Download Lindblom Mathematics and Science Academy

AP Statistics
Instructor:
Room:
Tutoring:
Mrs Sarah Doyle
321
Tuesday, after school.
Most days before school
Email: [email protected]
Phone: 309-657-3337
Prerequisites: Advanced Algebra w/ Trigonometry
Text(s):
Bock, Velleman, and DeVeaux. Stats: Modeling the World, 3E
Carroll, Carver, Peters, Ricks. Preparing for the Statistics AP Exam
Course Description:
The AP Statistics course has been designed to develop your ability in mathematical modeling, including the process of
data collection, representation, interpretation, and simulation. Through investigations of real-life contexts, you will
develop a rich understanding of statistical analysis and how to draw conclusions from data. This course incorporates the
frequent use of technology, projects, cooperative group problem solving, and writing, as the tools to developing your
understand of statistical methods.
Course Goals:
In addition to meeting national goals and objectives in learning statistics, we will work to achieve each the following:
 Enlarge your math vocabulary
 Improve your ability to communicate mathematically
 Foster clear thinking
 Increase your problem solving ability
 Develop your skills and conceptual understanding of statistics
 Build your confidence and ability to succeed in statistics
AP Statistics Exam
Students enrolled in the Advanced Placement Statistics course are required to complete an AP Statistics contract prior to
receiving the materials for class and take the AP Exam on May 16, 2012. Students who fail to take the examination will
receive an F for their course work.
Class Materials:
AP Statistics students are required to bring each of these items to class each day.
Three Ring Binder (1” or larger)
Graphing Calculator
Pencils
Notebook Paper
Technology:
The AP Statistics course will integrate several modes of technology into the course throughout the year. Each of these
modes of learning will help you achieve a greater understanding of statistics and its use.
Graphing Calculator
Students enrolled in the AP Statistics course are required to have access to a TI-84 plus graphing
calculator for use in class, at home, and on the AP exam. If you already have a graphing calculator, please
verify with the teacher whether or not it will meet the requirements of the course. In addition to the TI84, we will be using the TI-nSpire CAS calculator in class to explore different topics.
.
AP Statistics 2013 – 2014
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Homework Guidelines:
1. Homework will be assigned every class period. It will usually consist of problems and reading.
2. Homework will be checked for completion on a daily basis. Completion is meant that every problem is
authentically worked on.
3. While there is not a homework grade, a student who misses more than one assignment per unit is not allowed to
take that unit test.
Grading:
The grades for this class will be based on the following items:
55%
35%
10%
Exams
Quizzes
Final Exams
The points for quizzes and tests are subject to change in point value but not in the percentage of the grade.
Grading Scale:
Honors Classes
A
100 – 90%
B
89 – 80%
C
79 – 70%
D
69 – 60%
F
59% and below
Make – Up Work:
Students who miss class with a valid excuse are responsible for arranging dates and times for make-up work. Students
who fall into this situation will have two days after the absence date to complete the missed work. Work missed due to
cuts or unexcused absences may not be made up.
Study Habits:
All students are expected to be successful in this math class, through time dedicated to studying. Students are expected to
review material with or without formal assignments being issued.
Be respectful of the following:
1. Be prompt for class. Be in your seat and ready to work when the bell rings. Tardiness will be handled as specified
by the school procedures outlined in the school handbook.
2. Dress appropriately for school and the weather. The guidelines issued in your student handbook will be observed.
3. Exhibit mature behavior and treat all persons in the classroom with respect and courtesy. We all get respect by
showing respect.
Advice:
Ask questions on a daily basis, especially before school. An extra 5 minutes of questions per day is absolutely the
difference between passing the AP exam and not.
Student Math Resource Websites
Parent Math Resource Websites
http://www.gomath.com/
http://www.nctm.org/
http://mathforum.org/dr.math/
http://www.actstudent.org
http://www.education.ti.com
http://www.mathematicshelpcentral.com/graph_paper.htm
http://www.intuitor.com/statistics/
http://www.collegeboard.com/student/index.html?student
AP Statistics 2013 – 2014
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Course Outline: (Organized by the primary chapters in the textbook):
The following are the themes and ideas which will be covered during the course of the school year. Included in the table is
a summary of the major skills you will learn in this course.
Textbook Chapter
I. Exploring & Understanding Data
Stats Starts Here
Data

Identify the Who, What, When, Where, Why and How of data, or recognize
when some of this information has not been provided.
 Identify the case and variables in any data set
 Classify a variable as categorical or quantitative depending on its use
 For any quantitative variable, be able to identify the units in which the
variable has been measured
Displaying and Describing Categorical Data
 Recognize when a variable is categorical and choose an appropriate display
for it.
 Understand how to examine the association between categorical variables by
comparing conditional and marginal percentages
 Summarize the distribution of a categorical variable with a frequency table.
Describing Quantitative Data
 Know how to display the distribution of a quantitative variable with a stemand-leaf display, a dotplot, or a histogram
 Know how to make a timeplot of data that may vary overtime.
 Compare the distributions of two or more groups by comparing their shapes,
centers and spreads.
 Discuss any outliers in the data, noting how they deviate from the overall
pattern of the data.
Describing Distributions Numerically
 Know the basic properties of the median and mean.
 Know how to compute the mean and median of a set of data.
 Know how to compute the standard deviation and IQR of a set of data.
 Create a 5-number summary of a variable.
The Standard Deviation as a Ruler and the Normal Model
 Know what z-scores means and calculate the z-score of an observation.
 Know how to compare values of two different variables using their z-scores.
 Use the Normal models and the 68-95-99.7 Rule to estimate the percentage of
observations falling within 1,2, or 3 standard deviations of the mean.
 Know how to find the percentage of observations falling below any value in a
Normal model using a Normal table or appropriate technology.
 Check whether a variable satisfies the Nearly Normal Condition by making
Normal probability plot or a histogram.
II. Exploring Relationships Between Variables
Scatterplots, Association, and Correlation
 Know how to make a scatterplot by hand or with technology.
 Know how to compute the correlation of two variables.
 Know the conditions for correlation and how to check them.
 Know how to read a correlation table produced by a statistics program.
Linear Regression
 Know how to find a regression equation from the summary statistics for each
variable and correlation between the variables.
 Know how to find a regression equation using your statistics software and how
to find the slope and intercept values in the regression output table.
 Know how to use regression to predict a value of y for a given x.
 Know how to compute the residual for each data value and how to display
AP Statistics 2013 – 2014
Time Frame
Semester I
Semester I
Semester I
Semester I
Semester I
Semester I
Semester I
Semester I
Semester I
Semester I
3
them.
Know how R2 describes how much of the variation in y is accounted for by its
linear relationship with x.
Regression Wisdom
 Look for lurking variables whenever considering the association between two
variables.
 Know how to find residuals from a linear model by making a scatterplot of
residuals against predicted values or against the x-variable, and know what
patterns to look for in the picture.
 Know how to look for high-leverage and influential points by examining a
scatterplot of the data and how to look for points with large residuals by
examining a scatterplot of the residuals against the predicted values or against
the x-variable.
Re-expressing Data: Get It Straight
 Understand the value of re-expressing data to improve symmetry, to make the
scatter around a line more constant, or to make a scatterplot more linear.
 Know how to re-express data with powers and how to find an effective reexpression for data using statistics software or calculator.
 Reverse any of the common re-expressions to put a predicted value or residual
back into the original units.
III. Gathering Data
Understanding Randomness
 Recognize random outcomes in real-world situation.
 Know how to perform a simulation either by generating random numbers on a
computer or calculator, or by using some other source of random values such
as dice, a spinner, or a table of random numbers.
 Discuss the results of a simulation study and draw conclusions about the
question being investigated.
Sample Surveys
 Know the basic concepts and terminology of sampling.
 Recognize population parameters in descriptions of populations and samples.
 Know how to draw a simple random sample from a master list of a population,
using a computer or table of random numbers.
 Understand the value of randomization as a defense against bias.
Experiments and Observational Studies
 Identify observational studies as retrospective or prospective, and understand
the strengths and weaknesses of each method.
 Know the four basic principles of sound experiment design: control,
randomize, replicate, and block, and be able to explain each.
 Recognize the factors, the treatments, and the response variable in a
description of a designed experiment.
 Understand the importance of a control group and the need for a placebo
treatment in some studies.
 Design a completely randomized experiment to test the effect of a single
factor.
 Design an experiment in which blocking is used to reduce variation.
IV. Randomness and Probability
From Randomness to Probability
 Know the basic definitions and rules of probability.
 Know that the relative frequency of an outcome of a random phenomenon
settles down as we gather more random outcomes. Be able to state the Law of
Large Numbers.
 Use the facts about probability to determine whether an assignment of
probabilities is legitimate.
 Know how and when to apply the Addition Rule, Multiplication Rule and
Complement Rule.

AP Statistics 2013 – 2014
Semester I
Semester I
Semester I
Semester I
Semester I
Semester I
Semester II
Semester II
4

Know and be able to use correctly the terms “sample space”, “disjoint events”,
and “independent events”.
Probability Rules
 Understand that the probability of an event is the proportion of times it occurs
in many repetitions of a random phenomenon.
 Understand the concept of conditional probability is redefining the Who of
concern, according to the information about the event that is given.
 Understand the concept of independence.
 Know how and when to apply the General Addition Rule and the General
Multiplication Rule.
 Know how to find probabilities for compound events as fractions of counts of
occurrences in a two-way table.
Random Variables
 Recognize random variables.
 Understand that random variables must be independent in order to determine
the variability of their sum or difference by adding variances.
 Find the probability for a discrete random variable.
 Find the mean and the variance of a random variable.
 Use proper notation for these population parameters, μ or E(x) for the mean,
and σ, SD(x), σ2, or Var(x) when discussing variability.
 Know how to determine the new mean and standard deviation after adding a
constant, multiplying by a constant, or by adding or subtracting two
independent random variables.
 Interpret the meaning of the expected value and standard deviation of a random
variable in the proper context.
Probability Models
 Choose whether to use a Geometric or Binomial model for a random variable
involving Bernoulli trials.
 Know the appropriate conditions for using a Geometric, Binomial, or Normal
model.
 Know how to find the expected value of a Geometric model.
 Calculate Geometric probabilities.
 Know how to find the mean and standard deviation of a Binomial model.
V. From the Data at Hand to the World at Large
Sampling Distribution Models
 Demonstrate a sampling distribution by simulation.
 Use a sampling distribution model to make simple statements about the
distribution of a proportion or mean under repeated sampling.
Confidence Intervals
 Construct a one-proportion z-interval.
 Interpret a one-proportion z-interval in a simple sentence or two.
Testing Hypotheses about Proportions
 State the null and alternative hypotheses for a one-proportion z-test.
 Know the conditions that must be true for a one-proportion z-test to be
appropriate and how to examine your data for violations of those conditions.
 Identify and use the alternative hypothesis when testing hypotheses.
Understand how to choose between a one-sided and two-sided alternative
hypothesis and be able to explain your choice.
 Perform a one-proportion z-test.
 Interpret the meaning of a P-value in non-technical language.
More About Tests
 Identify and use the alternate hypothesis when testing hypotheses.
 Understand how to choose between a one-sided and two-sided alternative
hypothesis, and how to defend the choice of a one-sided alternative.
 Understand how the critical value for a test is related to the specified alpha
level.
AP Statistics 2013 – 2014
Semester II
Semester II
Semester II
Semester II
Semester II
Semester II
Semester II
Semester II
5
 Know how to complete a hypothesis test for a population proportion.
Comparing Two Proportions
 State the null and alternative hypotheses for testing the difference between two
popular proportions.
 Examine data for violations of conditions that would make inference about the
difference between two population proportions unwise or invalid.
 Find a confidence interval for the difference between two proportions.
 Perform a significance test of the natural null hypothesis that two population
proportions are equal.
VI. Learning About the World
Inferences About Means
 Know the assumptions required for t-test and t-based confidence intervals.
 Know how to examine data for violations of conditions that would make
inference about the population mean unwise or invalid.
 Compute and interpret a t-test and a t-based confidence interval for the
population mean.
Comparing Means
 Recognize situations in which we want to do inference on the difference
between the means of two independent groups.
 Examine data for violations of conditions that would make inference about the
difference between two population means unwise or invalid.
 Recognize when a pooled-t procedure might be appropriate and be able to
explain why you decided to use a two-sample method anyway.
 Perform a two-sample t-test using a statistics package or calculator.
Paired Samples and Blocks
 Recognize whether a design that compares two groups is paired or not .
 Find a paired confidence interval, recognizing that it is mechanically
equivalent to doing a one-sample t-interval applied to the differences.
 Perform a paired t-test.
VII. Inference When Variables Are Related
Comparing Counts
 Recognize when a test of goodness-of-fit, a test of homogeneity, or a test of
independence would be appropriate for a table of counts.
 Understand the degrees of freedom for a chi-square test depend on the
dimensions of the table and not the sample size.
 Display and interpret counts in a two-way table.
 Use the chi-square tables to perform chi-square tests.
 Compute a chi-square test.
 Examine the standardized residuals to explain the nature of the deviations from
the null hypothesis.
Inference for Regression
 Examine data and a scatterplot of y vs. x for violations of assumptions that
would make inference for regression unwise or invalid.
 Examine displays of the residuals from a regression to double check that the
conditions required for regression have been met.
 Test the standard hypothesis that the true regression slope is zero. Be sure to
state the null and alternative hypotheses.
 Find a confidence interval for the slope of a regression based on the values
reported in a standard regression output table.
Analysis of Variance
Multiple Regression
AP Statistics Practice Exams
AP Statistics 2013 – 2014
Semester II
Semester II
Semester II
Semester II
Semester II
Semester II
Semester II
Semester II
Semester II
Semester II
Semester II
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