AP Statistics 2007 : An Apex Learning Guide Book

About the Authors     ix
Kaplan Panel of AP Experts     xi
The Basics
Inside the AP Statistics Exam     3
Introduction to the AP Statistics Exam     4
Overview of the Test Structure     4
How the Exam Is Scored     7
Registration and Fees     7
Additional Resources     8
Strategies for Success: Preparing for the Exam     9
General Test-Taking Strategies     9
How This Book Can Help, Plus Specific AP Statistics Exam Strategies     10
How to Approach the Multiple-Choice Questions     11
How to Approach the Free-Response Questions     17
Stress Management     18
Countdown to the Test     21
Diagnostic Test
AP Statistics Diagnostic Test     25
Diagnostic Test     27
Diagnostic Test Correlation Chart     44
How to Use the Review Section     45
AP Statistics Review
Constructing and Interpreting Graphical Displays of Distributions of Univariate Data     49
What Is All This Data About?     49
Displaying Categorical Data Graphically     50
Displaying Quantitative Data Graphically     52
The Shape of a Distribution     58
If YouLearned Only Three Things in This Chapter     50
Review Questions     61
Answers and Explanations     65
Summarizing Distributions of Univariate Data     67
Measures of Center     67
Measuring the Spread     69
Measuring the Position     71
Boxplots     72
Effects of Changing Units of Summary Measures     74
If You Learned Only Four Things in This Chapter     75
Review Questions     75
Answers and Explanations     78
Comparing Distributions of Univariate Data     79
Comparing Distributions with Stem and Leaf Plots     79
Comparing Distributions with Dotplots     80
Comparing Distributions with Boxplots     81
Which Plot?     83
If You Learned Only Two Things in This Chapter     83
Review Questions     84
Answers and Explanations     88
Exploring Bivariate Data     91
Overview: Why Bivariate Data?     91
Analyzing Patterns in Scatterplots     92
Measuring Relationships Between Variables     94
Least Squares Regression Line     96
Residual Plots and Outliers     97
Transforming Data to Achieve Linearity     99
If You Learned Only Five Things in This Chapter     100
Review Questions     101
Answers and Explanations     104
Exploring Categorical Data     105
Frequency Tables and Bar Charts     105
Marginal and Joint Frequencies for Two-Way Tables     107
Conditional Relative Frequencies     108
Graphing Two-Way Tables     109
If You Learned Only Four Things in This Chapter     111
Review Questions     111
Answers and Explanations     114
Overview of Methods of Data Collection     115
Planning a Study: Overview     115
Observational Studies     116
Experiments     117
Statistics and Parameters     118
If You Learned Only Four Things in This Chapter     118
Review Questions     118
Answers and Explanations     122
Planning and Conducting Surveys     125
Collecting Data: Observational Studies and Surveys     125
Populations, Samples, and Random Selection     126
Sources of Bias     127
Simple Random Sampling     129
Stratified Random Sampling and Other Schemes     129
If You Learned Only Four Things in This Chapter     130
Review Questions     131
Answers and Explanations     134
Planning and Conducting Experiments     137
The Fundamentals of Experimental Design     137
Confounding and Sources of Bias     138
Experimental Design Schemes     139
Observational Studies Revisited: SRS, Strata, Clusters     141
If You Learned Only Three Things in This Chapter     142
Review Questions     143
Answers and Explanations     146
Generalizability of Results from Experiments, Observational Studies, and Surveys     149
Generalizability     149
Sample Size and Population Size     150
Observational Studies     150
Experiments and Statistical Significance     151
If You Learned Only Three Things in This Chapter     151
Review Questions     152
Answers and Explanations     155
Probability     157
What Are the Chances?     157
Modeling Probability     159
Rules of Probability     161
Possible Outcomes and Counting Techniques     164
If You Learned Only Five Things in This Chapter     165
Review Questions     166
Answers and Explanations     170
Random Variables     173
Discrete and Continuous Random Variables     173
Mean and Variance of Random Variables     176
Law of Large Numbers     179
Rules for Means and Variances of Random Variables     180
Binomial Distribution     181
Geometric Distribution     183
Simulating Random Behavior     185
If You Learned Only Five Things in This Chapter     188
Review Questions     189
Answers and Explanations     193
The Normal Distribution     195
Probability Density Functions     195
The Normal Density Curve     197
The Normal Distribution as a Model for Measurement     200
If You Learned Only Three Things in This Chapter     205
Review Questions     205
Answers and Explanations     209
Sampling Distributions     211
Sampling Distributions     211
The Distribution of the Sample Proportions     214
The Distribution of the Sample Means     217
The Central Limit Theorem     219
Simulation of Sampling Distributions     220
Other Sampling Distributions     221
If You Learned Only Two Things in This Chapter     223
Review Questions     224
Answers and Explanations     227
Estimation     229
Point Estimates and Margin of Error     229
Confidence Intervals for Large Samples     232
Confidence Intervals for Small Samples     236
Confidence Intervals for a Proportion     238
Confidence Intervals for the Difference Between Two Means     240
Confidence Intervals for the Difference Between Two Proportions     244
Confidence Intervals for the Slope of a Least-Squares Regression Line     245
Calculating Sample Sizes     248
If You Learned Only Four Things in This Chapter     249
Review Questions     250
Answers and Explanations     262
Hypothesis Testing     281
It All Starts with a Claim     281
Large Sample Test for a Proportion     288
Large Sample Test for the Difference Between Two Proportions     290
Test for a Mean     293
Tests for the Difference Between Two Means     296
Matched Pairs     297
If You Learned Only Four Things in This Chapter     301
Review Questions      303
Answers and Explanations     313
Chi-Square and Inferences for the Slope of a Regression Line     321
Chi-Square Test for Goodness of Fit, Homogeneity of Proportions, and Independence     321
Chi-Square Test for Goodness of Fit     322
Chi-Square Test for Homogeneity of Proportions     325
Chi-Square Test for Independence     326
Chi-Square Test for Independence vs. Chi-Square Test for Homogeneity     328
Test for the Slope of the Least Squares Regression Line     329
If You Learned Only Three Things in This Chapter     333
Review Questions     334
Answers and Explanations     339
Using the Graphing Calculator     343
Calculator Usage on the AP Statistics Exam     343
Calculator Tips for Exploring Univariate Data     344
Calculator Tips for Exploring Bivariate Data     348
Calculator Tips for Probability     353
Calculator Tips for Statistical Inference     361
Quick Reference List of Calculator Commands     372
Practice Tests
How to Take the Practice Tests     374
How to Compute Your Score     374
Practice Test 1     377
Answer Key     396
Answers and Explanations     397
Practice Test 2     409
Answer Key     428
Answers and Explanations     429
Formulas and Tables     441
Glossary     447