1.1 Data Stories: The People Behind the Numbers 2
1.2 An Introduction to Statistics 4
What Is Statistics? 4
Elements, Variables, and Observations 7
Qualitative and Quantitative Variables; Discrete and Continuous Variables 9
Levels of Measurement 11
Statistical Inference 11
1.3 Gathering Data 20
Random Sampling 20
More Sampling Methods 22
Selection Bias and Questionnaire Design 26
Experimental Studies and Observational Studies 28
Chapter 1 Vocabulary 36
Chapter 1 Review Exercises 36
Chapter 1 Quiz 37
2.1 Graphs and Tables for Categorical Data 40
Frequency Distributions and Relative Frequency Distributions 40
Bar Graphs and Pareto Charts 43
Pie Charts 44
Crosstabulations 45
Working with Tabular Data 47
Clustered Bar Graphs 48
2.2 Graphs and Tables for Quantitative Data 60
Frequency Distributions and Relative Frequency Distributions for Discrete and Continuous Data 60
Histograms and Frequency Polygons 65
Stem-and-Leaf Displays and Dotplots 68
Obtaining Information from Graphs and Tables 71
Distribution Shape, Symmetry, and Skewness 72
2.3 Further Graphs and Tables for Quantitative Data 87
Cumulative Frequency Distributions and Cumulative Relative Frequency Distributions 87
Ogives 88
Time Series Graphs 89
2.4 Graphical Misrepresentations of Data 95
Chapter 2 Vocabulary 103
Chapter 2 Review Exercises 103
Chapter 2 Quiz 105
3.1 Measures of Center 108
The Mean 108
The Median 112
The Mode 114
Skewness and Measures of Center 115
3.2 Measures of Variability 126
The Range 126
Population Variance and Population Standard Deviation 128
Compute the Sample Variance and Sample Standard Deviation 133
The Empirical Rule 135
Chebyshev's Rule 137
3.3 Working with Grouped Data 148
The Weighted Mean 148
Estimating the Mean for Grouped Data 149
Estimating the Variance and Standard Deviation for Grouped Data 151
3.4 Measures of Relative Position and Outliers 155
z-Scores 155
Detecting Outliers Using the z-Score Method 158
Percentiles and Percentile Ranks 159
Quartiles and the Interquartile Range 162
3.5 Five-Number Summary and Boxplots 172
The Five-Number Summary 172
The Boxplot 173
Detecting Outliers Using the IQR Method 177
Chapter 3 Formulas and Vocabulary 182
Chapter 3 Review Exercises 183
Chapter 3 Quiz 185
4.1 Scatterplots and Correlation 188
Scatterplots 188
Correlation Coefficient r 192
4.2 Introduction to Regression 209
The Regression Line 209
Predictions and Prediction Error 213
4.3 Further Topics in Regression Analysis 225
Sum of Squares Error (SSE) and Standard Error of the Estimate s 226
SST, SSR, and SSE 228
Coefficient of Determination r2 230
Chapter 4 Formulas and Vocabulary 236
Chapter 4 Review Exercises 237
Chapter 4 Quiz 237
5.1 Introducing Probability 240
Building Blocks of Probability 240
Classical Method of Assigning Probability 243
Relative Frequency Method 248
5.2 Combining Events 259
Complement, Union, and Intersection 259
Addition Rule 262
5.3 Conditional Probability 270
Introduction to Conditional Probability 270
Independent Events 274
Multiplication Rule 276
Approximating Probabilities for Dependent Events 282
Bayes' Rule 282
5.4 Counting Methods 291
Multiplication Rule for Counting 291
Permutations and Combinations 295
Computing Probabilities Using Combinations 301
Chapter 5 Formulas and Vocabulary 305
Chapter 5 Review Exercises 305
Chapter 5 Quiz 306
6.1 Discrete Random Variables 310
Random Variables 310
Discrete Probability Distributions 312
Mean and Variability of a Discrete Random Variable 315
6.2 Binomial Probability Distribution 326
Binomial Experiment 326
Computing Binomial Probabilities 328
Binomial Mean, Variance, Standard Deviation, and Mode 334
6.3 Poisson Probability Distribution 341
Requirements for the Poisson Distribution 341
Computing Probabilities for a Poisson Random Variable 342
The Mean, Variance, and Standard Deviation for a Poisson Distribution 344
Using the Poisson Distribution to Approximate the Binomial Distribution 345
6.4 Continuous Random Variables and the Normal Probability Distribution 348
Continuous Probability Distributions 349
Calculating Probabilities for the Uniform Probability Distribution 349
Introduction to Normal Probability Distribution 352
Finding Areas Under the Standard Normal Curve for a Given Z-Value 354
Finding Standard Normal Z-Values for a Given Area 359
6.5 Applications of the Normal Distribution 368
Finding Probabilities for Any Normal Distribution 368
Finding a Normal Data Value for a Given Area or Probability 372
Assessing Normality Using Normal Probability Plots 379
6.6 Normal Approximation to the Binomial Probability Distribution 385
Using the Normal Distribution to Approximate Probabilities of the Binomial Distribution 385
Chapter 6 Formulas and Vocabulary 390
Chapter 6 Review Exercises 391
Chapter 6 Quiz 392
7.1 Central Limit Theorem for Means 396
Sampling Distribution of ˉx for a Normal Population 396
Central Limit Theorem for Means 399
Finding Probabilities Using a Sampling Distribution 402
7.2 Central Limit Theorem for Proportions 415
Sampling Distribution of the Sample Proportion ˆp 415
Applying the Central Limit Theorem for Proportions 418
Chapter 7 Formulas and Vocabulary 423
Chapter 7 Review Exercises 424
Chapter 7 Quiz 424
8.1 Z Interval for the Population Mean 428
Calculate a Point Estimate of the Population Mean 428
The Z Interval for the Population Mean 429
Ways to Reduce the Margin of Error 437
Sample Size for Estimating the Population Mean 440
8.2 t Interval for the Population Mean 448
Introducing the t Distribution 448
t Interval for the Population Mean 451
8.3 Z Interval for the Population Proportion 463
Point Estimate ˆp of the Population Proportion p 463
Z Interval for the Population Proportion p 464
Margin of Error for the Z Interval for p 466
Sample Size for Estimating the Population Proportion 468
8.4 Confidence Intervals for the Population Variance and Standard Deviation 473
Properties of the χ2 (Chi-Square) Distribution 474
Constructing Confidence Intervals for the Population Variance and Standard Deviation 476
Chapter 8 Formulas and Vocabulary 482
Chapter 8 Review Exercises 483
Chapter 8 Quiz 484
9.1 Introduction to Hypothesis Testing 488
Constructing the Hypotheses 488
Type I and Type II Errors 493
9.2 Z Test for the Population Mean: Critical-Value Method 497
The Essential Idea About Hypothesis Testing for the Mean 497
Test Statistic Zdata 499
Critical Regions and Critical Values 500
Performing the Z Test for the Mean Using the Critical-Value Method 502
9.3 Z Test for the Population Mean: p-Value Method 507
The p-Value Method of Performing the Z Test for the Mean 507
Assessing the Strength of Evidence Against the Null Hypothesis 514
The Relationship Between the p-Value Method and the Critical-Value Method 515
Using Confidence Intervals for μ to Perform Two-Tailed Hypothesis Tests About μ 516
9.4 t Test for the Population Mean 525
t Test for μ Using the Critical-Value Method 525
t Test for μ Using the p-Value Method 529
Using Confidence Intervals to Perform Two-Tailed t Tests 534
9.5 Z Test for the Population Proportion 543
The Z Test for p Using the Critical-Value Method 543
Z Test for p: The p-Value Method 546
Using Confidence Intervals for p to Perform Two-Tailed Hypothesis Tests About p 549
9.6 Chi-Square Test for the Population Standard Deviation 556
χ2 (Chi-Square) Test for σ Using the Critical-Value Method 556
χ2 Test for σ Using the p-Value Method 559
Using Confidence Intervals for σ to Perform Two-Tailed Hypothesis Tests for σ 561
9.7 Probability of a Type II Error and the Power of a Hypothesis Test 564
Probability of a Type II Error 564
Power of a Hypothesis Test 567
Chapter 9 Formulas and Vocabulary 570
Chapter 9 Review Exercises 571
Chapter 9 Quiz 572
10.1 Inference for Mean Difference—Dependent Samples 576
Independent Samples and Dependent Samples 576
Dependent Sample t Test for the Population Mean of the Differences 577
t Confidence Intervals for the Population Mean Difference for Dependent Samples 582
Use a t Interval for μd to Perform t Tests About μd 583
10.2 Inference for Two Independent Means 589
Independent Sample t Test for μ1-μ2 589
t Confidence Intervals for μ1-μ2 594
Using Confidence Intervals to Perform Hypothesis Tests 595
t Inference for μ1-μ2 Using Pooled Variance 596
Z Inference for μ1-μ2 When σ1 and σ2 Are Known 598
10.3 Inference for Two Independent Proportions 606
Independent Sample Z Tests for p1-p2 606
Independent Sample Z Interval for p1-p2 612
Use Z Confidence Intervals to Perform Z Tests for p1-p2 613
10.4 Inference for Two Independent Standard Deviations 617
The F Distribution and the F Test 617
Perform the F Test for Comparing Two Population Standard Deviations: Critical-Value Method 619
Perform the F Test for Comparing Two Population Standard Deviations: p-Value Method 623
Chapter 10 Formulas and Vocabulary 627
Chapter 10 Review Exercises 628
Chapter 10 Quiz 629
11.1 χ2 Goodness of Fit Test 632
The Multinomial Random Variable 632
What Is a χ2 Goodness of Fit Test? 634
Performing the χ2 Goodness of Fit Test 637
11.2 χ2 Tests for Independence and for Homogeneity of Proportions 646
Introduction to the χ2 Test for Independence 646
Performing the χ2 Test for Independence 648
χ2 Test for the Homogeneity of Proportions 651
Chapter 11 Formulas and Vocabulary 660
Chapter 11 Review Exercises 661
Chapter 11 Quiz 662
12.1 One-Way Analysis of Variance (ANOVA) 666
How Analysis of Variance (ANOVA) Works 666
Performing One-Way ANOVA 673
12.2 Multiple Comparisons 685
Performing Multiple Comparisons Tests Using the Bonferroni Method 686
Tukey's Test for Multiple Comparisons 688
Using Confidence Intervals to Perform Tukey's Test 689
12.3 Randomized Block Design 693
Randomized Block Design Explained and Performed 693
12.4 Two-Way ANOVA 701
Constructing and Interpreting an Interaction Graph 702
Performing a Two-Way ANOVA 703
Chapter 12 Formulas and Vocabulary 710
Chapter 12 Review Exercises 711
Chapter 12 Quiz 712
13.1 Inference About the Slope of the Regression Line 716
The Regression Model and the Regression Assumptions 716
Hypothesis Tests for Slope β1 721
Confidence Interval for Slope β1 726
Using Confidence Intervals to Perform the t Test for the Slope β1 727
13.2 Confidence Intervals and Prediction Intervals 737
Construct Confidence Intervals for the Mean Value of y for a Given x 737
Construct Prediction Intervals for an Individual Value of y for a Given x 739
13.3 Multiple Regression 743
Finding the Multiple Regression Equation, Interpreting the Coefficients, and Making Predictions 743
The Adjusted Coefficient of Determination 745
The F Test for the Overall Significance of the Multiple Regression 746
The t Test for the Significance of Individual Predictor Variables 747
Dummy Variables in Multiple Regression 749
Strategy for Building a Multiple Regression Model 750
Chapter 13 Formulas and Vocabulary 757
Chapter 13 Review Exercises 757
Chapter 13 Quiz 759
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14.1 Introduction to Nonparametric Statistics 14-3
14.2 Sign Test 14-5
14.3 Wilcoxon Signed Rank Test for Matched-Pair Data 14-18
14.4 Wilcoxon Rank Sum Test for Two Independent Samples 14-29
14.5 Kruskal-Wallis Test 14-36
14.6 Rank Correlation Test 14-44
14.7 Runs Test for Randomness 14-55
Chapter 14 Formulas and Vocabulary 14-62
Chapter 14 Review Exercises 14-63
Chapter 14 Quiz 14-66
Notes and Data Sources 14-67