
Answers to Odd-Numbered Exercises15-29
CHAPTER 16 Nonparametric Tests 16-1
Introduction16-1
16.1The Wilcoxon Rank Sum Test16-3
Case 16.1 Price Discrimination?16-3
The rank transformation16-4
The Wilcoxon rank sum test16-5
The Normal approximation16-7
What hypotheses do the Wilcoxon test?16-8
Ties16-9
Case 16.2 Consumer Perceptions of Food Safety16-10
Rank versus tests16-12
Section 16.1 Summary16-12
Section 16.1 Exercises16-12
16.2The Wilcoxon Signed Rank Test16-15
The Normal approximation16-18
Ties16-19
Section 16.2 Summary16-21
Section 16.2 Exercises16-21
16.3The Kruskal-Wallis Test16-24
Hypotheses and assumptions16-25
The Kruskal-Wallis test16-25
Section 16.3 Summary16-27
Section 16.3 Exercises16-27
Chapter 16 Review Exercises16-29
Notes and Data Sources16-31
Answers to Odd-Numbered Exercises16-32
CHAPTER 17 Logistic Regression 17-1
Introduction17-1
17.1The Logistic Regression Model17-2
Case 17.1 Clothing Color and Tipping17-2
Binomial distributions and odds17-2
Model for logistic regression17-4
Fitting and interpreting the logistic regression model17-5
Section 17.1 Summary17-8
17.2Inference for Logistic Regression17-9
Examples of logistic regression analyses17-11
Section 17.2 Summary17-15
17.3Multiple Logistic Regression17-16
Section 17.3 Summary17-17
Chapter 17 Review Exercises17-17
Notes and Data Sources17-22
Answers to Odd-Numbered Exercises17-23