AP Statistics Syllabus
Mr. Vogler
Room 212
Phone: 928-773-8200 ext. 6418
E-mail: [email protected]
AP® Statistics involves the study of four main areas: exploratory analysis; planning a
study; probability; and statistical inference. According to the College Board, upon
entering this course students are expected to have mathematical maturity and quantitative
reasoning ability. Mathematical maturity could be defined as a complete working
knowledge of the graphical and algebraic concepts through Math Analysis, including
linear, quadratic, exponential, and logarithmic functions.
In contrast to many math classes, this course will require reading of the text.
This AP Statistics course is taught as an activity-based course in which students actively
construct their own understanding of the concepts and techniques of statistics.
Textbook: Bock, David E., Paul F. Velleman, and Richard D. De Veaux. 2010. Stats:
Modeling the World: 3rd Edition. Addison-Wesley.
Calculator: A TI-83 or TI-84 is required for successful completion of this course.
Technology is incorporated throughout the text, including the use of graphing calculators.
Each chapter in the text has a section on calculator use to give the student instruction and
practice with the statistical capabilities of the calculator. The calculator is used
throughout the course to:
- Display graphs, histograms, and various types of plots
- Generate simulation and probability data
- Analyze univariate and bi-variate data through t-tests, measures of central
tendency, regression, and chi-square analysis
Where necessary, students will use Excel or be given access to appropriate data reports
for interpretation.
Internet access is required for successful completion of this course. Assignments will be
posted on Edmodo. An Edmodo account is required.
Grades
- Practice (20%)
o Problem sets will be assigned throughout the course.
o Group quizzes: students will work on a research-based problem that
applies statistical concepts learned in class to real data.
- Performance (20%)
o Article Review: Each quarter, individual students will locate a news story
or study that applies statistics. Students will:
 Briefly summarize the content of the article and purpose of the
study.

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Describe the methodology applied in the study. This includes
sample sizes and statistical tests used.
 Critique the methods and offer at least one question for future
research.
o Unit Projects: For each unit, groups of students will collect and analyze
data using one of the methods discussed in the unit. All are group graded.
Reports will include:
 Answering the questions of who, what, when, where, why, and
how about the data.
 The question to be answered.
 A description of the method of analysis or display used, including
a list of the assumptions applicable to the model.
 An appropriate tabular, graphical, or data display from a statistics
program such as SPSS or a spreadsheet program such as Excel.
 A brief discussion of the results, including statistical inferences
and observations about the data.
o Individual Project: Each semester, students will complete one project that
applies statistical concepts from class. The first semester project is
outlined here. During the second semester, the project requires students to
design surveys or experiments, gather data, anticipate sources of bias or
confounding variables, analyze the data numerically and graphically, and
apply inferential statistics to draw conclusions for a population. Students
write formal reports on their projects using statistical language and present
their findings to the class through a poster and oral presentation. The first
semester project can be found at the end of this syllabus.
Measurement (60%)
o Unit Tests. Each unit test is cumulative. Measurement grades are based
on the average of all unit test scores or the most recent test score,
whichever is greater.
Attendance and tardiness: Regular, on-time class attendance is expected. Failure to get
an absence cleared may result in the loss of credit for the class. If you are placed on
attendance probation, expect to lose credit.
Late work: In general, late work is not accepted unless you were excused the day it was
due (and in accordance with district and school policy). Ignorance is not a legitimate
excuse for turning in assignments late. However, I will generally permit late work under
the following conditions for full credit:
- It isn’t a habit (after the second time, it will not be accepted).
- You talk to me about it.
- You made it up outside of class.
I will not expect you to make up quizzes or in-class work, but tests and homework are
always required.
Academic honesty: Cheating and plagiarism are forms of academic dishonesty. Cheating
means that you copied another student and there is evidence that you did so. Plagiarism
means that you copied, paraphrased, or summarized a source or classmate without
referencing them (this is a much lower threshold than copying: if it can be shown that you
have a similar work as someone else, then it is defined as plagiarism). At the least,
expect to fail the assignment (which may result in your failing the class). If this becomes
a habit, expect to be asked to complete assignments in the presence of a teacher and face
administrative disciplinary action.
Course Outline
(organized by chapters in primary textbook):
Graphical displays include, but are not limited to using boxplots, dotplots, stemplots,
back-to-back stemplots, histograms, frequency plots, parallel boxplots, and bar charts.
Unit 1: Exploring and Understanding Data Chapters 1-6
Graphing and Numerical Distributions
The student will:
- Identify the individuals and variables in a set of data.
- Identify each variable as categorical or quantitative.
- Make and interpret bar graphs, pie charts, dot plots, stem plots, and histograms of
distributions of a categorical variable.
- Look for overall patterns and skewness in a distribution given in any of the above
forms.
- Give appropriate numerical measures of center tendency and dispersion.
- Recognize outliers.
- Compare distributions using graphical methods.
- Graphing calculator is used to obtain summary statistics, to include the 5-number
summary.
- Graphing calculator and spreadsheet software are used to create pie charts and
histograms.
The Normal Distribution
Density Curves and the Normal Distribution; Standard Normal Calculations
- Know that areas under a density curve represent proportions.
- Approximate median and mean on a density curve.
- Recognize the shape and significant characteristics of a normal distribution,
including the 68-95-99.7 rule.
- Find and interpret the standardized value (z-score) of an observation.
- Find proportions above or below a stated measurement given relevant measures of
central tendency and dispersion or between two measures.
- Determine whether a distribution approaches normality.
Unit 2: Exploring Relationships Between Variables Chapters 7-10
Scatter Plots, Correlation; Least-Squares Regression
The student will:
- Identify variables as quantitative or categorical.
- Identify explanatory and response variables.
- Make and analyze scatter plots to assess a relationship between two variables.
- Find and interpret the correlation r between two quantitative variables.
-
Find and analyze regression lines.
Use regression lines to predict values and assess the validity of these predictions.
Calculate residuals and use their plots to recognize unusual patterns.
Graphing calculator and spreadsheet software is used to calculate r, r2, and
regression line equations.
Transformation of Relationships; Cautions About Correlation and Regression; Relations
in Categorical Data
- Recognize exponential growth and decay.
- Use logarithmic transformations to model a linear pattern, linear regression to find
a prediction equation for the linear data, and transform back to a nonlinear model
of the original data.
- Recognize limitations in both r and least-squares regression lines due to extreme
values.
- Recognize lurking variables.
- Explain the difference between correlation and causality.
- Find marginal distributions from a two-way table.
- Describe the relationship between two categorical variables using percents.
- Recognize and explain Simpson’s paradox.
Unit 3: Gathering Data Chapters 11-13
Designing Samples; Designing Experiments; Simulating Experiments
The student will:
- Identify populations in sampling situations.
- Identify different methods of sampling, strengths and weaknesses of each, and
possible bias that might result from sampling issues.
- Recognize the difference between an observational study and an experiment.
- Design randomized experiments.
- Recognize confounding of variables and the placebo effect, explaining when
double-blind and block design would be appropriate.
- Explain how to design an experiment to support cause-and-effect relationships.
Unit 4: Randomness and Probability Chapters 14-17
Idea of Probability; Probability Models; General Probability Rules
The student will:
- Describe and generate sample spaces for random events.
- Apply the basic rules of probability.
- Use multiplication and addition rules of probability appropriately.
- Identify disjointed, complementary, and independent events.
- Use tree diagrams, Venn diagrams, and counting techniques in solving probability
problems.
Discrete and Continuous Random Variables, Means, and Variances of Random Variables
- Recognize and define discrete and continuous variables.
- Find probabilities related to normal random variables.
- Calculate mean and variance of discrete random variable.
- Use simulation methods using the graphing calculator and the law of large numbers
to approximate the mean of a distribution.
- Use rules for means and rules for variances to solve problems involving sums,
differences, and linear combinations of random variables.
- Verify four conditions of a binomial distribution: two outcomes, fixed number of
trials, independent trials, and the same probability of success for each trial.
- Calculate cumulative distribution functions, cumulative distribution tables and
histograms, means and standard deviations of binomial random variables.
- Use a normal approximation to the binomial distribution to compute probabilities.
Binomial and Geometric Distributions
Binomial Distributions; Geometric Distributions
- Verify four conditions of a geometric distribution: two outcomes, the same
probability of success for each trial, independent trials, and the count of interest is
the number of trials required to get the first success.
- Calculate cumulative distribution functions, cumulative distribution tables and
histograms, means and standard deviations of geometric random variables.
- Use a graphing calculator and/or Excel spreadsheet software to conduct probability
experiments and generate random numbers, create histograms, and calculate
standard devitations.
Unit 5: From the Data at Hand to the World at Large Chapters 18-22
Sampling Distributions; Sample Proportions; Sample Means
The student will:
- Identify parameters and statistics in a sample.
- Interpret a sampling distribution, including bias and variability and how to
influence each.
- Recognize when a problem involves a sample proportion.
- Analyze problems involving sample proportions, including using the normal
approximation to calculate probabilities.
- Recognize when a problem involves sample means.
- Analyze problems involving sample means and understand how to use the central
limit theorem to approximate a normal distribution.
- Graphing calculator is used to calculate sample means.
Unit 6: Learning about the World Chapters 23-25
Estimating with Confidence, Tests of Significance, Interpreting Statistical Significance;
Inference As Decision
The student will:
- Describe confidence intervals and use them to determine sample size.
- State null and alternative hypotheses in a testing situation involving a population
mean.
- Calculate the one-sample z statistics and P-value for both one-sided and two-sided
tests about the mean μ using the graphing calculator.
- Assess statistical significance by comparing values.
- Analyze the results of significance tests.
- Explain Type I error, Type II error, and power in significance testing.
Inference for the Mean of a Population; Comparing Two Means
- Recognize when inference about a mean or comparison of two means is necessary.
- Perform and analyze a one-sample t test to hypothesize a population mean and
discuss the possible problems inherent in the test.
- Perform and analyze a two-sample t test to compare the difference between two
means and discuss the possible problems inherent in the test.
- Use the graphing calculator to obtain confidence intervals and test hypotheses.
Inference for Proportions
Inference for a Population Proportion; Comparing Two Proportions
- Recognize whether one-sample, matched pairs, or two-sample procedures are
needed.
- Use the z procedure to test significance of a hypothesis about a population
proportion.
- Use the two-sample z procedure to test the hypothesis regarding equality of
proportions in two distinct populations.
- Use the graphing calculator to obtain confidence intervals and test hypotheses.
- Use Excel spreadsheet software to obtain z and t-test statistics and reports for
analysis.
Unit 7: Inference When Variables are Related Chapters 26 and 27
Test for Goodness of Fit; Inference for Two-Way Tables
The student will:
- Choose the appropriate chi-square procedure for a given situation.
- Perform chi-square tests and calculate the various relevant components.
- Interpret chi-square test results obtained from computer output.
Inference About the Model, Predictions, and Conditions
The student will:
- Recognize when linear regression inference is appropriate for a set of data.
- Interpret the meaning of a regression for a given set of data.
- Interpret the results of computer output for regression.
First semester project:
Students will design and conduct an experiment to investigate the effects of response bias
in surveys. They may choose the topic for their surveys, but they must design their
experiment so that it can answer at least one of the following questions:
• Can the wording of a question create response bias?
• Do the characteristics of the interviewer create response bias?
• Does anonymity change the responses to sensitive questions?
• Does manipulating the answer choices change the response?
The project will be done in pairs. Students will turn in one project per pair.
A written report must be typed (single-spaced, 12-point font) and included graphs should
be done on the computer using JMP-Intro or Excel.
Proposal: The proposal should
• Describe the topic and state which type of bias is being investigated.
• Describe how to obtain subjects (minimum sample size is 50).
• Describe what questions will be and how they will be asked, including how to
incorporate direct control, blocking, and randomization.
Written Report: The written report should include a title in the form of a question and
the following sections (clearly labeled):
• Introduction: What form of response bias was investigated? Why was the topic
chosen for the survey?
• Methodology: Describe how the experiment was conducted and justify why the
design was effective. Note: This section should be very similar to the proposal.
• Results: Present the data in both tables and graphs in such a way that conclusions
can be easily made. Make sure to label the graphs/tables clearly and consistently.
• Conclusions: What conclusions can be drawn from the experiment? Be specific.
Were any problems encountered during the project? What could be done different
if the experiment were to be repeated? What was learned from this project?
• The original proposal.
Poster: The poster should completely summarize the project, yet be simple enough to be
understood by any reader. Students should include some pictures of the data collection in
progress.
Oral Presentation: Both members will participate equally. The poster should be used as
a visual aid. Students should be prepared for questions.