How to Use This Book x
Barron's Essential 5 xii
Exam Overview 1
Part 1 Diagnostic Test
Diagnostic Test 7
Answer Key 26
Answer Explanations 26
AP Score for the Diagnostic Test 37
Study Guide for the Diagnostic Test Multiple-Choice Questions 38
Part 2 Units Review
Unit 1 Exploring One-Variable Data 41
Categorical Variables 41
Representing a Quantitative Variable with Tables and Graphs 44
Describing the Distribution of a Quantitative Variable 49
Quiz 1 53
Summary Statistics for a Quantitative Variable 59
Graphical Representations of Summary Statistics 68
Comparing Distributions of a Quantitative Variable 73
Quiz 2 76
The Normal Distribution 82
Quiz 3 85
Summary 87
Unit 2 Exploring Two-Variable Data 89
Two Categorical Variables 90
Quiz 4 97
Two Quantitative Variables 101
Correlation 104
Least Squares Regression 106
Residuals 110
Outliers, Influential Points, and Leverage 114
More on Regression 117
Transformations to Achieve Linearity 118
Quiz 5 121
Quiz 6 129
Summary 134
Unit 3 Collecting Data 135
Retrospective Versus Prospective Observational Studies 136
Bias 137
Sampling Methods 138
Sampling Variability 141
Quiz 7 143
Experiments Versus Observational Studies 148
The Language of Experiments 149
Replication and Generalizability of Results 153
Inference and Experiments 154
Quiz 8 156
Summary 159
Unit 4 Probability, Random Variables, and Probability Distributions 161
The Law of Large Numbers 162
Basic Probability Rules 163
Multistage Probability Calculations 165
Quiz 9 167
Random Variables, Means (Expected Values), and Standard Deviations 172
Means and Variances for Sums and Differences of Sets 174
Means and Variances for Sums and Differences of Random Variables 176
Transforming Random Variables 177
Quiz 10 179
Binomial Distribution 182
Geometric Distribution 187
Quiz 11 190
Cumulative Probability Distribution 194
Summary 196
Unit 5 Sampling Distributions 197
Normal Distribution Calculations 198
Quiz 12 205
Central Limit Theorem 210
Biased and Unbiased Estimators 212
Sampling Distribution for Sample Proportions 215
Sampling Distribution for Differences in Sample Proportions 217
Sampling Distribution for Sample Means 219
Sampling Distribution for Differences in Sample Means 221
Simulation of a Sampling Distribution 224
Quiz 13 225
Summary 232
Unit 6 Inference for Categorical Data: Proportions 233
The Meaning of a Confidence Interval 234
Conditions for Inference 234
Confidence Interval for a Proportion 236
Quiz 14 241
Quiz 15 244
Logic of Significance Testing 247
Significance Test for a Proportion 248
Confidence Interval for the Difference of Two Proportions 251
Significance Test for the Difference of Two Proportions 253
Quiz 16 256
Quiz 17 261
Summary 266
Unit 7 Inference for Quantitative Data: Means 269
The t-Distribution 270
Confidence Interval for a Mean 271
Quiz 18 275
Significance Test for a Mean 279
Confidence Interval for the Difference of Two Means 281
Significance Test for the Difference of Two Means 282
Paired Data 284
Quiz 19 287
Simulations and P-Values 292
Quiz 20 294
More on Power, Type I Errors, and Type II Errors 297
Quiz 21 299
Confidence Intervals versus Hypothesis Tests 302
Summary 303
Unit 8 Inference for Categorical Data: Chi-Square 305
Chi-Square Test for Goodness-of-Fit 305
Chi-Square Test for Independence 309
Chi-Square Test for Homogeneity 313
Quiz 22 315
Summary 318
Unit 9 Inference for Quantitative Data: Slopes 319
Sampling Distribution for the Slope 319
Confidence Interval for the Slope of a Least Squares Regression Line 320
Hypothesis Test for Slope of Least Squares Regression Line 324
Quiz 23 328
Quiz 24 333
Summary 338
Part 3 Final Review
Final Review 341
Selecting an Appropriate Inference Procedure 341
Quiz 25 344
Quiz 26 346
Statistical Insights into Social Issues 348
Quiz 27 350
Quiz 28 359
The Investigative Task: Free-Response Question 6 366
Quiz 29 373
50 Misconceptions 380
50 Common Errors on the AP Exam 386
50 AP Exam Hints, Advice, and Reminders 389
Part 4 Practice Tests
Practice Test 1 397
Answer Key 415
Answer Explanations 415
Practice Test 2 427
Answer Key 442
Answer Explanations 442
Practice Test 3 453
Answer Key 472
Answer Explanations 472
Practice Test 4 483
Answer Key 502
Answer Explanations 502
Practice Test 5 515
Answer Key 533
Answer Explanations 533
Part 5 Appendices
Appendices 543
Formulas 543
Graphical Displays 546
Checking Assumptions for Inference 547
Independence 548
More on Residuals 549
Answer Explanations for Quizzes 1-29 550
AP Scoring Guide 613
Basic Uses of the T1-84 614
Basic Uses of the Casio Prizm 616
Basic Uses of the HP Prime 618
Table A: Standard Normal Probabilities 620
Table B: t-Distribution Critical Values 622
Table C: x 2 Critical Values 623
Index 625