AP Statistics
Syllabus
Overview of AP Statistics
The academic school year is divided into two 18 week semesters with four
grade progress reporting periods each. Students generally take six, 53 minutes,
periods per day.
Course Design
The knowledge acquired in AP Statistics is for the purpose of application.
Nonetheless, before such knowledge may be applied, understanding must
occur. Understanding is a measure of the number of cognitive connections that
are made between the concepts of a topic or subject. Moreover, a higher level
of understanding implies a well connected network of ideas. Therefore, AP
Statistics is designed to draw connections between all aspects of the statistical
process, including design, analysis, and conclusions. [C-3]
Additionally, this course will not only provide instruction with an emphasis on
exploring data, sampling experimentation, anticipating patterns, and statistical
inference, but will also teach students to communicate their methods, results,
and interpretations by using both the vocabulary of statistics and technology
such as a graphing calculator and computer output. [C-2, C-4]
Remarks
Students will receive a partially word processed set of class notes that includes
vocabulary, guiding questions, guided instruction, group work activities, and a
homework assignment. Each chapter will be introduced with a (textbook)
corresponding group work activity.
Furthermore, many of the chapters will provide for a significant use of the
graphing calculator as well as some computer output displays. [C-5] Lastly,
students will be expected to combine and demonstrate their “statistical literacy,
reasoning, and thinking” through semester ending projects. That is, use a set of
statistical language and tools to identify a question, collect data, interpret and
communicate results.
Additional assessments will be in the form of quizzes and chapter exams.
Primary Textbook
Yates, Daniel S., David S. Moore, and Daren S. Starnes. The Practice of
Statistics. New York: W.H. Freeman, 2003.
Technology
 All students will have access to a Texas Instrument TI-83 Graphing
Calculator for use in and out of the classroom.
 A variety of applets on the Internet will be utilized.
C-2
The course provides
instruction and emphasis in
the following broad
conceptual themes:
Exploring Data; Sampling
and Experimentation;
Anticipating Patterns;
Statistical Inference
C-3
The course draws
connections between all
aspects of the statistical
process, including design,
analysis, and conclusions
C-4
The course teaches
students how to
communicate methods,
results, and
interpretations using
vocabulary of statistics.
C-5
The course teaches students
how to use graphing
calculators and demonstrates
the use of computers and/or
computer output to enhance
the development of
statistical understanding
through exploring and
analyzing data, assessing
models, and performing
simulations.
Course Outline and Content
The organization of this content complements the primary textbook.
Course Content
Introduction to Exploring Data
C-2a
The course provides
instruction and emphasis
in the following broad
conceptual theme:
Exploring Data
Displaying Distributions with Graphs
Describing Distributions with Numbers
Introduction to The Normal
Distributions
Description
Activity 1 (Page 5) How Fast Is Your Heart Beating?
Introduction
Individuals and Variables
Categorical and Quantitative Variables
Distribution
Displaying Categorical Variables: Bar Graphs and Pie Graphs
Displaying Quantitative Variables: Dotplots and Stemplots
Overall Pattern of Distribution
Outliers
Interpreting Computer Output
Displaying Quantitative Variables: Histograms
Making Calculator Histograms (TI-83/89)
More about Shape
Symmetric and Skewed Distributions
Relative Frequency, Cumulative Frequency, Percentiles, and Ogives
Percentile
Time Plots
Summary
Measuring Center
The Mean
The Median
Comparing the Mean and the Median
Measuring Spread: The Quartiles
The first and third quartiles
The interquartile range
The 1.5 x IQR Criterion
The Five-Number Summary and (Modified) Boxplots
Calculator Boxplots and Numerical Summaries
Measuring Spread: The Standard Deviation and Properties
Choosing Measures of Center and Spread
Changing the Unit of Measurement
Linear Transformation and Effects
Comparing Distributions
Summary
Activity 2A (Page 76) – A Fine Grained Distribution
Activity 2B (Pages 76 & 77)– Roll a Normal Distribution
C-2a
The course provides
instruction and emphasis
in the following broad
conceptual theme:
Exploring Data
Density Curves and the Normal
Distributions
Standard Normal Calculations
Density Curves
The median and mean of a density curve
Normal Distributions
The 68-95-99.7 Rule
Summary
The Standard Normal Distribution
Standardizing and Z-Scores
Normal Distribution Calculations
Finding Normal Proportions
Finding a Value Given a Proportion
Assessing Normality
Introduction to Examining
Relationships
C-2a
The course provides
instruction and emphasis
in the following broad
conceptual theme:
Exploring Data
Scatterplots
Correlation
Least-Squares Regression
Introduction to More on TwoVariable Data
Normal Probability Plots on the TI-83/89
Summary
Finding Areas with ShadeNorm (TI-83/89)
Finding Areas with normalcdf (TI-83/89)
Finding Z-Values with invNorm (TI-83/89)
Activity 3 (Page 120) – SAT/ACT Scores
Introduction
Response Variable, Explanatory Variable
Interpreting Scatterplots
Examining a scatterplot
Positive Association, Negative Association
Adding Categorical Variables to Scatterplots
Making a Calculator Scatterplot
Summary
Correlation r
Using the Definition to Calculate Correlation (TI-83/89)
Facts About Correlation
Summary
Regression Line
Least Squares Regression Line
Equation of the Least Squares Regression Line
Least Squares Lines on the Calculator
Least Squares Regression Computer Output
The Role of r² in Regression – Coefficient of Determination
Facts About Least-Squares Regression
Residuals and Plots
Influential Observations
Outliers and Influential Observations in Regression
Residual Plots by Calculator
Summary
Activity 4 (Page 194) – Modeling the Spread of Cancer in the Body
C-2a
The course provides
instruction and emphasis
in the following broad
conceptual theme:
Exploring Data
Transforming Relationships
Cautions about Correlation and
Regression
First Steps in Transforming
Monotonic Functions
The Ladder of Power Transformations
Monotonicity of Power Functions
Concavity of Power Functions
Exponential Growth
Linear Versus Exponential Growth
The Logarithm Transformation
Algebraic Properties of Logarithms
Predictions in the Exponential Growth Model
Modeling Exponential Growth with the TI-83/89
Power Law Models
Predictions in Power Law Models
Power Law Modeling with Technology
Summary
Extrapolation
Lurking Variables
Relations in Categorical Data
Introduction to Producing Data
C-2b
The course provides
instruction and emphasis
in the following broad
conceptual theme:
Sampling and
Experimentation
Designing Samples
Designing Experiments
Simulating Experiments
Introduction to Probability: The
Study of Randomness
Using Averaged Data
The Question of Causation
Causation
Common Response
Confounding
Establishing Causation
Summary
Marginal Distributions
Describing Relationships
Conditional Distributions
Simpson’s Paradox
Summary
Activity 5 (Page 268) – A Class Survey
Introduction
Observation Versus Experiment
Designing Samples
Population and Sample
Sampling Versus a Census
Voluntary Response Sample
Convenience Sampling
Bias
Simple Random Samples
Simple Random Sample
Random Digits
Choosing an SRS
Other Sampling Designs
Probability Sample
Stratified Sample
Cautions About Sample Surveys
Undercoverage and Nonresponse
Inference About the Population
Summary
Designing Experiments
Experimental Units, Subjects, Treatment
Comparative Experiments
Placebo Effect
Control Group
Randomization
Randomized Comparative Experiments
Principles of Experimental Design
Statistical Significance
Cautions About Experimentation
Double Blind Experiment
Lack of Realism
Matched Pairs Designs
Block Designs
Summary
Simulating Experiments
Probability Model
Simulation
Simulations with the Calculator or Computer
Summary
Activity 6 (Page 328) – The Spinning Wheel
C-2c
The course provides
instruction and emphasis
in the following broad
conceptual theme:
Anticipating Patterns
The Idea of Probability
Probability Models
General Probability Rules
Introduction to Random Variables
C-2c
The course provides
instruction and emphasis
in the following broad
conceptual theme:
Anticipating Patterns
Discrete and Continuous Random
Variables
Means and Variance of Random
Variables
Introduction to The Binomial and
Geometric Distributions
The Idea of Probability
Randomness and Probability
Thinking About Randomness
The Uses of Probability
Probability Models
Multiplication Principle
Probability Rules
Assigning Probabilities: Finite Number of Outcomes
Probabilities in a Finite Sample Space
Assigning Probabilities: Equally Likely Outcomes
Independence and the Multiplication Rule
Applying the Probability Rules
General Probability Rules
Rules of Probability
General Addition Rules
Union
Addition Rule for Disjoint Events
General Addition Rule for Unions of Two Events
Conditional Probability
General Multiplication Rule for Any Two Events
Definition of Conditional Probability
Extended Multiplication Rules
Intersection
Bayes’s Rule
Independence Again
Independent Events
Decision Analysis
Summary
Activity 7 (Pages 390 & 391) – The Game of Craps
Introduction
Random Variable
Discrete Random Variables
Continuous Random Variables
Normal Distributions as Probability Distributions
Summary
The Mean of a Random Variable
Mean of a Discrete Random Variable
The Variance of a Random Variable
Variance of a Discrete Random Variable
Statistical Estimation and the Law of Large Numbers
Thinking About the Law of Large Numbers
Rules for Means
Rules for Variances
Combining Normal Random Variables
Summary
Activity 8 (Page 438) – A Gaggle of Girls
C-2c
The course provides
instruction and emphasis
in the following broad
conceptual theme:
Anticipating Patterns
The Binomial Distributions
The Geometric Distributions
Introduction to Sampling
Distributions
The Binomial Distributions
The Binomial Setting
Binomial Distribution
Finding Binomial Probabilities
Probability Distribution Function (pdf)
Cumulative Distribution Function (cdf)
Binomial Formulas
Binomial Coefficient
Binomial Probability
Binomial Mean and Standard Deviation
Mean and Standard Deviation of a Binomial Random Variable
The Normal Approximation to Binomial Distributions
Binomial Distribution with the Calculator (TI-83/89)
Simulating Binomial Experiments
Summary
The Geometric Distributions
The Geometric Setting
Rule for Calculating Geometric Probabilities
The Expected Value and Other Properties of the Geometric Random
Variable
The Mean and Standard Deviation of a Geometric Random Variable
Exploring Geometric Distributions (TI-83/89)
Simulating Geometric Experiments
Summary
Activity 9A (Pages 486 & 487) – Young Women’s Heights
C-2b
The course provides
instruction and emphasis
in the following broad
conceptual theme:
Sampling and
Experimentation
Sampling Distributions
Sample Proportions
Sample Means
Sampling Distributions
Parameter, Statistic
Sampling Distribution
Describing Sampling Distributions
The Bias of a Statistic
Unbiased Statistic
The Variability of a Statistic
Bias and Variability
Summary
The Sampling Distribution of p̂
Sampling Distribution of a Sample Proportion
Rule of Thumb 1
Using the Normal Approximation for p̂
Rule of Thumb 2
Summary
The Mean and the Standard Deviation of x
Mean and Standard Deviation of a Sample Mean
Sampling Distribution of a Sample Mean From a Normal
Population
Activity 9B (Pages 520 & 521)
The Central Limit Theorem
Introduction to Inference
C-2d
The course provides
instruction and emphasis
in the following broad
conceptual theme:
Statistical Inference
Estimating with Confidence
Tests of Significance
Making Sense of Statistical
Significance
Inference as Decision
Introduction to Inference for
Distribution
Summary
Activity 10 (Pages 534 & 535) – A Little Tacky!
Introduction
Statistical Inference
Statistical Confidence
Confidence Interval
Confidence Interval for a Population Mean
Conditions for Constructing a Confidence Interval For μ
Critical Values
Confidence Interval for a Population Mean
How Confidence Intervals Behave
Choosing the Sample Size
Sample Size for Desired Margin of Error
Some Cautions
Summary
Calculator Confidence Intervals (TI-83/89)
The Reasoning of Tests of Significance
Outline of a Test
More Detail: Stating Hypothesis
Null Hypothesis H 0
More Detail: P-values and Statistical Significance
p-Value
Statistical Significance
Test for a Population Mean
Significance Tests
Z Test for a Population Mean
Tests With Fixed Significance Level
Fixed Significance Level z Tests for a Population Mean
Tests From Confidence Intervals
Confidence Intervals and Two-Sided Tests
Summary
Performing Significance Tests (TI-83/89)
Choosing a Level of Significance
Statistical Significance and Practical Significance
Statistical Inference is not Valid for all Sets of Data
Beware of Multiple Analyses
Summary
Type I and Type II Errors
Error Probabilities
Significance and Type I Error
Power
Increasing the Power
Different Views of Statistical Tests
Summary
Activity 11 (Page 616) – Paper Airplane Experiment
C-2d
The course provides
instruction and emphasis
in the following broad
conceptual theme:
Statistical Inference
Inference for the Mean of a Population
Inference for the Mean of a Population
Conditions for Inference About a Mean
Standard Error
The t Distributions
Comparing Two Means
Introduction to Inference for
Proportions
The One-Sample t Statistic and the t Distributions
The t Confidence Intervals and Tests
The One-Sample t Procedures
Matched Pairs t Procedures
Robustness of t Procedures
Robust Procedures
Using the t Procedures
The Power of the t Test
Summary
t Procedures (TI-83/89)
Two-Sample Problems
Comparing Two Population Means
Conditions for Comparing Two Means
The Sampling Distribution of x1  x2
The Two-Sample t Procedures
Robustness Again
More Accurate Levels in the t Procedures
Approximate Distribution of the Two-Sample t Statistic
Two-Sample Inference (TI83/89)
The Pooled Two-Sample t Procedures
Summary
Activity 12 (Page 684) – Is One Side of a Coin Heavier?
C-2d
The course provides
instruction and emphasis
in the following broad
conceptual theme:
Statistical Inference
Inference for a Population Proportion
Comparing Two Proportions
Introduction to Inference for Tables:
Chi-Square Procedures
Conditions for Inference
Conditions for Inference About a Proportion
The z Procedures
Inference for a Population Proportion
Choosing the Sample Size
Sample Size for Desired Margin of Error
Summary
Inference for a Population Proportion (TI-83/89)
ˆ1  pˆ 2
The Sampling Distribution for p
Confidence Intervals for p1  p2
Confidence Intervals for Comparing Two Proportions
Significance Tests for p1  p2
Significance Test for Comparing Two Proportions
Summary
Comparing Proportions (TI-83/89)
Activity 13 (Pages 726 & 727) – “I Didn’t Get Enough Blues!”
C-2d
The course provides
instruction and emphasis
in the following broad
conceptual theme:
Statistical Inference
Test for Goodness of Fit
Chi-Square Test for Goodness Fit
Properties of the Chi-Square Distributions
The Chi-Square Distributions
Goodness of Fit Test
Goodness of Fit Tests (TI-83/89)
Graphing a Chi-Square Distribution (TI-83/89)
Conducting Inference by Simulation
Inference for Two-Way Tables
Follow-Up Analysis
Summary
The Problem of Multiple Comparisons
Expected Counts
The Chi-Square Test for Homogeneity of Populations
The Chi-Square Statistic
Chi-Square Test for Homogeneity of Populations
Cell Counts Required for the Chi-Square Test
Chi-Square Tests with Minitab
Chi-Square Tests (TI-83/89)
The Chi-Square Test of Association / Independence
Performing the
Introduction to Inference for
Regression
x
2
Test
Concluding Remarks
The Chi-Square Test and the z Test
Summary
Activity 14 (Page 780) – Can Arm Span Predict Height?
C-2d
The course provides
instruction and emphasis
in the following broad
conceptual theme:
Statistical Inference
Inference About the Model
Predictions and Conditions
Introduction to Analysis of Variance
Inference for Population Spread
One-Way Analysis of Variance
The Regression Model
Conditions for Regression Inference
Inference
Standard Error About the Least-Squares Line
Confidence Intervals for the Regression Slope
Confidence Interval for Regression Slope
Testing the Hypothesis of no Linear Relationship
Significance Tests for Regression Slope
Summary
Predictions and Conditions
Confidence and Prediction Intervals for Regression Response
Checking the Regression Conditions
Summary
Linear Regression t Test (TI-83/89)
Activity 15 (Page 816) – The Return of Paper Airplanes
Avoid Inference About Standard Deviations
The F Test for Comparing Two Standard Deviations
The F Statistic and F Distributions
Carrying Out the F Test
F Test (TI-83/89)
Summary
The Problem of Multiple Comparisons
The Analysis of Variance F Test
The Idea of Analysis of Variance
The Analysis of Variance Idea
The ANOVA F Statistic
Degrees of Freedom for the F Test
Conditions for Performing ANOVA
ANOVA Conditions
Checking Standard Deviations in ANOVA
One-Way ANOVA (TI-83/89)
Some Details of ANOVA
The ANOVA F Test
Summary