Index

I-1

Note: Page numbers in boldface indicates a definition; italics indicates a figure; t indicates a table.

Acceptance sampling, 300
Addition Rule, 262–265
- for mutually exclusive events, 264–265
Adjusted coefficient of determination , 745
(alpha), 495
Alternative hypothesis (), 489–490
Amount of gold in coins, 395, 407–409
Analysis of variance (ANOVA), 664–713, 666
- method of, 666–672
- multiple comparisons using Bonferroni method and, 686–688
- one-way, 673–679, 694–695
- randomized block design and, 693–701
- requirements for performing, 668–670
- table for, 672, 672t
- test statistic for, 671
- Tukey's test for multiple comparisons and, 688–691
- two-way, 701–710
AP exam scores, 309, 334–335, 371–373
Approximations. See also Point estimates; Pooled estimate; entries beginning with term Estimated
- binomial probability distribution and. See Binomial probability distribution
- pitfalls of using, 421
- of probabilities for dependent events, 282
April in Georgia, 369
Area under the curve. See also Standard normal probability distribution
- finding normal data values for, 372–378
Arithmetic mean. See Mean ()
Assumptions, of regression model, 718–721
Average. See Mean ()

Backward stepwise regression, 751–753
Balance point of data, mean as, 110, 110–111, 317–318
Bank loans, 575, 593–594, 595, 596–598
Bar graphs (bar charts), 43, 43–44, 44
- clustered, 48–50, 49
- inaccuracy in relative lengths of bars in, 100, 100
Bayes, Thomas, 282
Bayes’ Rule, 282–285, 283
Bell-shaped curve. See Normal probability distribution
(beta), 495, 565–567
Binomial discrete random variables, 327
- mean of, 334–335
- mode of, 335–336
- standard deviation of, 334–335
- variance of, 334–335
Binomial experiment, 326–328, 327
Binomial probability distribution, 326–341, 327, 385, 386
- approximating probabilities of, using normal distribution, 385–389
- binomial experiment and, 326–328
- computing binomial probabilities and, 328–334
- normal approximation to, 385–390, 386
- Poisson approximation to, 345–346
- tables for, T-3–T-8
Binomial probability distribution formula, 330–332
Blocking factors (blocks), 694
Bonferroni adjustment, 686–688
Boxplots (box-and-whisker plots), 173, 173–176
- comparison, 178
- constructing by hand, 174–175
- for left-skewed data, 176, 176
- for right-skewed data, 175, 175–176
- symmetric, 176, 176

Calculators. See Technology guides
California wildfires, 3
Categorical data analysis, 630–663
- goodness of fit test for, 632–645, 634
- test for homogeneity of proportions and, 651–655
- test for independence and, 646–651, 647
Causation, correlation vs., 198
Central Limit Theorem for Means, 399–402, 401
- finding probabilities using, 405–406
- finding two symmetric sample means using, 406–407
- when to use, 401
Central Limit Theorem for Proportions, 415–423, 418, 464
- determining whether the theorem applies and, 418
- finding percentiles using, 420–421
- finding probabilities using, 419–420
- minimum sample size for approximate normality and, 417, 418–419
- sampling proportion of the sample proportion and, 415–417
Chebyshev, P. L., 137, 138
Chebyshev's Rule, 137–140
- finding minimum percentages using, 137–140
- strengths and weaknesses of, 139
(chi-square) distribution, 474, 474
- confidence interval for population standard deviation, 475, 482
- confidence interval for population variance, 476, 482
- confidence intervals for the population variance and standard deviation and, 476–478
- finding critical values for, 475–476
- properties of, 474–476
- table for, T-12
(chi-square) goodness of fit test, 632–645, 634
- critical-value method for, 637–639
- -value method for, 639–641
(chi-square) test for homogeneity of proportions, 651–655
- test for independence compared with, 652
(chi-square) test for independence, 646–651, 647
- test for homogeneity of proportions compared with, 652
- critical-value method for, 648–649, 649–650
- -value method for, 650–651
(chi-square) test for population standard deviation, 556–564
- confidence intervals for population standard deviation to conduct two-tailed tests and, 561
- critical-value method for, 556–559
- essential idea about, 556
- -value method for, 559–560
Class(es), 61
- frequency and relative frequency distributions using, 61–62, 61t
Class boundary, 62–63
Class limits, upper and lower, 62–63
Class midpoint, 66
Class width, 62–63
Classical method of assigning probabilities, 243–248, 244
Clothing store sales, 487, 502–503
Cluster sampling, stratified sampling vs., 25
Clustered bar graphs, 48–50, 49
Coefficient of determination (), 230–232
- adjusted (), 745
- calculating correlation coefficient using, 232
- multiple (), 745
Combinations, 296–298
- acceptance sampling using, 300
- computing probabilities using, 301–302
- number of, 298, 328–329
Common variance, pooled estimate for, 596
Comparison boxplots, 178
Comparison dotplots, 70–71, 71
Complement of an event A (), 259–260
- probabilities for, 260
Computational formulas, 134. See also Formulas
Conditional probability, 270–291, 271
- “at least” problems and, 281
- Bayes’ Rule and, 282–285
- for dependent events, 282
- for independent events, 274–276
- interpretation of, 274
- Multiplication Rule and, 276–281
- for mutually exclusive events, 280
- 1% Guideline and, 282
- and and, 272
Confidence intervals, 426–485, 430. See also t interval for the population mean; entries beginning with term Z interval
- for difference in means, 594–595
- for difference in proportions, 612–613
- equivalence of two-tailed tests and, 517–518
- hypothesis testing and, 595–596
- interpreting, 433
- for mean of a normal population, 432–433
- for mean value of given , 737–738
- for population standard deviation, 476–478, 477
- for population variance, 476–478
- for population variance and standard deviation, 473–482
- for proportions to conduct two-tailed tests for , 549–551
- for regression, 726–730, 737–738, 740
- for slope of regression line, 726–730
- for standard deviation to conduct two-tailed tests for , 561
- interval for the population mean and, 448–462
- I-2
- Welch's, for difference in population means, 594–595
- interval for population mean and, 428–448
- interval for the population proportion and, 463–473
- for to conduct two-tailed tests for , 516–519
Confidence levels, 430
- decreasing, reducing the margin of error by, 438
Constant variance assumption, of regression model, 718
Contingency tables. See Crosstabulations
Continuity correction, 387
Continuous data, frequency distributions for, 63–65
Continuous probability distributions, 349–363
- normal probability distribution and. See Normal probability distribution
- probabilities for uniform probability distribution and, 349–351
- requirements for, 349
Continuous random variables, 311–312, 348–368
Continuous variables, 10
Controls, 28
Convenience sampling, 25
Correlation
- causation vs., 198
- negative, 197, 197
- positive, 196, 196
Correlation coefficient (), 192–198, 193
- calculating using coefficient of determination, 232
- interpreting, 198
- properties of, 195–197, 196–198
- slope of regression line related to, 211
Count, 41
Counting, 291–303
- computing probabilities using combinations and, 301–302
- Multiplication Rule for, 291–294, 293
- permutations and combinations and, 295–300
Critical regions, 500–501, 500t
Critical values
- for test (), 525
- for Tukey's test for multiple comparisons, table of, T-17–T-18
- for test (), 500–501, 500t
Critical-value method
- for goodness of fit test, 637–639
- for test for independence, 648–649, 649–650
- for test, 619–623
- for hypothesis test for difference in population proportions, 608–610
- for hypothesis testing for slope of regression line, 723
- paired sample test for population mean of differences using, 578–580
- for Welch's hypothesis test for difference in two population means, 591–592
- test for the population mean using, 502–504
- test for the population proportion using, 543–546
Crosstabulations, 45–47
- test for independence and, 646
Cumulative frequency distributions, 87–88, 88t
- Cumulative relative frequency distributions, 87–88, 88t

Data
- actual vs. predicted, 214
- continuous, frequency distributions for, 63–65
- discrete, frequency distributions for, 60–61, 61t
- fitting model to, 635
- gathering, 20–36
- grouped, 148–154
- mean as balance point of, 110, 110–111, 317–318
- misrepresentations by graphs, 95–103
- presenting same data set as both symmetric and left-skewed on graphs, 100–101, 101
- qualitative, frequency distributions for, 40–42, 41, 41t
- quantitative, frequency distributions for, 60–61, 61t
- tabular, 47–48
Data analysis, exploratory, 116–117
Data sets
- comparing data from different data sets using -scores, 157–158
- measures of center of. See Mean; Measures of center; Median; Mode
- measures of relative position and, 155–171. See also Percentile(s); -scores
- measures of variability of. See Measures of variability; Range; Standard deviation; Variance
- multimodal, 115
- quartiles of, 162–165
- unimodal, 115
Data stories, 2–4
Degrees of freedom
- in ANOVA, 671
- of distribution, 618, 619
- of distribution, 449
- for test for independent means, 593
Denominator degrees of freedom, 618
Density curves, 349
Dependent events, 274
- approximating probabilities for, 282
Dependent samples, 576–577
- intervals for mean difference for, 582–584
- test for mean of the differences and, 577–582
Dependent variables. See Response variables
Descriptive statistics, 7
- statistical inference vs., 15
Design your own T-shirt, 292
Deviation, 128–130. See also Standard deviation
- mean squared, 130
Dice, fair roll of, 247, 248–249
Discrete data, frequency distributions for, 60–61, 61t
Discrete probability distributions, mean as balance point of, 317–318
Discrete random variables, 311–312
- expected value of, 318–319
- identifying most likely value, 318
- mean of, 315–318
- most likely value of, 318
- probability distribution of, 312–315
- standard deviation of, 319–320
- variance of, 319–320
- -score method for determining unusual values and, 320
Discrete variables, 10
Disjoint events. See Mutually exclusive events
Dispersion, measures of. See Measures of variability; Range; Standard deviation; Variance
Distributions, 72. See also (chi-square) distribution; Frequency distributions; Probability distributions; Sampling distribution; distribution
- left-skewed, 73, 73, 176, 176
- right-skewed, 73, 73, 175, 175–176
- shape of, 72, 72–75, 73
- symmetric, 73
Dotplots, 70, 70–71
- comparison, 70–71, 71
Dummy variables, 749–750

Edward VI, King of England, 408
Elements, 7–9
ELISA test for HIV, 284–285
Empirical method of assigning probabilities, 248–252
Empirical Rule, 135, 135–137, 136
- finding percentages using, 136–137
- strengths and weaknesses of, 139
Equally likely outcomes, 244
Equation, regression. See Regression equation
Error
- experimentwise rate of (), 686
- margin of. See Margin of error (E); Margin of error for interval
- mean square (MSE), 671
- prediction, 214–215
- standard. See Standard error
- sum of squares. See Sum of squares error (SSE)
- Type I, 493–495, 494, 494t
- Type II. See Type II error
Estimate(s). See Approximations; Point estimates; Pooled estimate
Estimated mean, 150
- for data grouped into a frequency distribution, 149–150
Estimated standard deviation for data grouped into a frequency distribution, 151–152
Estimated variance for data grouped into a frequency distribution, 151–152
Euclid, 531
Events, 241
- complement of, 259–260
- dependent. See Dependent events
- independent. See Independent events
- intersection of, 261–262
- mutually exclusive (disjoint). See Mutually exclusive events
- union of, 261–262
Expected frequencies, 633
- for goodness of fit test, 635
- for test for independence, 647–648
Expected value (expectation) of a random variable , 318–319
Experiment(s), 240, 241
Experimental studies, 28–29, 30
Experimentwise error rate (), 686
Explanatory variables. See Predictor variables
Exploratory data analysis, 116–117
Extrapolation, 215–216
Extreme values
- lack of sensitivity of median to, 112–113
- sensitivity of mean to, 111–112
- I-3

curve, properties of, 618
distribution, 617–619
- finding critical values of, 619–621 table for, T-13–T-16
test, 617–625
- critical-value method for, 619–623
- for overall significance of multiple regression, 746–747
- -value method for, 623–625
Factorial symbol (n!), 294, 329
False-negative rate, 284–285
False-positive rate, 284–285
Fisher, Ronald A., 617
Fitted values, 719
Five-number summary, 172–173
Florida lotto, 301
Formulas
- adjusted coefficient of determination, 745
- binomial probability distribution, 330
- , 556, 570, 636
- coefficient of determination, 230
- confidence interval for population mean difference (dependent samples), 582, 627
- correlation coefficient, 236
- estimated mean, 150, 183
- estimated standard deviation, 151, 183
- estimated variance, 151, 183
- interquartile range, 166
- margin of error for interval for the mean, 454, 482, 594, 628
- margin of error for interval for the mean, 433, 482
- mean of a binomial random variable, 390
- mean of a discrete random variable, 316, 390
- minimum sample size, 417
- multiple coefficient of determination, 745
- number of combinations, 297, 305, 329, 390
- confidence interval for , 612, 628
- confidence interval for , 594, 627
- permutation, 299, 305
- Poisson probability distribution, 342, 390
- pooled estimate of , 608, 628
- pooled estimate of the common variance, 596, 628
- population standard deviation, 132, 182
- population variance, 130, 182
- sample proportion, 415
- sample size for estimating the population mean, 440, 482
- sample size for estimating the population proportion, 468, 482
- sample standard deviation, 182
- sample variance, 183
- slope of the regression line, 236
- standard deviation of a binomial random variable, 390
- standard deviation of a discrete random variable, 390
- standard deviation of sampling distribution of sample proportion, 416
- standard error of the estimate, 228
- standardizing a normal random variable, 368, 390
- standardizing a normal sampling distribution for means, 399, 423
- standardizing a normal sampling distribution for proportions, 419, 423
- sum of squares error, 226
- sum of squares regression, 236
- , 525, 570, 628
- total sum of squares, 236
- variance of a binomial random variable, 390
- variance of a discrete random variable, 390
- weighted mean, 149, 183
- confidence interval for , 599, 628
- interval for , 464, 482
- interval for population mean, 431, 482
- , 499, 543, 570, 599, 608, 610, 628
- -score, 155, 183
Frequency, 41
- expected. See Expected frequencies relative, 42
Frequency distributions
- choosing, 62
- for continuous data, 63–65
- cumulative, 87–88, 88t
- for discrete data, 60–61, 61t
- estimated mean for data grouped into, 149–150
- estimated standard deviation for data grouped into, 151–152
- estimated variance for data grouped into, 151–152
- for qualitative data, 40–42, 41, 41t
- for quantitative data, 60–61, 61t
- relative. See Relative frequency; Relative frequency distributions
- using classes, 61–62, 61t
Frequency polygons, 67, 67–68

Gambler's Fallacy, 275–276
Gardasil vaccine, 239, 250, 282, 283
Gold, amount in coins, 395, 407–409
Golden ratio, 531–533
Goodness of fit test, , 632–645, 634
Gosset, William Sealy, 449
Graphs
- bar, 43, 43–44, 44, 100, 100
- boxplots. See Boxplots
- choosing, 74–75
- discrete probability distributions as, 314, 314–315
- dotplots, 70, 70–71, 71
- interaction, in two-way ANOVA, 702–703
- manipulating scale of, 98, 98
- misrepresentations of data by, 95–103
- normal probability plots, 379
- obtaining information from, 71–72
- omitting zero on vertical scale, 97–98
- pie charts, 44–45, 45
- regression line. See Regression line
- scatterplots. See Scatterplots
- time series, 89–91, 90, 91
- unclear labeling of, 99, 100, 100
- using two dimensions for one-dimensional differences, 99
Grouped data, 148–154

Helmert, Friedrich, 474
Hinges of a boxplot, 173
Histograms, 65–67, 66
- shifting to the left, 66–67, 67
Homogeneity, of proportions, test for, 651–655
Hypotheses, 486–573, 488
- alternative (research), 489–490
- for ANOVA, 673
- null, 489–490
- strategy for constructing, 491–492
- testing. See Hypothesis testing for slope of regression line
- testing of. See Hypothesis testing
- validity of, 490–491
Hypothesis testing, 489
- confidence intervals for, 595–596
- confidence intervals for proportion for two-tailed tests and, 549–551
- critical regions and critical values and, 500–501, 500t
- for difference in population proportions, critical-value method for, 608–610
- for difference in population proportions, -value method for, 610–612
- left-tailed tests for, 501, 503
- for mean, essential idea about, 497–498
- power of a hypothesis test and, 567–568
- for proportion, essential idea about, 543
- right-tailed tests for, 501, 502–503
- for slope of regression line. See Hypothesis testing for slope of regression line
- for standard deviation, essential idea about, 556
- statistical significance and, 492–493
- test for the mean and. See t test for the population mean
- two-tailed tests for, 501, 504, 516–519
- Type I and Type II error and. See Type I error; Type II error
- test for the mean using critical-value method and, 502–504
- test for the mean using -value method and. See test for the mean using -value method
- and, 499–500
Hypothesis testing for slope of regression line, 721–725
- confidence intervals for, 726–730
- critical-value method for, 723
- -value method for, 723–725
- test for, 727–730

Independence, test for, 646–651, 647
Independence assumption, of regression model, 718
Independent events, 274–276

alternative method for determining, 279
Multiplication Rule for Independent Events, 280–281
Multiplication Rule for Two Independent Events, 277
mutually exclusive events vs., 275

Independent samples, 576–577, 607
- test for difference in means and, 589–594
- interval for proportion difference and, 612–613
- tests for proportion difference and, 606–612
Inference. See Statistical inference; Two-sample inference
Interaction, 702
- two-way ANOVA and, 702–706
Interaction plots, 702–703
Intercept, of regression line, 210, 211
Interquartile range (IQR), 165–166
- outlier detection using, 177–179
I-4
Intersection of events, 261–262
Intervals, 349. See also Confidence intervals; Prediction intervals; interval(s); interval for the population mean; interval; interval for the population mean; interval for the population proportion
- sign, 451
- Wilcoxon, 451
Intramural tennis league, 297
IQR. See Interquartile range (IQR)
IQR method of detecting outliers, 177–179

Law of Large Numbers, 249
Law of Total Probability, 241
- for Continuous Random Variables, 349
Least-squares criterion, 226
Least-squares regression line. See Regression line
Leaves, 68–69
Left-skewed distributions, 73, 73 boxplot for, 176, 176
Left-tailed tests, 501, 503
- test for the population mean using criticalvalue method as, 526–528
- test for the population proportion using critical-value method as, 503
Level of significance, 495
Levels of measurement, 11
Linear, definition of, 193
Linear regression. See Regression analysis
Lower bound, for interval, 439–440
Lower class limit, 62–63
Lower hinge of a boxplot, 173

Margin of error ()
- for intervals, 454, 594
- for interval. See Margin of error for interval
Margin of error for interval, 429, 433
- finding, given lower and upper bounds, 439–440
- for , 466–467
- for , 612
- reducing, 437–440
Matched-pair samples, 576
Mean (), 108–112
- as balance point of data, 110, 110–111, 317–318
- of binomial random variables, 334–335
- Central Limit Theorem for, 399–402, 401
- of differences. See Population mean difference ()
- of a discrete random variable , 315–320
- essential idea about hypothesis testing for, 497–498
- estimated, 150
- for grouped data, estimating, 149–150
- lack of representativeness of, 165
- of normal population, confidence intervals for, 432–433
- of normal probability distribution, 352–353
- notation for, 109
- of Poisson probability distribution, 344–345
- population. See Population mean ()
- sample. See Sample mean ()
- of the sample proportion, 416–417
- of sampling distribution of the sample mean, 397, 398–399
- of sampling distribution of the sample proportion, 416–417
- sensitivity to extreme values, 111–112
- standard error of, 398
- strategy for constructing hypotheses about, 491–492
- weighted, 148–149
Mean square, 671
Mean square error (MSE), 671
Mean square treatment (MSTR), 671
Mean squared deviation, 130
Measurement, levels of, 11
Measures of center, 108. See also Mean; Median; Mode
- skewness and, 115, 115–117
Measures of relative position, 155–171. See also Percentile(s); -scores
Measures of variability (measures of dispersion; measures of spread), 126–148, 127. See also Range; Standard deviation; Variance
- Chebyshev's Rule and, 137–140
- disagreement among, 140, 179
- Empirical Rule and, 135–137, 136
Measuring the human body, 187, 190–192
Median, 112–114
- lack of sensitivity to extreme values, 112–113
Mode, 114–115
- of binomial discrete random variables, 335–336
- lack of, 115
Models
- fitting to data, 635
- probability, 241–243, 251
- regression, 717–721, 718. See also Multiple regression model
Motor vehicle fuel efficiency, 427, 434, 436–437
MSE. See Mean square error (MSE)
MSTR. See Mean square treatment (MSTR)
Multimodal data sets, 115
Multinomial random variable, 632–634
Multiple coefficient of determination (), 745
Multiple comparisons, 685–688, 686
- Tukey's test for, 688–691
- using Bonferroni method, 686–688
Multiple regression, 743–757
- adjusted coefficient of determination and, 745–746
- dummy variables in, 749–750
- test for overall significance of, 746–747
- multiple regression coefficients and, 743, 744–745
- multiple regression equation and, 743, 744–745
- prediction and, 743–745
- test for significance of individual predictor variables and, 747–748
Multiple regression coefficients, 743–745
Multiple regression equation, 743–745
Multiple regression model
- population, 746
- strategy for building, 750–751, 751–753
Multiplication Rule, 276–281
- for counting, 291–294, 293
- for independent events, 280–281
- sampling with and without replacement and, 277
- for two independent events, 277
Murder rate in New York City, 2
Mutually exclusive events, 263–265
- conditional probability for, 280
- independent events vs., 275

Negative correlation, 197, 197
Negative linear relationship, 190, 191
Noncritical regions, 500, 500t
Nonlinear relationship, 192, 192
Normal approximation to the binomial probability distribution, 385–390, 386
Normal curve. See Normal probability distribution
Normal data values, for a given area or probability, finding, 372–378
Normal population confidence intervals for mean of, 432–433
Normal probability distribution, 351–354, 352
- approximating probabilities of binomial distribution using, 385–389
- assessing normality using normal probability plots and, 379
- finding normal data values for given areas or probabilities and, 372–378
- finding probabilities for, 368–372
- mean of, 352–353
- properties of, 352
- sampling distribution of sample mean for, 397–398, 399, 402
- shape of, 72, 72–73
- standard. See Standard normal probability distribution
- standard deviation of, 352–353
Normal probability plots, 379
Normal random variables
- finding probabilities for, 368–372
- standardizing, 368
Normality
- approximate, minimum sample size for, 417, 418–419
- of normal probability distribution, assessing using normal probability plots and, 379
Normality assumption, of regression model, 718
Notation
- for population size, sample size, and population mean, 109
- for random variables, 311
Null hypothesis (), 489–490
- decision whether to reject, 493–494
Number of combinations, 298, 328–329
Numerator degrees of freedom, 618

Observation(s), 7–9
Observational studies, 28, 30
Ogives, 88–89, 89
1% Guideline, 282
confidence interval
- for , 612
- for , 594
One-way ANOVA, unable to find significance, 694–695
Online dating, 631, 653–655
Outcomes, 240, 241
- equally likely, 244
- unusual or unlikely, determining, 243
I-5
Outliers, 158–159
- detecting using IQR method, 177–179
Overall sample mean (), 670–672

Paired sample(s), 576
Paired sample test

for population mean of differences, using critical-value method, 578–580
for population mean of differences, using -value method, 580–582

Pairwise comparisons, 686
Parameters, 12, 13–14, 428
- of Poisson probability distribution, 344
Pareto charts, 44
Patterns in randomness, 240
Pearson, Karl, 474
Pearson product moment correlation coefficient. See Correlation coefficient ()
Percentages
- finding using Empirical Rule, 136–137
- minimum, finding using Chebyshev's Rule, 138–139
Percentile(s), 159–161
- finding using Central Limit Theorem for Proportions, 420–421
Percentile ranks, 161–162
Permutations , 295–296, 298–300
- calculating number of, 298
- of nondistinct items, 299–300
Pie charts, 44–45, 45
Point estimates, 428
- of population mean, 428–429
- of population proportion, 463
Point estimation, 428
Poisson, Siméon Denis, 341
Poisson probability distribution, 341–348
- approximating binomial distribution using, 345–346
- mean of, 344–345
- recognizing when to use, 342
- requirements for, 341–342
Poisson probability distribution formula, 342
Poisson random variables, probabilities for, 342–344
Pooled estimates
- for common variance, 596
- of , 608
Pooled variance, test for mean difference using, 596–598
Pooled variance confidence interval for , 598
Population(s), 12–13
- potential, 26, 27
- target, 26, 27
Population mean (), 108–109
- point estimate of, 428–429
- reducing the margin of error and, 437–440
- sample size for estimating, 440, 440–441
- interval for, 451–455
- test for. See test for the population mean
- interval for, 429–437
- test for. See test for the mean using critical-value method; test for the mean using -value method
Population mean difference (), 590
- dependent test for, 577–582
- independent sample test for, 589–594
- paired differences and, 590
- pooled variance test for, 596–598
- intervals for, 594–595
- intervals for dependent samples and, 582–584
- inference for, when and are known, 598
- test for, when standard deviations are known, 598–599
Population multiple regression model, 746
Population proportion ()
- confidence intervals for to conduct twotailed tests about and, 549–551
- hypothesis testing for, essential idea about, 543
- independent sample interval for difference in, 612–613
- independent sample tests for difference in, 606–612
- point estimate of, 463
- -value compared with, 546
- sample size for estimating, 468–469
- two-sample inference for, 606–617
- confidence intervals to perform tests for difference in, 613
- interval for. See interval for the population proportion
- test for, using critical-value method, 543–546
- test for, using -value method, 546–549
Population regression equation, 718
Population size (), 109
Population standard deviation (), 131–132
- test for. See (chi-square) test for population standard deviation
- confidence intervals for, 476–478, 477
- test for comparing, 617–625
Population variance (), 130–131
- confidence intervals for, 476–478
Positive correlation, 196, 196
Positive linear relationship, 190, 191
Potential population, 26, 27
Power curve, 568
Power of a hypothesis test, 567–568
Prediction errors, 214–215
Prediction intervals
- for individual value of given , 739
- for regression, 739–740
- width of, 740
Predictor variables, 28, 188–189
- individual, test for significance of, 747–748
Prevalence rate, 284
Probability(ies), 238–307, 240
- Addition Rule and, 262–265
- binomial, 328–334
- building blocks of, 240–243
- classical method of assigning, 243–248
- complement, union, and intersection and, 259–262
- for complement of an event, 260
- computing using combinations, 301–302
- conditional. See Conditional probability
- for continuous distributions, 350
- counting methods and, 291–303
- expressing areas under the standard normal curve as, 359
- finding using binomial table, 332–333
- finding using Central Limit Theorem for Means, 405–406
- finding using Central Limit Theorem for Proportions, 419–420
- finding using sampling distribution, 402–409
- finding using technology, 333–334
- Law of Total Probability and, 241
- for normal distributions, finding, 368–372
- relative frequency method of assigning, 248–251
- rules of, 241
- subjective, 252
- subjective method for assigning, 251–252
- tree diagrams and, 245–246, 246
- of Type II error, 495, 564–566, 565–567
- for uniform probability distribution, 349–352, 350
Probability distributions, 308–393
- binomial. See Binomial probability distribution
- calculating probabilities for multiple values of and, 315
- continuous. See Continuous probability distributions
- of a discrete random variable, 312–315
- normal. See Normal probability distribution
- Poisson. See Poisson probability distribution
- random variables and, 310–312. See also Discrete random variables
- uniform, 349–351, 350
Probability models, 241–243, 251
Professors on Facebook, 665, 678
Proportion ()
- Central Limit Theorem for. See Central Limit Theorem for Proportions
- test for homogeneity of, 651–655
- population. See Population proportion ()
- sample. See Sample proportion ()
- sampling distribution for, normal, standardizing, 419
-value, 508
- estimating using table, 533–534
- population proportion compared with, 546
-value method
- goodness of fit test using, 639–641
- test for independence using, 650–651
- test using, 623–625
- hypothesis test for difference in population proportions using, 610–612
- hypothesis testing for slope of regression line using, 723–725
- paired sample test for population mean of differences using, 580–582
- Welch's hypothesis test for difference in two population means using, 592–594
- test for the population proportion using, 546–549

Qualitative data, frequency distributions for, 40–42, 41, 41t
Qualitative variables, 9–10
Quantitative data, frequency distributions for, 60–61, 61t
Quantitative variables, 9–10
Quartiles, 162–165
- for large data set, 164–165
- for small data set, 163–164
Questionnaire design, 27–28

Random numbers table, T-2
Random samples, 20–22, 21
- generating using technology, 21–22
- simple, 21
I-6
Random variables, 310–312
- continuous, 311–312
- discrete. See Discrete random variables
- multinomial, 632–634
- notation for, 311
- Poisson, probabilities for, 342–344
- randomness of, 310
- sample mean as, 396
Randomization, 29
Randomized block design ANOVA, 693–701, 694
- sum of squares error and, 696–697
Randomness
- patterns in, 240
- of intervals, 435
Range, 126–128, 127
Regression, 209–225
- coefficient of determination and, 230–232
- confidence intervals for, 726–730, 737–738, 740
- inference in, 714–759
- multiple. See Multiple regression
- prediction intervals for, 739–740
- standard error of the estimate and, 227–228
- stepwise, backward, 751–753
- sum of squares error and, 226–228
- total sum of squares and, 229–230
Regression analysis
- confidence interval for slope of regression line and, 726–730
- hypothesis testing for slope of regression line and, 721–725
- test for slope of regression line and, 727–730
Regression coefficients, multiple, 743–745
Regression equation
- multiple, 743–745
- population, 718
- prediction using, 213–214
- predictions using, 213–216
- of the regression line, 209–210
Regression line, 209–213, 210
- coefficient for, 210–211
- equation of, 209–210
- intercept of, 210, 211
- slope of, 210, 211–212
- slope of, inference about, 716–736
Regression model, 717–721, 718
- assumptions of, 718–721
Rejection rules, 509
- for using confidence intervals to perform Tukey's test, 689–691
Relative frequency, 42
Relative frequency distributions, 42, 42t
- cumulative, 87–88, 88t
- for discrete data, 60– 61, 61t
- using classes, 61–62, 61t
Relative frequency method of assigning probabilities, 248–252, 249
Replication, 29
Research hypothesis (), 489–490
Residuals. See Prediction errors
Response variables, 28, 188–189
- variance of, 229
Results, communicating, 132
Right-skewed distributions, 73, 73
- boxplot for, 175, 175–176
Right-tailed tests, 501, 502–503
- test for the population mean using -value method as, 530–531
- test for the population proportion using critical-value method as, 502–503
Rounding, 194
Rules for a discrete probability distribution, 313

Sample(s), 12–13
- dependent. See Dependent samples
- independent. See Independent samples
- matched-pair (paired), 576
Sample mean (), 109–110
- overall, 670–672
- sampling distribution of. See Sampling distribution of the sample mean
- symmetric, finding using Central Limit Theorem for Means, 406–407
Sample proportion (), 415
- mean of, 416–417
- sampling distribution of, 415–417, 416
- standard error of, 416, 416–417
Sample size (), 109
- for estimating the population mean, 440, 440–441
- for estimating the population proportion, 468–469
- increasing, decreasing the margin of error by, 439
- large, interval for population mean for, 434
- minimum, for approximate normality and, 417, 418–419
Sample space, 240, 241
Sample standard deviation (), 133–135
Sample variance (), 133–135
Sampling
- cluster, 24–25
- convenience, 25
- random. See Random samples
- with replacement, 277–278
- stratified, 23–24, 25
- systematic, 22–23
- without replacement, 277, 278–279
Sampling distribution
- for any statistic, 416
- of difference between sample proportions, 607
- of difference in sample means, 590
- for proportions, normal, standardizing, 419
- of sample mean. See Sampling distribution of the sample mean
- of sample proportion. See Sampling distribution of the sample proportion
Sampling distribution of the sample mean, 394–414, 396
- central limit theorem for means and, 399–402
- finding a value of, given a probability or area, 404–405
- finding probabilities using, 402–409
- mean of, 397, 398–399
- for a normal population, 397–398, 399, 402
- standard deviation of, 398–399
- standardizing, 399
- three possible cases for, 401
Sampling distribution of the sample proportion, 415–417, 416–417
- conditions for approximate normality of, 417
- mean of, 416–417
- standard deviation of, 416–417
Sampling variability, of sample mean, 396
SAT scores, 309, 334–335, 371–373
Scatterplots, 188–192
- constructing, 189–190
- predictor and response variables and, 188–189
- terminology for, 190
- types of relationships and, 190–192, 191, 192
Scoring in Scrabble, 715, 728–730
Secret Santas, 296
Selection bias, 26–27
Seymour, Thomas, 408
Sharington, William, 408
(Σ) (sigma), 130
Sign interval, 451
Significance, statistical, 492–493
Simulations, 248–249
Skewed distributions, 73, 73
Skewness, measures of center and, 115, 115–117
Slope of regression line, 210, 211–212
- confidence interval for, 726
- hypothesis testing for, 721–725
Split stems, 69
Spread, measures of. See Measures of variability; Range; Standard deviation; Variance
SSE. See Sum of squares error (SSE)
SSR. See Sum of squares regression (SSR)
SST. See Total sum of squares (SST)
SSTR. See Sum of squares treatment (SSTR)
Standard deviation (), 128
- of binomial random variables, 334–335
- of discrete random variables, 319–320
- estimated, for data grouped into a frequency distribution, 151–152
- hypothesis testing for, essential idea about, 556
- known, test for population mean difference and, 598–599
- of normal probability distribution, 352–353
- of Poisson probability distribution, 344–345
- population. See Population standard deviation ()
- sample, 133–135
- of sampling distribution of sample mean, 398–399
- of sampling distribution of the sample proportion, 416–417
- two-sample inference for, 617–627
Standard error
- of the estimate, 227–228, 722
- of the mean, 398
- of the population proportion, 543
- of the proportion, 543
- of the sample proportion, 416, 416–417
Standard normal probability distribution, 354–359
- expressing areas under as probabilities, 359
- find areas under, for given -values, 354–359
- finding areas under for given -values, 354–359
- table for, T-9–T-10
Standard normal random variable , 368
Standardizing
- normal random variables, 368
- normal sampling distribution for means, 399
- normal sampling distribution for proportions, 419
Statistic(s), 12, 13–14, 428
- appropriate, choosing, 97
- communicating the results, 132
- data stories, 2–4
- descriptive. See Descriptive statistics
- inappropriate use of, 96–97
- phases of, 5–7
- I-7
- sampling distribution for, 416
- test. See Test statistics
Statistical inference, 11–15, 14, 428
- descriptive statistics vs., 15
- parameters vs. statistics and, 13–14
- populations and samples and, 12–13
- two-sample. See Two-sample inference
Statistical literacy quiz, 15
Statistical significance, 492–493
Statistics (field)
- defined, 4–7, 5
- introduction to, 4–19
Stem(s), 68–69
Stem-and-leaf displays, 68–70, 69
Stepwise regression, backward, 751–753
Stock quotes, 9–10, 116–117, 128
Stratified sampling, cluster sampling vs., 25
Student-run café business, 49–50, 74, 97–98
Student's distribution. See t distribution
Subject(s), 28
Subjective probability, 252
Sum of squares, 671
Sum of squares error (SSE), 226–228, 671
- randomized block design and, 696–697
Sum of squares regression (SSR), 230
Sum of squares treatment (SSTR), 671
Summation sign (Σ), 130
Superstitions, 5–7
Symmetric boxplots, 176, 176
Symmetric distributions, 73
Systematic sampling, 22–23

distribution, 448–451, 449
- characteristics of, 450
- finding value of and, 450–452
- table for, T-11
interval(s)
- equivalence with two-tailed test, 727
- for mean difference for dependent samples, 582–584
- pooled variance, for , 598
- for population mean. See t interval for the population mean
interval for the population mean, 451–455
- conditions for, 452
- margin of error for, 454
- intervals compared with, 453
table, T-11
- estimating -value using, 533–534
test
- dependent, for mean of the differences, 577–582
- independent, for difference in means, 589–594
- for mean difference using pooled variance, 596–598
- for population mean. See test for the population mean
- for significance of individual predictor variables, 747–748
- for slope of regression line, 727–730
- two-tailed, equivalence with confidence interval, 727
test for the population mean, 525–542
- two-tailed, confidence intervals to perform, 534–536
- using critical-value method, 526–529
- using -value method, 529–534
Tables
- ANOVA, 671–672, 672
- frequency. See Frequency distributions
- obtaining information from, 71–72
- distribution, 533–534, T-11
Tabular data, 47–48
Target population, 26, 27
Technology guides
- ANOVA, 679–681
- bar graphs, 50–53
- binomial probabilities, 336–337
- boxplots, 179–180
- distribution, 479–480
- for independence, 656–657
- goodness of fit test, 641–643
- -value, 561–562
- test for homogeneity of proportions, 656–657
- combinations, 302
- confidence interval for , 599–601
- confidence intervals, 584–586, 741
- correlation, 199–200
- descriptive statistics, 117–118
- estimating mean, variance, and standard deviation for grouped data, 152
- test for comparing population standard deviations, 625
- factorials, 302
- frequency distributions, 50–53
- hypothesis tests for , 584–586
- mean of a discrete random variable, 321
- multiple comparisons, 691
- multiple regression, 753
- normal distribution areas, probabilities, and percentiles, 380–382
- normal probability plots, 380–382
- percentiles, 167
- permutations, 302
- pie charts, 50–53
- Poisson distribution, 346
- prediction intervals, 741
- probability simulations, 252–254
- quantitative data, 75–77
- quartiles, 167
- random sample generation, 30–32
- randomized block design, 698–699
- regression, 217
- regression analysis, 730–731
- scatterplots, 199–200
- standard deviation of a discrete random variable, 321
- confidence intervals, 455–457
- test for the mean, 537–538
- time series plots, 91–92
- two-sample test, 599–601
- two-way ANOVA, 707–708
- interval for difference in proportion, 614
- intervals, 441–442
- intervals for , 469–470
- test, 614
- test for proportion, 552
- test for the mean, 519–520
Test statistics, 499–500
- for ANOVA, 671
- for Bonferroni adjustment, 687
- for goodness of fit test, 636–637
- for test for independence, 648
- for difference in population standard deviations, 596
- for test for comparing population standard deviations, 618
- for hypothesis testing for slope of regression line, 721–722
- for independence of two categorical variables, 648
- for paired sample test, 579, 580, 581
- for test, 599, 608
Testing. See Hypothesis testing
Time series plots, 89–91, 90, 91
Total sum of squares (SST), 229–230, 671
Traveling salesman problem, 294, 295
Treatments, 28
- mean square, 671
- sum of squares, 671
Tree diagrams, 245–246, 246
Tukey, John, 68
Tukey's test for multiple comparisons, 688–691
- table of critical values for, T-17–T-18
Two-sample inference, 574–629
- independent and dependent samples and, 576–577
- for independent proportions, 606–617
- for independent standard deviations, 617–627
- for mean difference of dependent samples, 576–589
- for mean difference of independent samples, 589–606
Two-tailed tests, 501, 504, 516–519
- about , using confidence intervals for to perform, 549–551
- equivalence of confidence intervals and, 517–518
Two-way ANOVA, 701–710
- interaction graphs and, 702–703
- when interaction is present, 705–706
Two-way tables. See Crosstabulations
Type I error, 493–495, 494, 494t
Type II error, 493–495, 494, 494t
- power of a test and, 567–568
- probability of, 564–566

UFO sightings, 2–3
Uniform probability distribution, 349–352, 350
- probability for, 349–352, 350
Unimodal data sets, 115
Union of events, 261–262
Unusual outcomes, determining, 243
Upper bound, for interval, 439–440
Upper class limit, 62–63
Upper hinge of a boxplot, 173

Variability. See Measures of variability; Range; Standard deviation; Variance
Variables, 7–9
- categorical. See Categorical data analysis
- discrete vs. continuous, 10
- dummy, 749–750
- predictor. See Predictor variables
- qualitative vs. quantitative, 9–10
- random. See Discrete random variables; Random variables
- response, 28, 188–189, 229
Variance, 128
- of binomial random variables, 334–335
- of discrete random variables, 319–320
- estimated, for data grouped into a frequency distribution, 151–152
- I-8
- of Poisson probability distribution, 344–345
- pooled, test for mean difference using, 596–598
- population. See Population variance ()
- sample, 133–135
- of the ys, 229
Variation, amount of, 134
Video game sales, 1, 7–9, 21–22

Weighted mean, 148–149
Welch's confidence interval for difference in population means, 594–595
Welch's hypothesis test for difference in two population means
- critical-value method for, 591–592
- -value method for, 592–594
Whiskers of a boxplot, 173
Wilcoxon interval, 451

variables. See Predictor variables

intercept, of regression line, 210, 211
variables. See Response variables

distribution. See Standard normal probability distribution
inference for mean difference when and are known, 598–599
interval
- for difference in population means, 599
- for independent sample proportion difference, 612–613
- for population mean. See interval for the population mean
- for population proportion. See interval for the population proportion
- for tests of proportion difference, 613
interval for the population mean, 429–437, 431
- confidence intervals for mean of a normal population and, 432–433
- determining whether the interval may be used and, 431–432
- finding value of, 432 for large sample size, 434
- randomness of, 435
- interval for the population mean compared with, 453
interval for the population proportion, 463–473, 464, 464–466
- margin of error for, 466–467
- point estimate of the population proportion and, 463
- sample size for estimating the population proportion and, 468–469
table, 355
test
- independent, for proportion difference, 606–612
- for mean. See test for the mean using critical-value method; test for the mean using -value method
- for population proportion. See test for the population proportion; test for the population proportion using critical-value method
- of proportion difference, intervals for, 613
- test statistic for, 599
test for the mean using critical-value method, 502–504
test for the mean using -value method, 507–524
- confidence intervals for performing twotailed tests and, 516–519
- critical-value method compared with, 515–516
- one-tailed, 510–511
- rejection rule and, 509
- strength of evidence against the null hypothesis and, 514–515
- two-tailed, 512–514
test for the population proportion
- confidence intervals to perform tests for differences, 613
- using critical-value method. See test for population proportion using critical-value method
- using -value method, 546–549
test for the population proportion using critical-value method, 543–546, 545
- interpreting conclusions and, 502
- left-tailed, 503
- right-tailed, 502–503
- two-tailed, 504
, 499–500
Zero-mean assumption, of regression model, 718
-score(s), 155–159
- detecting outliers using, 158–159
-score method, for determining unusual values, 320
-values
- given, finding areas under standard normal curve for, 354–359
- standard normal, finding for given areas, 359–363
- I-9
- I-10
- I-11
- I-12
- I-13
- I-14
- I-15
- I-16
- I-17
- I-18