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AP Statistics
High School
Textbooks
Students are issued two textbooks and we use both during the course/year. Students are assigned
reading and problems from both textbooks.
Understandable Statistics. Brase and Brase. 7th edition. Houghton Mifflin Company. ISBN# 0618-20554-3. 2003.
Introduction to the Practice of Statistics. Moore, McCabe. 3rd edition. W. H. Freeman and
Company. ISBN# 0-7167-3502-4. 1999.
Additional Resources
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I have numerous statistics textbooks that I use to supplement materials/reading as needed.
I have downloaded all of the College Board Free Response questions since 1997 and use these
problems during the course. Each unit test includes 2-4 Free Response questions applicable to
that topic/unit.
I have all the 1997/2002 multiple choice questions and use these problems to help students
master concepts.
I recently purchased the booklet, AP Statistics Module: Sampling and Experimentation:
Planning and Conducting a Study.
I have a number of review books/manuals that I use and lend to students as applicable including:
College Board Statistics – Teacher Guide
College Board AP Statistics 2006-2007 Professional Development Workshop Materials
Special Focus: Interface
McGraw-Hill 5 Steps to a 5: AP Statistics Review Book. Duane C. Hinders
D&S Marketing Systems AP Statistics Multiple Choice and Free Response Questions Test
Prep Booklet
Texas Instruments – Explorations Statistics Handbook for the TI-83
Venture Publishing – Introduction to Statistics with the TI-83 Graphing Calculator. Robert
Schneider, George Best.
Barron’s – How to Prepare for the AP Statistics Exam. 3rd edition. Martin Sternstein.
Activity Based Statistics – Richard Scheaffer.
AP Exam
All our students are strongly encouraged to take the AP exam in May. Our school will pay for this
exam for students that cannot afford the exam fee.
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Technology
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All students are expected to have a TI-83, 83+, 84, 84+ for their use in class and for homework
assignments. For students that cannot afford a calculator our school will provide a loaner
calculator for that student for the course.
All students have access to the two computer labs at our school.
The graphing calculator is used everyday in class and students are instructed daily on how to
use this technology to help them understand statistical concepts.
Students are required to use computer software for their projects during the year. John Bapst
uses Fathom Software for AP Statistics. During the course students are exposed to “generic
software” outputs and become proficient at reading these outputs. After the AP Exam we use
Fathom extensively for their final project.
Students are exposed to numerous applets during the course and I have a computer and LCD
projector in my classroom.
Course Introduction (from our Student Handbook)
AP Statistics
Prerequisite or Co-requisite: 90% average in Honors Pre-Calculus
This is a year long college-level statistics course. Students will be required to do a lot of
reading/work on their own. Topics include: Exploring Data, Planning a Study, Probability, and
Statistical Inference. Graphing calculators are integral to this course, John Bapst will provide if
needed. It is strongly encouraged that all students take the AP Exam in May.
Course Objectives
By the end of this class students should be able to analyze data to make relevant, intelligent, real
world decisions and:
1. Be able to analyze data using numerous graphical/tabular types
2. Be able to analyze data using density/normal curves
3. Understand correlation/causation with data samples
4. Use the LSRL to describe a data set
5. Model and describe non-linear relationships
6. Design an appropriate experiment that is valid and reliable
7. Understand randomness as it is related to probability/data sampling
8. Solve probability problems using both a binomial and geometric distribution
9. Understand sampling distributions as a basis for statistical inference
10. Use confidence intervals and tests of significance to analyze data
11. Understand the difference between a Type I and II error
12. Compare two sample means for statistical inference
13. Use population proportions for statistical inference
14. Use inference/two-way tables to test for goodness of fit
15. Use inference for the regression line and slope of the LSRL
16. To communicate concepts and ideas in a clear manner, using correct statistical vocabulary
and notation.
17. Use technology to help solve problems, experiments, interpret results, and verify
conclusions.
18. To recognize and develop a thorough plan for collecting data in order to make a valid
conjecture.
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Throughout the course students are required to communicate their thoughts well, using correct
statistical language/knowledge in the context of the problem. Throughout the course, connections are
made between the four major themes of the course so students can see how these concepts are
interrelated. I want the course to be a continuous learning process, not a number of isolated topics.
Inference is talked about on the first day of class, as is the role of controlled experiments.
Course Outline
Itemized below is a detailed summary of the major topics/concepts covered in each unit/chapter.
Since I use two different textbooks, the order of the units does not correspond exactly with the
chapters in either textbook.
Unit 1: Exploring Data – Numerically and Graphically Univariate Data (2 weeks)
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Types of data
Reading, Interpreting, Analyzing Graphs
Graph types including:
Pie Charts
Bar Graphs
Histograms
Dot Plots
Stem and Leaf Plots/Back to Back Stem and Leaf
Cumulative Frequency Graphs
Ogives
Normal Probability Plots
Scatter Plots
Connected Scatter plots – Time Plot
Box Plots – Regular and Modified
Analyzing graphs including SOCS
Shape
Outliers
Center
Spread
Numerical analysis of data including - Calculating and Interpreting:
Mean
Median
Mode
Range-Spread
IQR
Q1
Q3
Standard Deviation/Variance
Mean Absolute Deviation
Outliers
Unit 2: Density Curves/Normal Curves/Normal Distribution (2 weeks)
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Density curves – shape/properties
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Skewness – left/right
Mean/median of density curves
Resistance
Normal distributions
Empirical Rule (1,2,3 Standard Deviations)
Chebyshev’s Theorem
Percentiles
Standardizing Data – Z scores
Reading a Z Table
Normal/Curve Equation – Points of Inflection
Area under a curve – percentile/probability
Normal probability plot
Normal “looking” data – Assessing Data for Normalcy
Unit 3: Bivariate Data – Graphing/Describing (2.5 weeks)
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Scatterplots
Explanatory/Response Variable
Correlation – Positive/Negative
Interpreting Scatterplots
Outliers/Influential Points – The difference between the two
Correlation Coefficient (r) – Meaning/Interpreting/Properties of
Covariance
High correlation does not imply/prove causation
The Least Squares Regression Line (LSRL)
Properties of the LSRL
The components of the LSRL
Residuals – Residual Plots – How to interpret residual plots
Coefficient of Determination (r2) – How to calculate, meaning of
Reading/Interpreting Generic Computer Outputs
Unit 4: Linearizing Data – Exponential/Power Models (1.5 weeks)
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Linearizing non-linear data
Review of Rules of Logs/Natural Logs
Residuals – Residual Plots – What they mean/how to interpret
Extrapolation/Interpolation
Lurking Variables/Confounding Variables
Correlation does not prove causation
2 way tables – Interpreting
Marginal/Conditional Distributions
Describing relations between categorical variables
Simpson’s Paradox
Unit 5: Samples/Experiments/Simulation (3 weeks)
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Data collection
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Bias – How to minimize bias when collecting data
Types of bias – Undercoverage/Non-response/Question Wording
Sample vs. Population
Sampling Methods
Convenience Sampling
Cluster Sampling
Systematic Sampling
Random Sampling
Simple Random Sampling (SRS)
Stratified Random Sample
Multi-Stage Random Sample
Experimental Design
Control
Randomization
Replication
Placebos/Placebo Effect
Control Groups/Control
Control for lurking and confounding variables
Blocking
Factors/Levels/Treatments
Matched Pairs
Observational Studies
Surveys
Scope of Inference
Simulations- Using the calculator random digit tables
Reading/Using Random Digit tables
Unit 6: Probability (1.5 weeks)
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Basic Probability Rules/Concepts/Compliment of
Randomness/Chance Behavior
Independent vs. Dependent
Sample Space/Total Events
Probability Diagrams/Tress
Venn Diagrams
With Replacement/Without Replacement
Disjoint/Mutually exclusive events
Joint Probability
Conditional Probability
Additional/Multiplication Rules for Probability
Bayes Theorem
Unit 7: Random Variables (1.5 weeks)
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Discrete vs. Continuous Variables/Distributions
Discrete probability histograms
Continuous random variables/distributions/graphs
Area under a curve concept/probability
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Means/Variances of Random Variables
Why variances add and standard deviations don’t
Law of large numbers
Fallacy of the “Law of Small Numbers”
Unit 8: Binomial and Geometric Distributions (1.5 weeks)
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Binomial Distributions
4 requirements of a binomial setting
Binomial Probability Distribution Function
Binomial Cumulative Distribution Function
TI-83 calculator steps
Binomial probability formulas
Mean/Standard Deviation of a binomial random variable
Geometric Distributions
4 requirements of a geometric setting
Geometric probability distribution function
TI-83 calculator steps
Geometric probability formulas
Mean/Standard Deviation of a geometric random variable
Unit 9: Sampling Distributions (2 weeks)
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Introduction to Statistical Inference
Samples-Statistics
Population – Parameters
Sampling Variability – The importance of sample size
Sampling Distributions
Unbiased Statistics
Bias/Variability
Sample Proportions
Standard Deviation of a sample proportion distribution
Rules of thumb for comparing a distribution to a normal distribution
Sample Means
Standard deviation of a sample mean
Central Limit Theorem
Sample statistics as unbiased estimator of the population parameter
Unit 10: Introduction to Statistical Inference (2.5 weeks)
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Confidence Intervals – Meaning of/Constructing
Margin of Error/Meaning of/How it is calculated
Z Score critical values (mention t-score for future chapters) upper/lower
Standard error
Importance of sample size to minimize error
Tests of significance (Hypothesis Tests)
Null Hypothesis/Alternate Hypothesis
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Z Score to calculate P (Probability Value)
Significance Level/Meaning of
Checking conditions/assumptions for Hypothesis Testing
HAMC =
1. State Hypothesis
2. Check Assumptions
3. Do the Math – Calculate the P Value
4. Conclusion in the context of the problem
Confidence Interval vs Hypothesis Tests – How these 2 tests can “tell” us the same information
Practical uses/interpretations of hypothesis tests
Type I/Type II errors – Real world examples
Power of a hypothesis test = (1-Type II error)
Unit 11: Inference for Means – T Distributions (2 weeks)
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T distributions – Family of Curves
T table vs. Z table/Reading a T table
Degrees of Freedom (again)
ZAPTAX – Mr. T is always mean (Z table always for Proportions/T table always for Means)
One sample T statistic
Standard error
Matched Pairs Design
Confidence Intervals/Hypothesis Tests for one sample mean
Sample size and normalcy
Comparing 2 sample means (difference of)
Confidence intervals/hypothesis tests for 2 sample means
TI-83 steps
Choosing d(f) (degrees of freedom) for 2 samples – 3 methods – How/when to use each method
Reading/Interpreting generic computer outputs
Unit 12: Inference for Proportions (2weeks)
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Inference for 1 sample proportions
Standard deviation of the sample proportion
Standard Error
Relate proportions to a binomial/setting/distribution
When n is large enough, assume normalcy reading a Z table
Assumptions/Rules of Thumb
Confidence Intervals/Hypothesis Test for 1 sample proportion
Calculating sample size
Comparing two sample proportions
Confidence Intervals/Hypothesis Test for 2 sample proportions (difference of)
Pooling for 2 samples
TI-83 calculator step
Making decisions based upon inference tests
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Unit 13: Inference Using Chi-Square (2 weeks)
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Chi-Square Distributions
Degrees of Freedom
Reading/Interpreting a Chi-Square Table
Chi-Square Goodness of Fit Test
TI-83 calculator steps
Chi-Square formulas
Assumptions when using Chi-Square Tests
Chi-Square test for Homogeneity
2 way tables
Chi-Square Test for Independence
Calculating expected counts
Degrees of Freedom – How to calculate
Discuss when to use each of these Chi-Square tests
Importance of sample size/expected count size
Unit 14: Inference of Regression (1.5 weeks)
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Review scatter plots
Predicted LSRL
True Regression Line
Unbiased estimators for True Slope (β), True Intercept (α), and Standard Deviation (σ)
Standard Error about the LSRL
Degrees of Freedom
Confidence Intervals for the True Slope (β)
Hypothesis Testing for the True Slope (β)
TI-83 calculator steps
Assumptions required for this type of inference
Reading/Interpreting generic computer outputs for the Inference for Regression
Using inference to make accurate interpretations and predictions with data
Unit 15: Review for AP Statistics Exam – (2-3 weeks or as time/schedule permits)
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Complete the 2002 AP Exam under time constraints in class
Review major concepts/themes of the course
Review calculator usage
Exam strategies/tips
Preparing for the AP Statistics Exam
AP Statistics Grading Policies/Assessment
Homework:
Homework is typically assigned every night and will include reading and practice problems.
Consistent with our school policies, homework will count as 20% of each quarters final grade.
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Quizzes:
Quick in-class quizzes will be given on an as needed basis
Tests:
Major/rigorous exams will be given for each unit/chapter. Exams/quizzes/projects will count as
80% of each quarters final grade.
Test Corrections (see attached policy):
Students are strongly encouraged to take advantage of my test correction policy for each exam.
These are an integral component of the learning process for this course and will help students learn
the required material/concepts.
AP Statistics Projects (see attached sample project):
This course lends itself to some interesting and fun, real world projects. Students will collect and
interpret data using the tools/skills learned in this course. A major project is typically assigned for
each quarter and this grade will be equivalent to a test grade. Projects must be typed, professional
and include graphs/tables/charts as applicable. Students will use Fathom Software to produce these
graphs as applicable. Projects typically count as 1-2 test grades in that quarter.
AP Statistics Post Exam:
Students work on/complete their final, year end inclusive project which ties in the different major
themes of the course after the AP Exam. Emphasis on this final project includes connecting the
four major themes of the course as well as using Fathom Software. Depending upon time
constraints we may continue with ANOVA and/or multiple regression.
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Test Corrections
High School
Test corrections allow you to earn back up to one half of the points you missed on every test. In order
to earn the maximum amount of credit, you must do the following things for each question.
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Identify in writing what your mistakes are.
This may include a lack of understanding of the question, operational errors, faulty solving
method, or something else. “I was clueless” is not an acceptable answer. Your errors need to
be explained.
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Indicate in writing how to solve the problem.
Explain in a few words the process you will use to solve the problem.
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Work out the problem showing step-by-step detail, arriving at the correct solution.
Your solution must be correct in every way. (Fractions reduced, like term combined, radicals
rationalized, etc.)
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No credit is given for an incorrect solution.
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Label each question and indicate the number of points lost for each question (i.e.: I lost 3 points
on question #4)
Your corrections must be typed, provided that ALL questions missed are attempted; however, in no
instance will a student be given points that would bring their test grade over a score of 99.
Research aids you may use to determine the correct solution include your text, other students, teachers,
parents, the Internet, or any other source you choose. You may not receive help from a teacher on the
day the corrections are due.
Work will be neat, clearly labeled, and stapled to the front of your test.
TEST CORRECTIONS ARE DUE 1 WEEK FROM THE DAY YOUR TESTS ARE PASSED
BACKED TO YOU. THERE ARE NO EXCEPTIONS TO THE DUE DATE. Papers will be
handed in at the beginning of class on the due date. If you are absent from school on the due date, the
paper must be handed in before first period on your next school day. Do not wait until the next class,
as your work will not be accepted.
Summary
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Neat, clear work stapled to the front of the quiz or test.
Explanation of what the errors were.
A detailed solution leading to the correct answer.
Work completed on time.
You can only ask the teacher questions on no more than 2 problems, the goal of this exercise is
for you to learn how to solve the problem and do the appropriate work/research.
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Since test corrections are a privilege, not a right, it is important that you “earn” this privilege. When I
pass out an exam I will randomly pick 4-6 homework problems from the chapter that I assigned for
homework. As you begin the exam, I will check these homework problems. If you have not done
these homework problems and/or do not have them in class with you, you will be “ineligible” to do test
corrections for that chapter. I assume that you do your homework every night and keep them in your
notebook, so this policy is inherently fair to every student.
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AP Statistics Project
In this portfolio /project you will collect, interpret, analyze and then present data that is of specific
interest to you. You must collect at least 100 data points and present your findings in at least two
different types of graphs/charts/tables (of your choice). Your data must be real world, accurate, and
easy for someone to verify. You must have an original hypothesis and use your presentations to help
“prove or disprove” your original thoughts. As a minimum you must:
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Graphs/charts/table should be computer/calculator generated or extremely neatly produced.
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State how you collected your data
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A discussion of how comfortable you are with your data (Is it good, reliable data?)
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At least 3 additional things you could do to make your data/presentation better.
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A detailed discussion (in typed paper format) of what you are trying to prove/show and how
you could use your graphs to persuade someone else of your point of view.
Due Date: ___________________________
Late portfolios are penalized 15 points off per day late!
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Statistics Project (source unknown)
This project counts as one test grade and requires that you select a topic to study that will yield
numerical data. That is, you will need to find 100 or more distinct data points that you will use in your
research. Your proposal should start with a null and alternate hypothesis; something along the lines of
“I think that the average number of….” Or “I am interested in trying to determine the average number
of…”
Minimum requirements for this project are listed below.
1. Explain what it is that you wish to investigate. State your null hypothesis and your alternate
hypothesis. Use H0 and Ha format. Justify the choice of <, > or ≠ for Ha.
2. Explain and justify your data collection method, making sure you’ve minimized bias as much
as possible.
3. Collect your data and present it appropriately (graphically), using at least 2 different graph
types. Include the data, mean, median, range, sample standard deviation, and sample size (n).
4. Choose two different confidence levels.
5. Compute a confidence interval and explain what this interval really means in the context of
your project.
6. Find the sample size you would need to take for the margin of error to be half of what you
found in your confidence interval.
7. Test your hypothesis and explain the results. Include z – scores and normal distribution graph.
8. Find the p – value for your test. What does this tell you? Explain your reasoning.
9. Write up your findings in a non-technical manner. That is, your explanation should be written
as if it would be read by a person who had never taken a statistics course. For example, a
report to your friends or a submission to the school newspapers.
Project Assigned: ________________________________
Project Due Date: ________________________________
Grading will be based on the attached rubric.
Late projects will be deducted 15 points per day late.
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Portfolio Assessment Rubric
Presentation Organization
0 Portfolio is disorganized; entries are no identified; entries are not neat
1 Portfolio is somewhat organized
2 Portfolio entries are well identified, organized OR neat
3 Portfolio entries are well identified AND neat
Accuracy
0 Outcome is not addressed
1 Outcome is partially addressed with many misstatements and errors
2 Outcome is partially addressed or has many misstatements and errors
3 Portfolio entries contain some misstatements, or is lacking in depth
4 Portfolio entries contain very few misstatements and explorations go into detailed analysis
Quality
0 Outcome is poorly addressed
1 Portfolio entries show minimal understanding of the concepts which are the focus. Few
applications are present
2 Portfolio entries show some understanding of the concepts. Entries are ORIGINAL student
work. Some applications are present
3 Portfolio entries are ORIGINAL students work and show thorough understanding of the
concepts with applications present
4 Portfolio entries are ORIGINAL student work and show thorough understanding of the
concepts with applications present. Evidence of extensions of the concepts have been
submitted.
Creativity
0 Portfolio has no personal creativity
1 Portfolio has little to no creativity
2 Portfolio has minimal creativity
3 Portfolio shows some creativity in topic presentation
4 Student shows creativity in both examining the topic and its presentation
Grammar/Writing Style
0 Writing contains so many grammatical errors it takes away from the paper/portfolio
1 Writing contains many grammatical errors
2 Writing contains few grammatical errors
Technical Skills
1 Portfolio addresses only some of the objectives
2 Portfolio addresses most of the objectives
3 Portfolio addresses all of the objectives/outcomes of the assignment
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