Discovering the Fundamentals of Statistics

Title Page......Page 2
Copyright Page......Page 3
BRIEF CONTENTS......Page 4
Contents......Page 5
Preface to the Student......Page 12
About the Author......Page 23
 Case study Does Friday the 13th Change Human Behavior?......Page 26
 1.1 Data Stories: The People Behind the Numbers......Page 27
  What Is Statistics?......Page 30
  Descriptive Statistics: The Building Blocks of Data Analysis......Page 33
  Inferential Statistics: How Do We Get There from Here?......Page 36
  Random Sampling......Page 42
  More Sampling Methods......Page 45
  Selection Bias and Questionnaire Design......Page 48
  Experimental Studies and Observational Studies......Page 50
   Chapter 1 Review Exercises......Page 56
   Chapter 1 Quiz......Page 57
 Case study The Caesar Cipher......Page 58
  Frequency Distributions and Relative Frequency Distributions......Page 59
  Bar Graphs and Pareto Charts......Page 62
  Pie Charts......Page 63
  Crosstabulations......Page 64
  Clustered Bar Graphs......Page 65
  Frequency Distributions and Relative Frequency Distributions......Page 74
  Histograms and Frequency Polygons......Page 79
  Stem-and-Leaf Displays and Dotplots......Page 81
  Distribution Shape, Symmetry, and Skewness......Page 83
  Cumulative Frequency Distributions and Cumulative Relative Frequency Distributions......Page 91
  Ogives......Page 92
  Time Series Graphs......Page 93
 2.4 Graphical Misrepresentations of Data......Page 98
  Chapter 2 Vocabulary......Page 103
  Chapter 2 Review Exercises......Page 104
  Chapter 2 Quiz......Page 105
 Case study Can the Financial Experts Beat the Darts?......Page 106
  The Mean......Page 107
  The Median......Page 111
  The Mode......Page 113
  Skewness and Measures of Center......Page 115
  The Range......Page 121
  Population Variance and Population Standard Deviation......Page 123
  Compute the Sample Variance and Sample Standard Deviation......Page 127
  The Empirical Rule......Page 130
  Chebyshev’s Rule......Page 132
  The Weighted Mean......Page 139
  Estimating the Mean for Grouped Data......Page 140
  Estimating the variance and Standard Deviation for Grouped Data......Page 142
  z-Scores......Page 145
  Detecting Outliers Using the z-Score Method......Page 149
  Percentiles and Percentile Ranks......Page 150
  Quartiles and the Interquartile Range......Page 153
 3.5 Five-Number Summary and Boxplots......Page 159
  The Five-Number Summary......Page 160
  The Boxplot......Page 161
  Detecting Outliers Using the IQR Method......Page 164
   Chapter 3 Formulas and Vocabulary......Page 169
   Chapter 3 Review Exercises......Page 170
   Chapter 3 Quiz......Page 172
 Case study Worldwide Patterns of Cell Phone Usage......Page 174
  Scatterplots......Page 175
  Correlation Coefficient......Page 177
  Test for Linear Correlation......Page 183
  The Regression Line......Page 189
  Predictions and Prediction Error......Page 193
  Sum of Squares Error (SSE) and Standard Error of the Estimate s......Page 203
  SST, SSR, and SSE......Page 206
  Coefficient of Determination r²......Page 208
   Chapter 4 Review Exercises......Page 214
   Chapter 4 Quiz......Page 215
 Case study The ELISA Test for the Presence of HIV......Page 218
  Building Blocks of Probability......Page 219
  Classical Method of Assigning Probability......Page 222
  Relative Frequency Method......Page 225
  Complement, Union, and Intersection......Page 234
  Addition Rule......Page 236
  Introduction to Conditional Probability......Page 242
  Independent Events......Page 244
  Multiplication Rule......Page 246
  Approximating Probabilities for Dependent Events......Page 249
  Multiplication Rule for Counting......Page 259
  Permutations and Combinations......Page 262
  Computing Probabilities Using Combinations......Page 267
   Chapter 5 Formulas and Vocabulary......Page 271
   Chapter 5 Review Exercises......Page 272
   Chapter 5 Quiz......Page 273
 Case study Text Messaging......Page 276
  Random Variables......Page 277
  Discrete Probability Distributions......Page 280
  Mean and Variability of a Discrete Random Variable......Page 282
  Binomial Experiment......Page 291
  Binomial Probability Distribution Formula......Page 293
  Binomial Distribution Tables......Page 297
  Binomial Mean, Variance, Standard Deviation, and Mode......Page 298
 6.3 Continuous Random Variables and the Normal Probability Distribution......Page 304
  Continuous Probability Distributions......Page 305
  Calculating Probabilities for the Uniform Probability Distribution......Page 306
  Introduction to Normal Probability Distribution......Page 307
  Finding Areas Under the Standard Normal Curvefor a Given Z-Value......Page 313
  Finding Standard Normal Z-Values for a Given Area......Page 318
  Finding Probabilities for Any Normal Distribution......Page 323
  Finding a Normal Data Value for a Given Area or Probability......Page 327
  Using the Normal Distribution to Approximate Probabilities of the Binomial Distribution......Page 336
   Chapter 6 Formulas and Vocabulary......Page 341
   Chapter 6 Review Exercises......Page 342
   Chapter 6 Quiz......Page 343
 Case Study Trial of the Pyx: How Much Gold Is in Your Gold Coins?......Page 346
 7.1 Introduction to Sampling Distributions......Page 347
  Sampling Distribution of the Sample Mean ẍ......Page 348
  Sampling Distribution of ẍ for a Normal Population......Page 350
  Finding Probabilities and Percentiles Using a Sampling Distribution......Page 351
  Assessing Normality Using Normal Probability Plots......Page 357
  Sampling Distribution of ẍ for Skewed Populations......Page 358
  Applying the Central Limit Theorem for Means......Page 359
  Sampling Distribution of the Sample Proportion ṗ......Page 367
  Applying the Central Limit Theorem for Proportions......Page 370
   Chapter 7 Formulas and Vocabulary......Page 375
   Chapter 7 Quiz......Page 376
 Case study Health Effects of the Deepwater Horizon Oil Spill......Page 378
  Calculate a Point Estimate of the Population Mean......Page 379
  The Z Interval for the Population Mean......Page 380
  Ways to Reduce the Margin of Error......Page 387
  Sample Size for Estimating the Population Mean......Page 389
  Introducing the t Distribution......Page 395
  t Interval for the Population Mean......Page 398
  Point Estimate ṗ of the Population Proportion p......Page 407
  Z Interval for the Population Proportion p......Page 408
  Margin of Error for the Z Interval for p......Page 410
  Sample Size for Estimating the Population Proportion......Page 411
 8.4 Confidence Intervals for the Population Variance and Standard Deviation......Page 417
  Properties of the x² (Chi-Square) Distribution......Page 418
  Constructing Confidence Intervals for the Population Variance and Standard Deviation......Page 420
   Chapter 8 Formulas and Vocabulary......Page 425
   Chapter 8 Review Exercises......Page 426
   Chapter 8 Quiz......Page 427
 Case study The Golden Ratio......Page 430
 9.1 Introduction to Hypothesis Testing......Page 431
  Constructing the Hypotheses......Page 432
  Type I and Type II Errors......Page 435
  The Essential Idea About Hypothesis Testing for the Mean......Page 438
  Performing the Z Test for the Mean, Using the Critical-Value Method......Page 440
  The p-Value Method of Performing the Z Test for the Mean......Page 447
  Assessing the Strength of Evidence Against the Null Hypothesis......Page 453
  The Relationship Between the p-Value Method and the Critical-Value Method......Page 454
  Using Confidence Intervals for μ to Perform Two-Tailed Hypothesis Tests About μ......Page 455
  t Test for μ Using the Critical-Value Method......Page 462
  t Test for μ Using the p-Value Method......Page 465
  Using Confidence Intervals to Perform Two-Tailed t Tests......Page 469
  The Z Test for p Using the Critical-Value Method......Page 477
  Z Test for p: the p-Value Method......Page 480
  Using Confidence Intervals for p to Perform Two-Tailed Hypothesis Tests About p......Page 483
  x² (Chi-Square) Test for s Using the Critical-Value Method......Page 488
  x² Test for s Using the p-Value Method......Page 491
  Using Confidence Intervals for σ to Perform Two-Tailed Hypothesis Tests for σ......Page 493
  Probability of a Type II Error......Page 497
  Power of a Hypothesis Test......Page 499
   Chapter 9 Review Exercises......Page 503
   Chapter 9 Quiz......Page 505
 Case Study Do Prior Student Evaluations Influence Students’ Ratings of Professors?......Page 508
  Independent Samples and Dependent Samples......Page 509
  Dependent Sample t Test for the Population Mean of the Differences......Page 510
  t Intervals for the Population Mean Difference for Dependent Samples......Page 516
  Use a t Interval for μd to Perform t Tests About μd......Page 517
  Independent Sample t Test for μ₁ – μ₂......Page 522
  t Confidence Intervals for μ₁ – μ₂......Page 528
  Using Confidence Intervals to Perform Hypothesis Tests......Page 529
  t Inference for μ₁ – μ₂ Using Pooled Variance......Page 531
  Z Inference for μ₁ – μ₂ When σ₁ and σ₂ Are Known......Page 533
  Independent Sample Z Tests for p₁ – p₂......Page 539
  Independent Sample Z Interval for p₁ – p₂......Page 545
  Use Z Confidence Intervals to Perform Z Tests for p₁ – p₂......Page 546
   Chapter 10 Formulas and Vocabulary......Page 550
   Chapter 10 Quiz......Page 551
 Case Study Online Dating......Page 554
 11.1 x² Goodness of Fit Test......Page 555
  The Multinomial Random Variable......Page 556
  What Is a x² Goodness of Fit Test?......Page 557
  Performing the x² Goodness of Fit Test......Page 559
  Introduction to the x² Test for Independence......Page 568
  Performing the x² Test for Independence......Page 570
  Test for the Homogeneity of Proportions......Page 573
  F Distribution......Page 582
  How Analysis of Variance (ANOVA) Works......Page 583
  Performing One-Way ANOVA......Page 590
  The Regression Model and the Regression Assumptions......Page 600
  Hypothesis Tests for Slope β₁......Page 604
  Confidence Interval for β₁......Page 608
  Using Confidence Intervals to Perform the t Test for Slope β₁......Page 609
   Chapter 11 Formulas and Vocabulary......Page 614
   Chapter 11 Review Exercises......Page 615
   Chapter 11 Quiz......Page 617
Answers to Odd-Numbered Exercises and Chapter Quizzes......Page 620
Tables Appendix......Page 674
 Table A: Random numbers......Page 675
 Table B: Binomial distribution......Page 676
 Table C: Standard normal distribution......Page 682
 Table D: t-Distribution......Page 684
 Table E: Chi-square (x²) distribution......Page 685
 Table F: F-Distribution critical values......Page 686
 Table G: Critical values for correlation coefficient......Page 690
Notes and Data Sources......Page 692
Index......Page 696