Master Math: AP Statistics

256 Pages·2010·3.68 MB·English

by  Gerry McAfee

Master Math:
AP® Statistics
Gerry McAfee
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Table of Contents
Acknowledgments vii
About the Author ix
Introduction xi
Preparing for the AP Statistics Exam xiii
Chapter 1: Exploring and Graphing Univariate Data 1
1.1 Describing Distributions 2
Shape, Center, and Spread 2
1.2 Displaying Data with Graphs 9
Modified Boxplots 9
Histograms 10
Stemplots 12
Dotplots 13
Bar Graphs 13
Pie Charts 14
Chapter 2: Exploring and Graphing Bivariate Data 17
2.1 Scatterplots 18
Correlation 22
Least Squares Regression 23
2.2 Modeling Data 27
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Chapter 3: Normal Distributions 41
3.1 Density Curves 42
3.2 Normal Distributions 44
The Empirical Rule (the 68, 95, 99.7 Rule) 46
3.3 Normal Calculations 48
Assessing Normality 55
Chapter 4: Samples, Experiments, and Simulations 57
4.1 Sampling 58
4.2 Designing Experiments 63
4.3 Simulation 68
Chapter 5: Probability 73
5.1 Probability and Probability Rules 74
5.2 Conditional Probability and Bayes’s Rule 82
5.3 Discrete Random Variables 87
5.4 Continuous Random Variables 91
5.5 Binomial Distributions 97
5.6 Geometric Distributions 102
Chapter 6: Sampling Distributions 107
6.1 Sampling Distributions 108
6.2 Sample Means and the Central Limit Theorem 111
6.3 Sample Proportions and the Central Limit Theorem 119
Chapter 7: Inference for Means 121
7.1 The t-Distributions 122
7.2 One-Sample t-Interval for the Mean 124
Interpreting Confidence Intervals 129
Table of Contents v
7.3 One-Sample t-Test for the Mean 131
7.4 Two-Sample t-Interval for the Difference Between Two Means 135
7.5 Two-Sample t-Test for the Difference Between Two Means 141
7.6 Matched Pairs (One-Sample t) 144
7.7 Errors in Hypothesis Testing: Type I, Type II, and Power 147
Chapter 8: Inference for Proportions 149
8.1 One-Sample z-Interval for Proportions 150
Margin of Error 153
8.2 One-Sample z-Test for Proportions 156
8.3 Two-Sample z-Interval for Difference Between
Two Proportions 159
8.4 Two-Sample z-Test for Difference Between Two Proportions 162
Chapter 9: Inference for Related Variables:
Chi-Square Distributions 167
9.1 The Chi-Square Statistic 168
9.2 Chi-Square Test for Goodness of Fit 170
9.3 Chi-Square Test for Homogeneity of Populations 176
9.4 Chi-Square Test for Independence/Association 181
Chapter 10: Inference for Regression 185
10.1 The Regression Model 186
10.2 Confidence Intervals for the Slope (cid:2) 189
10.3 Hypothesis Testing for the Slope (cid:2) 193
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Appendix A: Tables 199
Table A: Standard Normal Probabilities 200
Table B: Random Digits 202
Table C: t Distribution Critical Values 203
Table D: χ2 Critical Values 204
Appendix B: Formulas 205
Formulas Given on the AP Exam 206
Formulas Not Given on the AP Exam 210
Normal Distribution 210
Probability 210
Inferential Statistics 213
Appendix C: Assumptions and Conditions for Inference 217
Glossary 223
Index 231
Acknowledgments
I would like to thank Chris True, AP Statistics teacher and consultant,
for reading and editing this book for content. I appreciate his helpful
comments and suggestions. I would also like to thank Dan Foster for
all of his efforts in editing this book. Dan was extremely easy to
work with and provided me with excellent feedback. I am grateful to
Judy Littlefield for all of her hard work on the many illustrations and
equations.
I extend my thanks to Emi Smith, Senior Acquisitions Editor, and
Stacy Hiquet, Publisher and General Manager, for the opportunity to
write this book. Their patience, support, and trust are truly appreciated.
I would also like to thank Brad Crawford for proofreading. Additional
thanks to Sarah Panella, Heather Talbot, Jordan Castellani, Jeff Cooper,
and Larry Sweazy.
I am grateful to have had some great teachers while growing up. I want
to specifically thank Sandy Halstead for teaching me algebra, algebra 2,
trigonometry, and physics. I am grateful to Karen Ackerman for teaching
me honors English.
To my students, past and present, thank you for motivating me to be the
best teacher I can be. I am inspired by the efforts you make in preparing
for the AP Exam. I hope you continue those efforts in all aspects of
your lives.
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Finally, I would like to thank my friends and family. To my friends—
especially John, Chris, Brad, and Tim—thank you for all your support
and encouragement. To my friend and department head, Dan Schermer,
thanks for always guiding me in the right direction. To Dean and my
“painting buddies,” thanks for providing me many hours of fun and
stress relief as we worked together. Special thanks to Nick and Chad for
helping me with graphs and images. To Bob and Carol, thanks for all of
your support. To all of my extended family, thank you for all of the help
you have given to me, Lori, and our children. To my parents, Don and
Joan McAfee, thank you for being great parents and helping me develop
a strong work ethic and for instilling me with strong values. To my sister,
Lynn McAfee, and her family, thank you for all of your encouragement
and support. To my children, Cassidy and Nolan, thank you for being
such great kids and working so hard in school. Your talents and hard
work will pay off. I appreciate you constantly asking me, “Are you done
with your book yet, dad?” This question motivated me to keep pressing
on. And finally, to my wife, Lori, I could not have done it without you!
Thanks for doing more than your fair share and always believing in me!
About the Author
Gerry McAfeebegan his teaching career as an undergraduate at Purdue
University. He is currently teaching AP Statistics in Brownsburg, Indiana,
and has been teaching mathematics for 17 years. In addition to teaching
AP Statistics, Gerry also teaches dual-credit mathematics, including
finite math, through Indiana State University, and applied calculus,
through Ball State University. Gerry has also taught a wide range of
additional math courses including basic math, pre-algebra, algebra, and
algebra 2. Gerry has won teaching awards including the Brownsburg High
School National Honor Society Teacher of the Year, Who’s Who Among
American Teachers, and the Fellowship of Christian Athletes–Positive
Role Model. He was also chosen for teacher recognition by an
Indianapolis StarAcademic All Star student.
Gerry graduated from Purdue University with a Bachelor of Science
degree in Mathematics in 1993. He also holds a Master of Arts degree
in Education from Indiana Wesleyan University.
In his spare time, Gerry enjoys spending time with his wife, Lori, and
two children, Cassidy and Nolan. Family activities include many hours
of school functions and sporting events, along with family vacations.
In the summer, Gerry enjoys spending time with his teaching colleagues
outdoors painting houses. Other activities that Gerry enjoys include
fishing, running, and most recently triathlons. Gerry has run seven
marathons and has run the Boston Marathon two times (not in the
same day).
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