AP Statistics Syllabus
Primary Textbook
Daniel Yates, David Moore, Daren Starnes. The Practice of Statistics, TI - 83/89 Graphing
Calculator Enhanced, 2nd Edition. New York. W.H.Freeman and Company, 2003.
Technology
All students are required to have a TI-83 Plus, TI-84, or TI-89 graphing calculator for use in
class, at home, and on the AP Exam. Most concepts are initially taught without the use of the
graphing calculator in order to ensure a conceptual understanding of the fundamental ideas.
After a concept is thoroughly explored, students are then led through the process of using the
statistical capabilities of the calculators. This is initially demonstrated by projecting the
calculator skin on the smartboard as the class works through a problem. The textbook also
provides step-by-step instructions for the statistical functions of these calculators.
In addition, students are exposed to statistical computer software output from various statistical
packages, such as Minitab, DataDesk, and Fathom. This is done to familiarize the students with
the various formats so that they can interpret the output. The interactive functions of Fathom are
utilized in conjunction with the smartboard during class to demonstrate the effects of various
parameter changes. Students are challenged to predict consequences of parameter changes, make
the changes, and observe the actual consequences.
Course Outline
I. Planning a Study
After defining statistics, students spend the first two weeks learning how to sample and design a
study. The purpose is to make the students understand that the validity of statistics rests squarely
on the shoulders of good information. If the sample is not representative of the population, then
all conclusions are suspect. Sampling methods and experimental design are thoroughly covered.
This section is used as an introduction before continuing on to communication and interpretation
of information, so that the students understand its importance.
Chapter 5: Producing Data (3 weeks)
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Census vs. sample
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bias in sampling
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simple random sample
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stratified random sample
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cluster sample
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systematic sample
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observational study vs. experiment
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designing experiments
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control groups
treatments
blocking
activity- Random Rectangles - In this activity, students will utilize all four
sampling methods on one set of data, and then compare the results using dotplots
of the entire classes’ data. They will be required to describe the differences in the
resultant distributions. This hands-on activity reinforces the distinction between
the sampling methods and also introduces the students to the communications
methods which are required throughout the course.
II. Exploring Data
Students are introduced to the various methods of displaying and describing both univariate and
bivariate data in order to discern patterns, as well as the distinction between causation and
association.
Chapter 1: Exploring Data (1 week)
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categorical vs. quantitative data
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displaying categorical data - pie charts, bar charts
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displaying quantitative data - dotplots, histograms, stemplots, boxplots, ogives
(Students will create graphs manually and also with their calculators)
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describing center - mean, median
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describing spread - range IQR, standard deviation, outliers, variance
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effects of linear transformations
Chapter 2: The Normal Distribution (3 weeks)
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density curves
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uniform distributions
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normal distribution
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empirical rule
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standard normal distribution
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z-score, using z-table
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normal probability plot on calculator
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normalcdf on calculator
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invnorm on calculator
Chapter 3: Examining Relationships (3 weeks)
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introduction to bivariate data - explanatory and response variables
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scatterplots
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correlation coefficient
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coefficient of determination
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least squares regression line
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residual plots
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influential points vs. outliers
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activity - matching scatterplots and correlation coefficients (Rice University
website)
Chapter 4: More on Bivariate Data (2 weeks)
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transformations on bivariate data
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power models and exponential models
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marginal distributions
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Simpson’s paradox
III. Anticipating Patterns
Chapter 6: Probability: The Study of Randomness (4 weeks)
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definitions of probability, outcomes, and events
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law of large numbers
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activity -Coin tossing 50 times - graphing the outcome illustrates the law of large
numbers. Students then use simulation on their calculators and compare results.
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simulation on Fathom to demonstrate law of large numbers
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simulation using calculators
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probability models
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sample space
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conditional probability
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independent events
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mutually exclusive events
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general probability rules
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tree diagrams
Chapter 7: Random Variables (3 weeks)
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properties of discrete random variables
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properties of continuous random variables
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expected value (mean) of a discrete random variable
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normal distributions as probability distributions
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Benford’s law
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variance and standard deviation of a discrete random variable
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law of small numbers
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rules for means and variances of random variables
Chapter 8: Binomial and Geometric Distributions (2 weeks)
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conditions for a binomial distribution
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conditions for a geometric distribution
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finding binomial probabilities - initially manually, and then using calculator
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finding geometric probabilities - initially manually and then using calculator
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binomial mean and standard deviation
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geometric mean and standard deviation
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normal approximation to binomial distributions
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binomial and geometric simulations on the calculator
Chapter 9: Sampling Distributions (2 weeks)
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definition of sampling distribution
unbiased statistic
variability of a statistic
sampling distributions of sample proportions
using the normal approximation for the sampling distribution of sample
proportions - conditions
sampling distributions of sample means
means and standard deviations for sampling distributions of sample means
central limit theorem - activity - age of pennies
IV. Statistical Inference
Chapter 10: Introduction to Inference (3 weeks)
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confidence intervals - creating and understanding
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activity - Tossing coins. Students record the proportion of times a single coin
lands heads up. They then construct a 95% confidence interval around their
sample proportion. They then graph their confidence interval on one graph with
the remainder of the class. This gives a graphical representation of the concept of
what a confidence interval represents, when compared to the true population
proportion of .5.
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confidence interval for a population mean
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calculator use for construction of confidence intervals
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margin of error
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tests of significance
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null and alternative hypotheses - requirements for symbolic representation as well
as verbal explanation in the context of a particular problem.
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p-values and statistical significance
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one-sided and two-sided tests
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statistical significance vs. practical significance
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type I and type II errors
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calculating Type II error
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power
Chapter 11: Inference for Means (3 weeks)
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hypothesis test for a population mean (t-test)
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t-distributions for one sample
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checking conditions
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standard error
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t-distributions for difference of 2 samples; conditions
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matched-pairs hypothesis test
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activity - Helicopter manufacture. Students will design and test helicopters. They
will need to conduct an experiment for a 2-sample t-test, a one-sample t-test, and
a matched-pair t-test. The experimental design must be detailed enough so that
the instructor can replicate the experiment.
Chapter 12: Inference for Proportions (2 weeks)
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inference for a population proportion; conditions
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confidence interval for a population proportion
comparing two proportions; conditions
confidence interval for comparing two proportions
Chapter 13: Inference for Tables: Chi-Square Procedures (2 weeks)
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activity - M&M’s - students compare their sample’s distribution of colors to the
published distribution from the company. Students perform a Chi-square
goodness-of-fit test.
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chi-square distribution
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conditions for chi-square
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Goodness-of-Fit
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Homogeneity
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Association/independence
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use of calculator for all three tests
Chapter 14: Inference for Regression (2 weeks)
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hypothesis test for the slope of the LSRL
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standard error about the LSRL
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residuals and error
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confidence intervals for the regression slope
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prediction intervals for regression response
Review for the AP exam/ Final exam (1 week)
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students will take one complete AP exam (2002 exam)
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practice on other free-response problems
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activity - AP Murder Mystery - a comprehensive activity based on the game of
Clue, which serves as a review before the final exam.
Assessments
Students will take a test for each chapter in a format which mirrors the format of the AP exam.
There will be multiple choice questions followed by free-response questions. Some of the freeresponse questions will be actual questions from previous AP exams, others will not be. In either
case, the student must demonstrate the communication skills required to explain their answers.
The free-response will be graded using the same standards as are used on the actual AP exam.
This is extremely important so that the students recognize the need for communication of ideas
throughout the course. Additionally, there will be periodic assessments (quizzes) as needed.
This course also emphasizes the need for student interaction, and consequently there are weekly
projects/worksheets which the students work on in groups for a grade. A sampling of some of
the project activities has been included in this syllabus. Throughout the year, approximately
30% of the class time is spent working in groups.