Download AP Statistics * Course Syllabus

AP Statistics – Course Syllabus 2016-2017
Twinsburg High School
Mr. Porinchak
Course Expectations:
Reasoning based on probability and statistics gives modern society the ability to cope with
uncertainty. It has astonishing power to improve decision-making accuracy and test new ideas. It's a
key analytical tool used in education, the social sciences, and business administration and is often a
required college subject for majors in those areas. Statistics is frequently used for data analysis in the
sciences and forms the mathematical basis for quality control in manufacturing. AP Statistics is a
college level class for students who have been highly successful in Algebra II or Pre-Calculus. It
covers the topics needed for the American College Board AP Statistics exam. Students passing this
test may receive college credit. In today's world most statistical analysis is done on calculators or
computers. Students will learn how to perform statistical analysis on TI -83 calculators and Excel
spreadsheets with computers as well as more traditional techniques. All students taking AP
Statistics are REQUIRED to take the AP Statistics Exam at the end of the semester.
Who Should Take This Class:
Students with an interest in careers related to: business, the social sciences including psychology,
education, or math. The class is also helpful to careers in engineering and the sciences.
Materials:
-Book: The Practice of Statistics (5th edition), by Starnes, Tabor, Yates, and Moore, W. H. Freeman &
Co., 2014.
-Ti-83 calculator, all students MUST have one of their own.
-Three-ring binder with folder and loose leaf paper.
Additional Recommended Readings:
1.) Cartoon Guide to Statistics by Larry Gonick and Woollcott Smith
2.) AP Statistics by Robin Levine-Wissing, David Thiel
3.) How to Prepare for the AP Statistics by Martin Sternstein
Communicating Through the Vocabulary of Statistics:
This course is organized as an activity-based course where each day is setup with a short lecture and
afterwards students will be engaged in the exploration of statistical relationships and realities.
Because of this students will be asked to read on a daily basis to stay up to date on what we are
engaged in learning. Communication with your classmates and me is crucial to student achievement.
Students will learn many statistical techniques and will be taught and required to communicate these
in a variety of ways in the context of activities, projects, quizzes, tests, and discussions. As students
become more proficient “statisticians,” they will learn to communicate their processes, analysis,
results, findings, and conclusions using correct and effective statistics vocabulary. This idea of
communication through statistics is one of the main goals of this course. Statistics are all around us
and many people see them and recognize them, but truly being able to understand statistics, what
they mean, and what they infer is what is most important. This course will teach students how to
communicate these understandings in an organized and meaningful way.
Course Content Overview:
The topics for AP Statistics are divided into four major themes: exploratory analysis (20-30 percent of
the exam), planning and conducting a study (10-15 percent of the exam), probability (20-30 percent of
the exam), and statistical inference (30-40 percent of the exam).
1.) Exploratory analysis of data makes use of graphical and numerical techniques to study patterns
and departures from patterns. Students will be able to examine distributions of data and detect
important characteristics, such as shape, location, variability, and unusual values. Students will be
able to observe patterns in data and generate conjectures about relationships among variables. The
idea of one variable being associated with another and the difference between association and
causation is an important conceptual topic.
2.) Data must be collected according to a well developed plan if valid information is to be obtained. If
data are to be collected to provide an answer to a question of interest, a careful plan must be
developed. Both the type of analysis that is appropriate and the nature of conclusions that can be
drawn for that analysis depend in a critical way on how the data was collected. Collecting data in a
reasonable way, through either sampling or experimentation, is an essential step in the data analysis
process.
3.) Probability is the tool used for anticipating what the distribution of data should look like under a
given model. Random phenomena are not haphazard; they display an order that emerges only in the
long run and is described by a distribution. The mathematical description of variation is central in
statistics. The probability required for statistical inference is not primarily axiomatic or combinatorial,
but it is oriented toward using probability distributions to describe data.
4.) Statistical inference guides the selection of appropriate models. Models and data interact in
statistical work: models are used to draw conclusions from data, while the data are allowed to criticize
and evenly falsify the model through inferential and diagnostic methods. Inference from the data can
be thought as the process of selecting a reasonable model, including a statement of probability
language, of how confident one can be about the selection.
Unit Overviews:
The text breaks the chapters into units of 4 to 6 chapters. I further broke those units and chapters
down into topics. A unit in the text may discuss a particular topic over all the chapters in that unit. By
breaking the units and chapters down in topic I we can pinpoint exactly where and when we will learn
a particular topic and in what context.
Unit I - Exploring and Understanding Data
Topic 1: Graphical Displays – Dotplots; bar charts; histograms; cumulative frequency plots; stemplots;
center and spread; clusters and gaps; outliers; modes; shape.
Topic 2: Summarizing Distributions – Measuring the center; median and mean; measuring the
spread; range, interquartile range, variance, and standard deviation; measuring position: simple
ranking, percentile ranking, and z-score; empirical rule; histograms and measures of central
tendency; histograms, z-scores, and percentile rankings; cumulative frequency and skewness;
boxplots; effect of changing units.
Topic 3: Comparing Distributions – Dotplots; double bar charts; back-to-back stemplots; parallel
boxplots; cumulative frequency plots.
Unit II – Exploring Relationships Between Variables
Topic 4: Exploring Bivariate Data – Scatterplots; correlations and linearity; least squares regression
line; residual plots, outliers, and influential points; transformations to achieve linearity.
Unit III – Gathering Data
Topic 5: Overview of Methods of Data Collection – Census; sample survey; experiment; observational
study.
Topic 6: Planning and Conduction Studies – Simple random sampling; characteristics of a well
designed and well conducted survey; sampling error; the variation inherent in a survey; sources of
bias in surveys; other sampling methods.
Topic 7: Planning and Conducting Experiments – Experiments versus observational studies versus
surveys; confounding, control groups, placebo effects, and blinding; treatments, experimental units,
and randomization; completely randomized design for two treatments; randomized paired comparison
design; replication, blocking, and generalizability of results.
Unit IV – Randomness and Probability
Topic 8: Probability as Relative Frequency – The law of large numbers; addition rule, multiplication
rule, conditional probabilities, and independence; multistage probability calculations; discrete random
variables and their probability distributions; simulations of probability distributions, including binomial
and geometric; mean (expected value) and standard deviation of a random variable, including
binomial.
Topic 9: Combining Independent Random Variables – Independence versus dependence; mean and
standard deviation for sums and differences of independent random variables.
Topic 10: The Normal Distribution – Properties of the normal distribution; using tables of the normal
distribution; the normal distribution as a model for measurement; commonly used probabilities and zscores; finding means and standard deviations; normal approximation to the binomial.
Unit V – From the Data at Hand to the World at Large
Topic 11: Sampling Distributions – Sampling distribution of a sample proportion; central limit theorem;
sampling distribution of a difference between two independent sample proportions; the t-distribution.
Topic 12: Confidence Intervals for Proportions.
Topic 13: Testing Hypotheses about Proportions – Logic of significance testing; null and alternative
hypotheses, P-values, one and two sided test, Type I and Type II errors, and the concept of power.
Topic 14: Comparing Two Proportions – Confidence intervals for the difference between two
proportions; hypothesis tests for the difference between two proportions.
Unit VI – Learning About the World
Topic 15: Sampling Distributions – Sampling distribution of a sample mean; central limit theorem;
sampling distribution of a difference between two independent sample means; the t-distribution.
Topic 16: Confidence Intervals for Sample Means
Topic 17: Testing Hypotheses about Sample Means – Logic of significance testing; null and
alternative hypotheses, P-values, one and two sided test, Type I and Type II errors, and the concept
of power.
Topic 18: Comparing Two Sample Means – Confidence intervals for the difference between two
sample means; hypothesis tests for the difference between two sample means; tests for paired
samples and blocks.
Unit VII – Inferences When Variables are Related
Topic 19: Tests of Significance: Chi Squared– Chi-squared test for goodness of fit; chi-squared test
for independence; chi-squared test for homogeneity of proportions.
Topic 20: Test of Significance: Slope of Least Squares Line – Inference for slope of least squares
line.
AP Statistics Test Date: Thursday, May 11th, 2017, 12 noon – 3:30 pm
Practice Test: A full-scale practice test will be set up for you. It is extremely beneficial to take a
mock test not only for practice but so that you are comfortable with the exam when you actually take
it. A full length practice exam will be given to use in early May, and will be graded as your FINAL
EXAM.
Preparing for the AP Exam:
Students will be prepared for the AP Exam as we move throughout the semester. Tests and quizzes
will be modeled after the AP Exam. We will also look at past AP questions on a regular basis as we
learn new topics. Each student will take a full length practice exam in preparation for the exam. We
will also work in groups where students will solve extended response questions and then grade each
others. In the groups students will discuss what they think should be included in a correct response
and what each other were missing. This preparation step is crucial because students need to hear
from each other and see what others are thinking as they work through problems. We will have
around a week at the end of the course before the AP Exam to study and practice extensively in
class.
Note on Graphing Calculator and other Technology:
The use of the Ti-83 graphing calculator is an integral part of this course. They will be used on a daily
basis. I will be using the Ti-83 calculator as an overhead and on the computer projector so that you
can follow along with me at all times. You will use this technology routinely to construct your own
understanding of the principles and practices of statistics. You will be actively engaged in using your
calculator to explore and analyze data, assess models, and perform simulations. Will also be using
internet websites to assess models and run simulations. Our text also provides us with ActivStats.
This is a computer software package that will allow us to look deeper into many of the statistical
topics we will cover. We will use this program as a class to analyze data and run various simulations.
Tests and Quizzes:
There will be 4 main tests in this course, two the first nine weeks and two the second nine weeks.
There will also be quizzes throughout the semester as well. Finally, there will also be very small
quick quizzes often during the semester. The 4 main tests will be set up as one day exams. They
will consist of both multiple choice and free-response questions. They will be graded in the same
format as the AP exam (which will be explained in class). Quizzes and quick quizzes will be far
shorter and in several different formats.
Projects:
Throughout the semester many INVESTIGATIVE TASKS will be given. These tasks will require you
to bring together and make connections between all aspects of the statistical process, including
design, analysis, and conclusions. Most look at real world situations and scenarios and you must use
what we have learned up to that point to create a well developed report of what is asked of you. You
will find that the investigative tasks will increasingly get harder and longer since we will of course be
learning new information that you will continue to bring into these tasks. Each task will require formal
writing so that students can gain experience in developing statistical studies and experiments in a
formal manner. These tasks will also help you develop into interpreters and investigators of statistical
data and information. Your analysis of statistical data and information is extremely important and
thus you must be able to provide proof that gives both statistical and algebraic justification that will
deepen your understanding of statistics, these tasks will require you to do this. Each task will ask you
to draw formal written conclusions of your analysis starting from your statistical hypothesis to your
findings based on interpreting the data and information. Rubrics will be provided for you for each task
to guide you through what is expected of you. At the conclusion of the year you will be asked to
complete a rather large investigative task that will combine everything we have learned throughout
the semester. This task will require you to make connections between many topics, design and
analyze your own experiment, and create a concluding report of all of your findings. You will find at
the end that this project proves that everything we have leaned about in the statistical process is
indeed connected.
Homework:
Homework will be given usually on a nightly basis. Unless told to you, homework will come out of the
book. There is not enough time to go over every homework problem every day. The good news is
that the answers to all problems are in the back of the book. Each night as you work on homework
you should be checking your answers with those in the back of the book. If you get a problem wrong,
work on trying to correct your mistake. If you can’t find the solution then bring up the problem the
next day in class. Homework will be checked periodically for points. Note that the chances of you
being successful in this class depend on how hard you are willing to work outside of the classroom on
homework and studying. Just because I do not check homework everyday does not mean you do not
have to do it everyday. Each night I will give you a long list of problems that you should be able to do.
That does not mean you have to do all of the, but you should be able to. We will then spend 10
minutes each day going over the homework and then it will follow with a homework quiz where a few
problems will be taken right from the homework and be graded.
Absences and Make-Up Work:
Being in class every day is extremely important. The more you are in class, the more you will learn.
Any work that is missed due to an absence must be made up the day you return. You have the same
number of days you missed to make up your work. I do not chase students down to make up work, if
you do not get it made up, you will receive a zero.
Breakdown of Grades
The following list gives the percentage of you grade that comes from the areas of the course.
Tests – 50%
Group Assessment – 15%
Quizzes – 20%
Projects – 10%
Homework – 5%
Grade Scale:
A
B
C
D
F
90 – 100
80 – 89
70 – 79
60 – 69
59 or lower
Classroom Expectations:
 There is basically one rule in my classroom – treat all other students and the teacher with
respect at all times.
 I have zero tolerance for disrespect towards others or myself.
 If I feel you break this rule you will be asked to leave immediately and be sent to the principal’s
office.
 Be on time each and every day and be prepared as soon as the bell rings.
 Sleeping in class is absolutely prohibited. If you do so you will be asked to leave immediately.
 NO cell phones in class. If I even see one, I will take it and you can get it back at the end of
the day. If it happens a second time it will be taken to a principal.
 You must follow the school dress code that is described in your agenda, any violators will be
sent to the principal’s office.
Course Description and Outline
Part I – Organizing Data
A.) Exploring Data
1.) Displaying distributions with graphs
2.) Describing distribution with numbers
B.) The Normal Distributions
1.) Density Curves and the Normal Distributions
2.) Standard Normal calculations
C.) Examining Relationships
1.) Scatter-plots
2.) Correlation
3.) Least-Squares Regression
D.) More on Two Variable Relationships
1.) Transforming Relationships
2.) Cautions about Correlation and Regression
3.) Relations in categorical data
Part II – Producing Data
A.) Producing Data
1.) Designing samples
2.) Designing experiments
3.) Simulating experiments
Part III – Probability
A.) Probability and Randomness
1.) The idea of probability
2.) Probability Models
3.) General probability rules
B.) Random Variables
1.) Discrete and continuous random variables
2.) Means and variances or random variables
C.) Binomial and Geometric Distributions
1.) The Binomial distribution
2.) The Geometric distribution
D.) Sampling Distributions
1.) Sampling distributions
2.) Sample proportions
3.) Sample means
Part IV – Inference
A.) Introduction to Inference
1.) Estimating with confidence
2.) Tests of significance
3.) Making sense of statistical significance
4.) Inference as decision
B.) Inference for Distributions
1.) Inference for the mean of a population
2.) Comparing two means
C.) Inference for Proportions
1.) Inference for a population proportion
2.) Comparing two proportions
D.) Chi-Square Procedures (Inference for Tables)
1.) Test for goodness of fit
2.) Inference for two-way tables
E.) Inference for Regression
1.) Inference about the model
2.) Predictions and conditions