A
Academy Awards age discrimination problem, 41, 45, 48,

75, 81, 99, 112–115, 119–122, 471–474

Accuracy, 17
Achievement tests, 567
Addition rule, 151–155, 164
Adjusted Wald confidence interval, 331
Air bag study, 487
Aircraft

altimeter production problem, 733, 735–736, 740–741,

742–744, 749–750

navigation equipment, 351
seating problem, 315
weight problem, 245, 293–294

Analysis of variance (ANOVA), 634–672. See also

Variance

definition, 636
degrees of freedom, 642
experiment design, 645–646
F distribution, 636–637, 640–643
interaction, 655–657
MS(treatment), 645
one-way, 637–649
sample size, 641–646
SS(total), 644–645
treatment (factor), 638
two samples, 636
two-way, 655–660

Arithmetic mean. See Mean
Aspirin, 460
Assignable variation, 738
“at least one,” 168–169
Attributes, control charts, 748–750
Average, 81

B
Bank customer line problem, 92–93, 95–96
Bar codes, 185
Baseball batting problem, 96
Basketball free throw problem, 141
Bayes’ theorem, 190
Bear study, 719–720
Bell-shaped distribution, 100–101
Bimodal data, 80
Binomial distribution, 213–220

binomial probability formula, 216–217, 219–220

definition, 214
mean, variance, standard deviation, 225–227
normal distribution approximation, 291–298
notation, 214–215
Poisson approximation, 232–233
technology, 218–219, 220

Binomial probability formula, 216–217,

219–220

Birthday problem, 145, 175–176
Birth weight problem, 356–357
Bivariate data, 517
Blinding, 23–24
Blocks, experimental, 24
Body mass index problem, 358, 697–698
Body temperature problem, 285–286, 684–685
Bombing problem, 231–232
Bonferroni multiple comparison test, 647–649
Bootstrap resampling, 380–381
Boundary, class, 43, 44
Boxplots (box-and-whisker diagram), 120–122

modified, 123–126

Bribery, 743
b

1

slope, 542–544

Burger, Joanna, 383

C
Calculator. See Software/calculator results
Cancer and smoking study, 711
Car crash problem, 72
Car dashboard design problem, 264–265
Card shuffles, 183
Carpal tunnel syndrome problem, 455, 458–460,

461–462

Carvalho, Barbara, 243
Castaneda v. Partida, 199, 201, 206, 208, 215–217,

219–220, 225–227

Causality, vs. correlation, 17, 525
Census, 45, 326, 356
Center, 42, 76–86

best measure, 84
definition, 77
mean, 77–78, 83–84, 85
median, 78–79, 85
midrange, 80–81, 85
mode, 80, 85

Centerline, 739

Index

857

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Central limit theorem, 280–287

applications, 282–286
continuity corrections, 294–297
finite population correction, 286–287

Centroid, 530–531
Chebyshev’s theorem, 101
Children’s Defense Fund, 322
Chi-square distribution, 364–367, 590

critical value, 365–367
hypothesis testing, 437–439, 445, 592–600

Chuang-Stein, Christy, 197
Cigarette smoking problems, 180–181, 711
Class

boundary, 43, 44
midpoint, 43
width, 43

Class attendance, 680
Class length problem, 247–249
Class size, 79, 477
Clinical trial problems, 183, 185, 261
Cloning poll, 142–143
Cluster sampling, 27, 28

vs. stratified sampling, 29

Coefficient of determination, 559
Coefficient of variation, 103–104
Coin flip problem, 613–614
Coincidence, 170
Coke versus Pepsi problem, 498–501
College rank problem, 675, 710–712
Combinations rule, 185
Commercials, 419
Compact disc manufacture, 568
Complement, 144
Complementary events, 144–145, 155
Completely randomized experiment, 25, 646
Composite sampling, 171
Compound event, 151
Conditional probability, 161, 169–171
Condominium prices, 545
Confidence interval (interval estimate)

bootstrap method, 380–381
data comparison, 323, 359
definition, 322
interpretation, 322–323
limits, 340
margin of error, 326–328, 340, 351–352, 357
matched pairs, 485
mean, 339–342, 351–353, 421–422, 470–471,

474–476, 477

mean (standard deviation not known), 352, 430–431
overlapping, 359, 368–369
point estimate, 330–331, 357

prediction intervals, 560–562
proportion, 322–323, 326–328, 410–413,

460–463

rationale, 342, 370
round-off rule, 326, 341
standard deviation, 440
two proportions, 458
variance, 367–370

Confidence level (confidence coefficient, degree of

confidence), 322

Confounding, 23
Confusion of the inverse, 171
Consumer’s Report, 63
Contingency tables, 606–615

definition, 606
expected frequency, 608–610
P-values, 610–611
test of homogeneity, 611–614
test of independence, 607–608

Continuity corrections, 294–297
Continuous (numerical) data, 6–7
Control charts, 732–756

attributes, 748–750
centerline, 739
interpretation, 741–742
mean, 743–744
p chart, 748–750
process data, 734–735
R chart, 738–741
run charts, 735–738
upper/lower control limits, 739, 741–742
variation, 738–741

chart, 743–744

Convenience sampling, 27, 28
Corn seed problem, 681–682, 691–693
Correlation, 517–532

centroid, 530–531
definition, 517
errors, 525
explained variation, 524–525
formal hypothesis test, 525–532
linear correlation coefficient, 518, 520–524
rank, 708–713
scatterplots, 518, 519, 530
vs. causality, 17, 525
vs. linearity, 525

Cost of Laughing Index, 110
Cotinine problem, 180–181
Count five method, 501
Counting, 179–186

combinations rule, 185
factorial rule, 181–182

x

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fundamental counting rule, 180
permutations rule, 182–184, 185

Course grades, 7–8
Crimean War, 63, 65
Critical region (rejection region), 392
Critical thinking, 11–17, 29, 76

aircraft seating, 315
axial loads, 750
bladder cancer identification, 451
draft lottery, 729
drug approval, 671
Duragesic, 586
fear of flying, 512
fraud, 632
frequency distribution, 46–48
gender discrimination, 38
gender-selection methods, 241
goodness-of-fit, 72
keyboard configuration, 133
measures of center, 81–82
photo-cop survey, 381
pregnancy test, 196

Critical value, 324–325, 351–352, 393–394

chi-square distribution, 365–367
definition, 324
goodness-of-fit test, 593
Kruskal-Wallis test, 703
linear correlation, 527–529
margin of error, 325–326
matched pairs, 485, 487
McNemar’s test, 622
mean, 419, 426
notation, 324
sign test, 685
standard deviation/variance, 496–497
test of independence, 607
two variances, 496–497
variance, 365–367
Wilcoxon tests, 690, 696

Cross-sectional study, 22
Crowd size, 357
Cumulative frequency distribution, 46
Curbstoning, 326
CVDOT, 42, 65, 763

D
Data

bell-shaped, 100–101
bimodal, 80
bivariate, 517
center, 42, 76–86. See also Center
characteristics, 42

continuous (numerical), 6–7
definition, 45
discrete, 6–7
distribution, 42
interval, 8, 9
missing, 16, 52
multimodal, 80
nominal, 7, 9, 682–683
ordinal, 7–8, 9
outlier, 42, 119–120, 121
paired, 517
phony, 16
process, 734–735
qualitative (categorical, attribute), 6
quantitative, 6
range, 93
ratio, 8–9
reliability, 94
runs test, 717–722
skewed, 85–86
symmetric, 85
time, 42
types, 5–9
validity, 94
variation, 42
visualization, 56–65

Death penalty, 462
Death postponement study, 543
Decimal, percentage conversion from, 15
Degrees of freedom, 351–352, 470, 642

chi-square distribution, 364, 437
definition, 351

Density curve (probability density function), 248–249
Dependent events, 162, 163–164
Deviation. See Standard deviation; Variation
Dice simulation, 176–177
Diet pills, 474
Discordant pairs, 624–625
Discrete data, 6–7
Disjoint events, 153–155
Disobedience study, 7
Dispersion. See Variation
Distortions, 17
Dotplot, 58
Double-blind study, 24
Drug approval process, 408
Drug testing problem, 137, 152–154, 160–161, 170–171
Duragesic, 586

E
E-mail survey, 329–330
Empirical rule, 100–101

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Errors

controlling, 399–400
nonsampling, 30
notation, 399
sampling, 30–31
type I, 398–400
type II, 398–400

Estimating, 318–382

chi-square distribution, 364–367
confidence intervals, 322–323. See also Confidence

interval (interval estimate)

critical value, 324–325. See also Critical value
degrees of freedom, 351, 364
margin of error, 325–326. See also Margin of error
mean, 338–359
point estimate, 321, 330–331, 338–339, 357, 367
probability, 140–141
proportion, 320–332
sample mean, 338–339, 350
sample proportion, 321, 325
sample size, 328–331, 338, 342–345, 370–371
sample variance, 367–370
sampling distribution, 276–277
standard deviation, 98–99
Student t distribution, 350, 353–357
variance, 363–371

Estimator, 97, 339, 367
Ethics, 427
Event(s)

complementary, 144–145, 155
compound, 151
definition, 139
dependent, 162, 163–164
disjoint, 153–155
independent, 162, 163–164

Excel. See Software/calculator results
Expected frequency, 592–598, 608–610
Expected value, 208–209
Experiment, 21–31

blinding, 23–24
blocks, 24
completely randomized, 25, 646
confounding, 23
definition, 21
design, 21–31, 488–489
ethics, 427
power, 402–403
randomized block, 24, 25
replication, 25–26
rigorously controlled, 25
sample size, 25–26

sampling errors, 30–31
sampling strategies, 26–30
types, 21–22
variables, 23–25

Experimental units (subjects), 21
Explained/unexplained deviation, 557–559
Exploratory data analysis (EDA), 119–126
Extrasensory perception, 393

F
Factorial rule, 181–182
Factorial symbol (!), 181
False negative, 137
False positive, 137, 609
F distribution, 495–498, 636–637, 640–643
Fear of flying, 512
Federalist Papers, 44
Fertilizer problem, 24, 25, 488–489
Finite population correction, 286–287
Fisher exact test, 614–615
Five-number summary, 121
Fluoride, 486
Flynn effect, 736
Football problem, 271–272
Formal addition rule, 153
Formal multiplication rule, 162
Foy, Jeffrey, 673
Fraction, percentage conversion from, 15
Fraud detection problem, 589, 597–598
Free throw problem, 141
Frequency, 43

expected, 592–598, 608–610
relative, 45

Frequency distribution, 42–48

classes, 43–44
construction, 44–45
cumulative, 46
definition, 43
interpretation, 46–48
mean, 83–84
relative, 45–46

Frequency polygon, 57
Fundamental counting rule, 180
Fuzzy central limit theorem, 286

G
Gallup poll, 21
Gambling problems, 140, 142, 146, 175
Gender problems

birth probabilities, 143, 144, 168, 170
discrimination, 38

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medical tests, 690
polling, 612–613
selection methods, 164, 174, 184, 241, 386–387,

388–389, 682–683

U.S. Senate, 273

Genetics problems, 142, 411–413
Geometric distribution, 224
Geometric mean, 91
Gillespie, Angela, 731
Goodness-of-fit test, 72, 591–600
Graph(s), 56–65

boxplots, 120–126
design, 62–65
dotplot, 58
frequency polygon, 57
histogram, 51–54, 203–204
misleading, 13–14
normal quantile plot, 302–306
ogive, 57–58
Pareto chart, 59, 60
pie chart, 59–60
probability histogram, 203–204
purposes, 65
relative frequency histogram, 52
residual plots, 550–552
scatterplot, 60–61, 518, 519, 530
stemplot, 58–59
time-series, 61–62

Graunt, John, 5
Growth charts, 47

H
Handedness, 428
Harmonic mean, 91
Haskell, Mark D., 587
Hawthorne effect, 24
Heart attack rate, 460
Height problem, 46–47, 103–104, 110–111, 303–306
Histogram, 51–54, 203–204
Holzman, Robert S., 135
Home field advantage, 612
H test, 702–705
Hydroxyurea study, 261
Hypergeometric distribution, 224
Hypothesis. See also Hypothesis testing

alternative, 390–391
definition, 386
null, 389–391, 394–400
research, 390

Hypothesis testing, 384–451. See also Test statistic

chi-square distribution, 437–439, 445, 592–600

components, 389–394
conclusions, 394–400
confidence interval, 395, 400, 410–413, 421–422,

430–431, 440

critical region, 392, 393
critical value, 393–394
errors, 398–400
left-tailed, 394, 395, 396, 529
linear correlation, 525–532
matched pairs, 485–488
mean, 418–422, 445, 475–476, 477
mean (standard deviation not known), 426–431
multiple-negative conclusions, 397–398
one-tailed, 529
power, 400, 402–403
proportion, 407–413, 445, 458–460
P-value method, 394–397, 401, 409–412, 419–421,

429–430, 440, 458–460, 488, 501, 610–611

right-tailed, 394, 395, 396, 529
significance level, 392–393, 403
simulations, 450
standard deviation/variance, 436–440, 445, 495–501
summary, 445
test statistic, 391–392. See also Test statistic
traditional method, 401, 410, 412, 421, 427–428, 460,

485–487, 495–500, 609–610

two-tailed, 394, 395, 528, 529

I
Identity theft, 180
Independent events, 162, 163–164
Inferences, 763–765
Inferences from two samples, 454–512

confidence interval, 458, 460–463, 470–471, 474–475, 488
F distribution, 495–498
hypothesis testing, 458–460, 472–474, 475–478,

485–487

matched pairs, 484–489
means, 469–478
proportions, 456–463
variance/standard deviation, 495–501

Influential points, 548
Interaction, 655–657
Internet Project, 38

analysis of variance, 672
central limit theorem, 316
confidence intervals, 382
contingency tables, 632
control charts, 750
data summary, 134
graphs, 72

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Internet Project (Continued)

hypothesis testing, 451
linear regression, 586
nonparametric tests, 730
probabilities, 196
probability distribution, 242
testing hypothesis, 512

Internet use problem, 296–297
Interquartile range, 123
Interval data, 8, 9
Interval estimate. See Confidence interval (interval

estimate)

Intuitive addition rule, 153
Intuitive multiplication rule, 162–163
Inverse, confusion of, 171
IQ score problems, 101–102, 261–262, 344–345, 736

J
Jet engine problem, 160
Job search problem, 385, 408
Journalism, 15
Jury selection problem, 199, 201, 206, 208, 215–217,

219–220, 225–227

K
Kruskal-Wallis test, 702–705

L
Laughing index, 110
Law of large numbers, 141–144
Lead monitoring problem, 78, 79, 81
Least-squares property, 548–550
Lebbos, Nabil, 633
Left-tailed test, 394, 395, 396, 529
Levene-Brown-Forsythe test, 501
Lie detector, 388
Limits, class, 43
Linear correlation coefficient, 518, 520–524

definition, 518
interpretation, 522–524
properties, 524
rounding, 521–522

Linearity, vs. correlation, 525
Lipitor study, 59
Literary Digest poll, 13
Loaded questions, 16
Logistic regression, 572
Lognormal distribution, 306
Lottery problems, 161, 181, 202, 209, 233, 271, 292, 303
Lower class limits, 43
Lower control limits, 739, 741–742
Lung cancer, 711

Lurking variable, 525
Lycett, Mark T., 513
Lying study, 126

M
Madison, James, 44
Mann-Whitney U test, 695
Margin of error, 458

definition, 325–326
mean, 339–342, 352, 357
polls, 458
proportion, 325–326, 328

Marginal change, 547–548
Marijuana testing problem, 137, 152–154, 160–161, 170–171
Mars Climate Orbiter, 739
Matched pairs, 469, 615

confidence interval, 458
experimental design, 488–489
hypothesis testing, 485–488
inferences, 484–489
McNemar’s test, 621–625
sign test, 680–682
Wilcoxon signed-ranks test, 689–693

Mathematical modeling, 576–579
McNemar’s test, 621–625
Mean, 85, 204–205, 338–359. See also Estimating;

Standard deviation

binomial distribution, 225–227
confidence interval, 339–342, 351–353, 470–471,

474–476, 477

control chart, 743–744
definition, 77
expected value, 208–209
frequency distribution, 83–84
geometric, 91
harmonic, 91
hypothesis testing, 475–476, 477
inference about two means, 469–478
margin of error, 339–342, 352, 357
multiple comparison test, 647–649
point estimate, 350, 357
quadratic, 91
randomness above and below, 721–722
range test, 646–647
sample mean, 282, 338–339
sample size, 338–339, 342–345
sampling distribution, 274–275
standard deviation not known, 349–359, 426–431
standard error, 282
testing a claim, 418–422, 426–431, 445
trimmed, 90
weighted, 84

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Mean absolute deviation, 102–103
Mean square (MS), 645
Measurement

interval level, 8, 9
nominal, 7, 9
ordinal, 7–8, 9
ratio level, 8–9

Measure of center, 77
Median, 78–79, 85

randomness above and below, 721–722
sign test, 684–685

Mesnick, Sarah, 39
Meta-analysis, 430
Meteorite problem, 142
Midpoint, class, 43
Midrange, 80–81, 85
Milgram, Stanley, 7
Minitab. See Software/calculator results
Miringoff, Lee, 243
M&Ms quality control problem, 427–428
Mode, 80, 85
Modeling, 576–579
Morrison, Kathleen, 513
Motorcycle helmet problem, 609–610
Motor vehicle accidents, 476
MS(treatment), 645
Multimodal data, 80
Multinomial distribution, 224
Multinomial experiments

definition, 591
expected frequencies, 592–598
goodness-of-fit, 591–600
P-value, 594, 598–600

Multiple coefficient of determination, 568–569
Multiple comparison test, 647–649
Multiple regression, 566–573
Multiplication rule, 159–164

N
Napoleon’s army, 63, 64
NBA salaries, 570
NFL kicker, 572
Nicotine patch therapy, 330–331
Nightingale, Florence, 63, 65
Nominal data, 7, 9

sign test, 682–683

Nonparametric methods, 674–730

advantages, 676
definition, 676
disadvantages, 676–677
efficiency rating, 677
Kruskal-Wallis test, 702–705

matched pairs, 680–682
median of single population, 684–685
nominal data, 682–683
rank correlation, 708–713
ranks, 677–678
runs test for randomness, 717–722
sign test, 678–686
summary, 725
ties in ranks, 678
Wilcoxon rank-sum test, 695–699
Wilcoxon signed-ranks test, 689–693

Nonresponse, 16
Nonsampling errors, 30
Normal distribution, 46–48, 245–316. See also Standard

normal distribution

applications, 259–265
assessment, 302–306
binomial distribution approximation, 291–298
bivariate, 520
central limit theorem, 280–287
data transformation, 306–307
definition, 246
finding values, 262–266
histogram, 53
nonstandard, 260
normal quantile plot, 302–306
sampling distribution, 269–278

Normality, 338, 426
Normal quantile plot, 302–306
Null hypothesis, 389–391, 394–400

accept/fail to reject, 396–397

Numbers, precise, 17
Numerical data, 6–7

O
Obermayer, Joel B., 317
Observational study, 21, 22

vs. clinical trial, 23

Odds, 145–146
Odds ratio, 150–151
Ogive, 57–58
Old Faithful geyser problem, 515–516, 523–524, 527–529,

544, 546–547, 559, 561, 562, 567–568

One-tailed test, 529
Oral report, 758
Oranges, 355
Ordinal data, 7–8, 9
O’Toole, Dan, 757
Outliers, 42, 119–120, 121, 548

extreme, 129
mild, 129

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P
Paired data, 517
Palmistry, 519
Parachuting safety, 293
Parameter, 5
Pareto chart, 59, 60
Passwords, 182
Payoff odds, 145–146
p chart, 748–750
Pearson product moment correlation coefficient, 518,

520–524

Penny weight problem, 47, 48, 369–370
Percentages

decimal conversion, 15
misleading, 14–15
principles, 15
proportion conversion, 321

Percentiles, 111–115
Permutations rule, 182–184, 185
Personal security codes, 182
Phone numbers, 180
Photo-cop survey, 381
Pictographs, 14, 15
Pie chart, 59–60
Pinball machine problem, 712–713
Placebo effect, 24, 285
Plant selection problem, 163
Point estimate, 321, 330–331, 357, 367
Poisson distribution, 230–233
Polio study, 23–24, 26, 461
Polling. See Surveys
Pooled estimate, 476–477
Pooled sample proportion, 457
Poplar tree weight problem, 635, 639–640, 703–705
Population

definition, 4
finite, 286–287
size, 330
standard deviation, 96

Population mean. See Mean
Population model, 578–579
Population proportion. See Proportion
Population variance. See Variance
Power, 400, 402–403
Precise numbers, 17
Prediction, regression equation, 544–547
Prediction intervals, 560–562
Predictor variable, 541
Pregnancy test problem, 196
Probability, 138–146

addition rule, 151–155

“at least one,” 168–169
classical approach, 140
combinations rule, 185
complementary events, 144–145, 155
complements, 168–171
conditional, 161, 169–171
counting, 179–186
factorial rule, 181–182
law of large numbers, 141–144
multiplication rule, 159–164
notation, 139, 159
odds, 145–146
permutations rule, 182–184
rare event rule, 138
relative frequency approximation, 139, 140
rounding off, 144–145
rules, 139–140
simulations, 174–177
subjective, 140–141
z score, 249–256

Probability distribution, 198–242. See also Normal

distribution; Standard normal distribution

binomial, 213–220
definition, 201
expected value, 208–209
mean, 204–205
Poisson distribution, 230–233
probability histogram, 203–204
random variables, 201–209
requirements, 203–204
standard deviation, 204–205
unusual results, 205–208, 236
variance, 204–205

Probability histogram, 203–204
Probability sample, 26–27
Procedures, 763–765
Process data, 734–735
Projects, 758–763
Proportion, 320–332

confidence interval, 322–323, 326–328, 460–463
critical values, 324–325
definition, 321
hypothesis testing, 407–413, 458–460
inferences about two proportions, 456–463
margin of error, 328
notation, 321
point estimate, 321, 330–331
sample size, 328–331
sampling distribution of proportion, 270–274
testing a claim, 407–413, 445
test statistic, 408, 457

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Prospective (longitudinal, cohort) study, 22
Publication bias, 17
Pulse rate problem, 47, 48, 99, 124–126, 339, 341–342
Push polling, 439
P-value method, 401

contingency tables, 610–611
hypothesis testing, 394–397, 409–412, 419–421,

429–430, 440, 458–460, 488, 501, 610–611

multinomial experiment, 594, 598–600
multiple regression, 569
Student t distribution, 429–430

Q
Quadratic mean, 91
Qualitative (categorical, attribute) data, 6
Quality control. See Control charts
Quality control problems, 427–428, 438–439
Quantitative data, 6
Quartiles, 111–115
Queing theory, 231
Questions

loaded, 16
nonresponse, 16
order of, 16

R
Racetrack gambling, 142
Rainfall problem, 720–721
Randomness, runs test, 717–722
Random numbers, 175–176, 175–177, 282–283
Random sampling, 26–27, 28
Random selection, 4, 45
Random variables, 201–209

binomial probability distribution, 213–219
continuous, 201–203
definition, 201
discrete, 201–202, 208–209
expected value, 208–209
probability histogram, 203–204
uniform distribution, 247–248

Range, 93
Range chart, 738–741
Range rule of thumb, 98–99, 205–206
Range tests, 646–648
Rank, 8, 677–678
Rank correlation test, 708–713
Rare event rule, 138, 207–208, 285, 386
Ratio data, 8–9
Ratio test, 9
R chart, 738–741
Refusals, 16

Regression, 541–552

coefficient of determination, 559
guidelines, 547
influential points, 548
interpretation, 547–548
least-squares property, 548–550
logistic, 572
marginal change, 547–548
multiple, 566–573
outliers, 548
predictions, 544–547
regression equation/line, 542–544
residuals, 548–550
standard error of estimate, 560–561
stepwise, 571

Relative frequency histogram, 52
Relative risk, 150
Relative standing, 110–116

percentiles, 111–115
quartiles, 111–115
z score, 110–111. See also z score

Reliability, 94
Replication, 25–26
Residual, 548–550
Residual plots, 550–552
Retrospective (case-control) study, 22
Right-tailed test, 394, 395, 396, 529
Rigorously controlled experiment, 646
Root mean square, 91
Rosenthall effect, 24
Round-off rule, 81, 98

confidence interval, 326, 341
linear correlation coefficient, 521–522
mean, 205
probabilities, 144–145
proportion, 326
regression, 543
sample size, 329, 343
standard deviation, 205
variance, 205

Run charts, 735–738
Runs test for randomness, 717–722

S
Saccucci, Michael, 452–453
Salk vaccine study, 23–24, 26, 461
Sample(s)

bad, 12–13
definition, 4, 45
dependent, 469
independent, 469

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Sample(s) (Continued)

mean, 282, 338–339
multistage design, 29–30
probability, 26–27
random, 26–27
simple random, 26–27
small, 13
space, 139
standard deviation, 367, 426. See also Standard deviation
variance, 97–98, 367
variance between, 640
variance within, 640
voluntary response (self-selected), 12–13

Sample proportion, 321, 325
Sample size (n), 25–26, 77

equal, 641–643
mean, 338–339, 342–345
proportion, 328–331
round-off rule, 329
standard deviation, 344–345
unequal, 643–646
variance, 370–371

Sampling

bootstrap, 380–381
cluster, 27, 28
composite, 171
convenience, 27, 28
distribution, 269–278
errors, 30–31
multistage, 29–30
random, 28
with replacement, 163, 277
simple random, 28
stratified, 27, 28
systematic, 27, 28
variability, 275
without replacement, 163, 277

Sampling distribution, 269–278

central limit theorem, 280–287
estimators, 276–277
mean, 274–275
proportion, 270–274

Sampling variability, 275
SAT scores, 567
Scatterplot (scatter diagram), 60–61, 518, 519, 530

outlier/influential point, 458
quadrants, 530

Sehlinger, Bob, 73
Self-interest study, 17
Shakespeare, William, 152
Sickle cell anemia study, 261
Sign test, 678–686

Significance level, 392–393, 403
Simple event, 139
Simple random sample, 26–27
Simulations, 143, 174–177, 450
Six degrees of separation, 3, 30
Six Sigma programs, 749
Skewness, 85–86
Slope, regression equation, 542–544
Soda can weight problem, 498–501
Software/calculator results, 37

binomial probabilities, 218–219
boxplots, 127
central limit theorem, 314
confidence interval, 332, 357, 358
contingency tables, 615
control charts, 744–745, 750
correlation, 532
descriptive statistics, 86, 116
graphs, 66
histogram, 53–54
hypothesis testing, 422, 431, 440, 450
Kruskal-Wallis test, 705
matched pairs, 489
McNemar’s test, 621–625
modeling, 579
multinomial experiments, 600
multiple regression, 573
normal distribution, 265
normal quantile plot, 307
one-way ANOVA, 649
p chart, 750
Poisson distribution, 233
probability distribution, 218–219, 220
random number generation, 175–176
rank correlation, 713
regression, 552
run chart, 735–736
runs test, 721
runs test for randomness, 721–722
sample size, 332, 345, 370–371
sign test, 686
standard deviation/variance, 501
standard normal distribution, 250–251
two means, 478
two population proportions, 463
two variances, 501
two-way ANOVA, 661
variation, 563
Wilcoxon tests, 693, 699
z score, 257

Spearman’s rank correlation coefficient, 708
Spearman’s rank correlation test, 708–713

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Spock, Benjamin, 199
Spread. See Variation
SS(total), 644–645
Standard deviation, 204–205

binomial distribution, 225–227
calculation, 94–96
Chebyshev’s theorem, 101
comparing two samples, 495–501
confidence interval, 440
definition, 94
empirical rule, 101–102
estimation, 98–99, 102–103
interpretation, 98–101
mean absolute deviation, 102–103
population, 96
range rule of thumb, 98–99
rationale, 101–103
sample size, 344–345
testing a claim, 436–440, 445

Standard error of estimate, 560–561
Standard error of the mean, 282
Standard normal distribution, 247–257

definition, 249
density curve, 249–250
finding probabilities, 250–254
finding z scores, 254–255

Standard score. See z score
STATDISK. See Software/calculator results
Statistic, 5
Statistically stable process, 736, 742–743
Statistics, 4

descriptive, 76
in education, 766
inferential, 76
jobs in, 577
journalism, 1134
misleading, 11–17, 29, 322, 392

Stemplot (stem-and-leaf plot), 58–59
Stepwise regression, 571
Stock return problem, 99
Stowaway age problem, 357
Stratified sampling, 27, 28

vs. cluster sampling, 29

Student t distribution, 350–351, 353–354, 427

P-value, 429–430
vs. z score, 354–357

Subjective probability, 140–141
Successes, 458
Sugging, 16
Super Bowl game, 476, 558
Surveys

callbacks, 215

cloning, 142–143
e-mail, 329–330
gender effects, 612–613
medium, 613
preelection, 458
project, 759–760
question wording, 656
repondent sensitivity, 262
resistance, 642
self-selected, 12–13
voluntary response samples, 12–13

Symmetric data, 85
Syphilis testing, 171
Systematic sampling, 27, 28

T
Tampering, 740
Tank serial numbers, 340
t distribution. See Student t distribution
Teacher evaluations, 522
Teachers’ salaries, 82–83
Temperature forecasting, 542
Temperature forecasting problem, 485–488
Test of homogeneity, 611–614
Test of independence, 607–608
Test of significance. See Hypothesis testing
Test statistic, 391–392, 703

ANOVA, 645
critical region, 392, 393
critical value, 393–394
goodness-of-fit tests, 593–594, 599–600
Kruskal-Wallis test, 703
linear correlation, 527–529
matched pairs, 485
McNemar’s test, 622
mean, 391–392, 419, 426, 470, 474–475
one-way ANOVA, 640
proportion, 391–392, 408, 413
P-value, 394, 396
rank correlation, 710
runs test for randomness, 719
significance level, 392–393
sign test, 680
standard deviation/variance, 392, 436
test of homogeneity, 611–613
test of independence, 607–608
two means, 470, 474–475
two proportions, 457
two variances, 496
Wilcoxon rank-sum test, 696–697
Wilcoxon signed-ranks test, 690

Thanksgiving Day problem, 144

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Theft, 473
Thermometer testing problem, 251–254, 255–256
TI-83/84. See Software/calculator results
Time, data change, 42, 78
Time-series graph, 61–62
Tinea pedis problem, 623–624
Toothpaste, 486
Topics, project, 760–763
Total deviation, 558
Touch therapy problem, 319, 321, 327–328
Transmission gearbox quality, 497
Traveling salesman problem, 182
Treatment (factor), 638
Tree diagram, 160
Trimmed mean, 90
Twin research, 499
Two-tailed test, 394, 395, 528, 529
Type I errors, 398–400
Type II errors, 398–400

U
Unbiased estimator, 97, 339, 367
Unexplained deviation, 557–559
Uniform distribution, 247–248
Unusual results, 205–208, 236, 297–298
Unusual values, 111
Upper class limits, 43
Upper control limits, 739, 741–742

V
Validity, 94
Variable

controlling, 23–25
dichotomous, 571–572
dummy, 571–572
explanatory (predictor, independent), 541
lurking, 525
predictor, 541
random. See Random variables
response (dependent), 541

Variance, 97–98, 204–205. See also Analysis of variance

(ANOVA)

between/within samples, 640
binomial distribution, 225–227
chi-square distribution, 364–367
comparing two samples, 495–501
confidence interval, 363–371
definition, 97
sample, 370–371
sample size, 370–371

sample variance, 97–98
testing a claim, 436–440, 445

Variation, 92–104, 557–563

assignable, 738
coefficient, 103–104
coefficient of determination, 559
control chart, 738–741
definition, 42
explained/unexplained deviation, 557–559
mean absolute deviation, 102–103
measures, 92–104
prediction intervals, 560–562
random, 738
range, 93
standard deviation, 94–96, 98–101
standard error of estimate, 560–561

Venn diagram, 154–155
Voltaire, 292
Voluntary response (self-selected) sample, 12–13
Voting behavior, 174, 459

W
Water taxi problem, 260–261, 263–264, 283–285
Weighted mean, 84
Weight problem, 103–104
Weight report problem, 591–592, 594–596
Width, class, 43
Wilcoxon rank-sum test, 695–699
Wilcoxon signed-ranks test, 689–693
Wildlife population size, 339
Wilson score confidence interval, 331
World War II bomb problem, 231–232
Written report, 759

X

, sampling distribution, 281–287

chart, 743–744

Y
y intercept, 542–544

Z
z score, 110–111

critical value, 324–325
definition, 110
finding, 254–255
notation, 324
standard normal distribution, 250–254
unusual values, 111
vs. area, 262
vs. student t distribution, 354–357

x

x

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