Download AP Statistics Course Syllabus

AP Statistics Course Syllabus
COURSE DESCRIPTION:
The AP Statistics course is designed to provide students with the opportunity to study and learn
material that would be the equivalent to a college level statistics course. The purpose of this course is
to introduce students to the major concepts and tools for collecting, organizing, analyzing, and drawing
conclusions from data. This course fulfills the requirements from the College Board Advanced
Placement Course in Mathematics for AP Statistics. Students taking this class will be strongly
encouraged to take the AP exam. A graphing calculator is required (from the TI family of calculators).
PREREQUISITE:
Students will have successfully completed algebra II and be recommended by their teacher.
COURSE GOALS:
The purpose of the AP course in statistics is to introduce students to the major concepts and tools for
collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad
conceptual themes as outlined by the College Board:
1. Exploring Data: Describing patterns and departures from patterns
2. Sampling and Experimentation: Planning and conducting a study
3. Anticipating Patterns: Exploring random phenomena using probability and simulation
4. Statistical Inference: Estimating population parameters and testing hypotheses
In AP Statistics, students are expected to learn how to:
• produce convincing oral and written statistical arguments, using appropriate terminology, in a
variety of applied settings.
• use various techniques for producing data through surveys, experiments, and simulations;
analyzing data using graphical & numerical summaries; modeling data using probability,
random variables, and sampling distributions; and drawing conclusions (inferences) from data
using confidence intervals and significance tests
• become better educated consumers by studying ways in which statistics can be improperly used
to mislead, confuse, or distort the truth.
• use various forms of technology to aid in solving statistical problems
COURSE RESOURCES: (Textbooks, handbooks, and technology)
Textbooks and other handbooks:
Primary Text: The Practice of Statistics (4th edition), by Starnes, Yates, and Moore,
W. H. Freeman & Co., 2010
Text:
Text:
Text:
Text:
Stats Modeling the World, by Bock Velleman and DeVeaux; Pearson Addison Wesley, 2004
Statistics in Action, by Watkins, Scheaffer, and Cobb, Key Curriculum Press, 2004
Elementary Statistics, by Pelosi and Sandifer, John Wiley and Sons, 2003
Statistics Through Application, (2nd edition) by Starnes, Yates, and Moore, W. H. Freeman &
Co., 2011
Handbook: AP Statistics Workshop Handbook 2010-2011 by the College Board
Technology:
TI Graphing Calculators preferably the TI-84 or TI Nspire
Fathom Software
Geogebra Software
Microsoft Excel
Minitab
Numerous websites including, but not limited to:
http://apcentral.collegeboard.com/
http://noncontinuo.us/index.php/2011/05/green-lake-2011-ray-klein-intro-to-ti-nspire/
http://stattrek.com/online-tutorials/tutorial-list.aspx
http://www.whfreeman.com/tps4e
http://www.rossmanchance.com/
TEACHING STRATEGIES
Learning in the class is largely student-centered. Students will work independently, collaboratively,
and as an entire class as they make presentations and participate in class discussions in order to meet
the class learning targets. They will need to be able to explain concepts mathematically, as well as
demonstrate understanding of the fundamental concepts of statistics, through homework problems, in
class activities, computer applications, tests, and extended class projects. Review of practice AP
problems throughout the year will also help to assess student progress.
STUDENT ACTIVITIES AND PROJECTS
Throughout the year, various activities and projects will be integrated into the curriculum in order to
provide different and unique ways of assessing and presenting information and topics. The graphing
calculator will be a tool relied on heavily to help students gain a better understanding of the course
topics. In addition to several small projects during the year, students will complete a final project on a
topic of their choice. The purpose of the project is for students to demonstrate an integrated
understanding of all aspects of the statistical process (design, analysis, and conclusions) and the major
conceptual themes of AP statistics: Exploring Data; Sampling and Experimentation; Anticipating
Patterns; and Statistical Inference. Students are expected to communicate their methods, results, and
interpretations using proper statistical vocabulary.
STUDENT EVALUATIONS
Mixed in with their regular tests, quizzes, projects, and homework assignments will be numerous AP
problems from past AP exams. These multiple choice questions and free response problems will be
scored the same as they would be on the AP exam so students will get a feel for the proper way to
communicate their answers. Students will also be asked to verbally explain their answers when they
are asked to present selected problems to the rest of the class.
COURSE OUTLINE
(Organized by units in primary textbook)
1. Exploring Data (10 days)
1.0 Making Sense Out of Data – the pilot simulation problem
(Create random 2-digit integers on graphing calculator to simulate selections for pilot problem)
Introduction – what is statistics?
1.1 Analyzing Categorical Data (including Simpsons Paradox)
Compare frequency tables, conditional distributions, bar graphs, and pie charts
(Use Minitab outputs to analyze 2-way tables for conditional distributions)
(Students will create and analyze their own graphs using Microsoft excel)
1.2 Displaying Quantitative Data with graphs
Construct and interpret graphical displays of univariate data (dotplot, stemplot, histogram)
Describe the shape of a distribution
Analyze the center, spread, clusters, gaps, skewness, and outliers of a distribution
(Use the graphing calculator to create and analyze histograms)
1.3 Describing Quantitative Data with numbers
Summarize and compare univariate data with the median and mean
Describe the spread around the mean using the standard deviation
(Use spreadsheets on Microsoft-Excel and graphing calculator to calculate standard deviation)
Create and analyze the shape, center, and spread of box plots using the five-number summary
(Use the graphing calculator to create and analyze box plots)
(Use graphing calculator to do a one-variable analysis for data sets)
(Use descriptive statistics on Microsoft-Excel to analyze single variable data sets)
Histogram mini-project
Exploring Data quiz
Take Home AP statistics practice test using chapter 1 learning targets
2. Modeling Distributions of Data (9 days)
2.1 Describing Location in a Distribution
Distinguish the mean and median of a density curve
Describe the location in a distribution using z-scores and percentiles
Analyze the effects of transformations when changing units on summary measures
(Use graphing calculators to analyze the effects of these transformations)
2.2 Normal Distributions
Create the normal distribution curve and apply the empirical rule for areas and probabilities
Use z-scores with the standard normal table to find probabilities (areas) and vice versa
Compare, contrast, and analyze data sets of different normal distributions (ACT vs. SAT scores)
(Use Geogebra software package to analyze the area under the curve for z-scores)
(Use the shadenorm and normalpdf features on graphing calculator to create and analyze normal distributions)
(Use normalcdf and invnorm feature on graphing calculator to convert from z-scores to areas and vice-versa)
Modeling Distributions of Data quiz
Take Home AP statistics practice test using chapter 2 learning targets
3. Describing Relationships of Bivariate Data (10 days)
3.1 Scatterplots and Correlation
Analyze bivariate data patterns in scatterplots
(Use the graphing calculator, Minitab, and excel to create and analyze scatterplots)
Calculate and interpret the meaning of correlation as it relates to linearity
(Use the correlation and regression applet from whfreeman.com to analyze data patterns)
3.2 Least Squares Regression
Fit linear regression trend lines to bivariate data patterns on scatterplots
Find and interpret the meaning of residuals and the standard deviation of residuals
(Use the correlation and regression applet from whfreeman.com to analyze least squares regression lines)
(Use graphing calculator to find and analyze linear regression lines for bivariate data sets)
(Use Fathom software to standardize both variables to see how well the data fits residual plots)
(Use spreadsheet on graphing calculator or Excel to find and interpret the standard deviation of the residuals)
Analyze how outliers and influential observations affect correlation and regression lines
Explain how cause and effect doesn’t always determine why there is a strong association
Determine the role of the coefficient of determination (r2) for regression
(Use Minitab and graphing calculator to interpret regression output)
Performance Assessment Project: What can be done to solve the killing of manatees in Florida?
Describing Relationships of Bivariate Data quiz
Take Home AP statistics practice test using chapter 3 learning targets
4. Designing Studies (12 days)
4.1 Sampling and Surveys
Interpret the difference between a census and a sample from a population
Conduct a well designed random sample survey and interpret any bias within the study
What are the pros and cons of sampling method used (SRS, stratified random, and cluster sampling)
(Use the randInt generator on a graphing calculator to conduct these samples)
4.2 Experiments
Compare and contrast the results of an observational study to an experiment
Plan and conduct a well designed experiment applying the principles of experimental design
Control for lurking variables, random assignment of experimental units, and enough replication
Analyze how bias, random design, block design, the placebo effect and blinding affect results
(Use Fathom software dotplots to compare and contrast random design to matched pairs design)
4.3 Using studies wisely
Generalize the results that can be drawn from observational studies, experiments and surveys
Complete the experimental study on nitrogen filled vs. air filled tires
Create an original well constructed experimental study
Designing Studies quiz
Cumulative AP Practice Test with Mid-semester Exam (1 day)
5. Probability What Are the Chances (15 days)
5.1 Randomness, Probability, and Simulation
(Use the Probability Applet from whfreeman.com to do a coin simulation)
Interpret probability including long-run relative frequency interpretation
Understand the concept of the Law of Large Numbers
Simulate probability problems using random numbers (The 1 in 6 wins game)
(Use randInt feature on a graphing calculator to generate a simulation of rolling a single die)
5.2 Probability Rules
Apply the addition rule mutually exclusive OR problems
Use Venn diagrams to model probability problems
Conduct one and two dice simulation problems using probability
(Use the randInt feature on a graphing calculator to complete these simulations)
5.3 Conditional Probability and Independence
Apply the multiplication rule for independent probabilities
(Use cards, dice, spinners, and random numbers to simulate probability and independence)
Apply the conditional probability rule to solve probability problems
Use tree diagrams to model sample spaces with probability
Use two way tables to find solutions to probability problems
Probability What Are the Chances quiz
Take Home AP statistics practice test using chapter 5 learning targets
6. Random Variables (13 days)
6.1 Discrete and Continuous Random Variables
Create discrete and continuous random variables and analyze their probability distributions
(Use the spreadsheet and statplot feature on the graphing calculator to analyze random variables)
(Use the normalcdf & ShadeNorm feature on graphing calculator to find probabilities for normal distributions)
Find the mean (expected value), variance, and standard deviation of a discrete random variable
(Use spreadsheet on calculator and Excel to find and analyze all of these values)
6.2 Transforming and Combining Random Variables
Interpret the effects of a linear transformation on the mean and standard deviation
(Use spreadsheets on calculator or Excel to generate linear transformations to compare how these values change)
Find the mean, std. deviation and variance for the sum and difference of two random variables
(Use Fathom software to take 1000 SRSs to compare histograms of these sums and differences)
(Use randNorm feature on calculator to generate lists of normal distributions to add, subtract, and compare)
Compare and contrast the difference between independence vs. dependence
6.3 Binomial and Geometric Random Variables
Analyze the mean and standard deviation of a binomial random variable
(Use spreadsheet on calculator or Excel to generate and analyze the mean and std. dev. of a binomial rand. var.)
Describe the distribution for a binomial random variable
(Use spreadsheet and statpolot on graphing calculator to generate and analyze binomial distributions)
Apply the sampling without replacement condition when modeling with binomial distributions
Apply the rule of normal approximation for binomial distributions
Describe the distribution for a geometric random variable
(Use spreadsheet and statpolot on graphing calculator to generate and analyze geometric prob distributions)
Do AP Statistics Workshop problems for random variables
Random Variables quiz
Take Home AP statistics practice test using chapter 6 learning targets
7. Sampling Distributions (12 days)
7.1 What is a Sampling Distribution
Compare and contrast the parameter and statistic from data sets (German tank problem)
Simulate sampling distribution and analyze shape, center, and spread
(Use Fathom software to simulate a sampling distribution of 500 chips of two colors)
7.2 Sample Proportions
Analyze the effect of n and p on shape, center, and spread of sample proportions
(Use the Reese’s pieces java applet from rossmanchance.com to create and analyze these distributions)
Simulate proportion distributions and find the mean and standard deviation
Compare sampling proportion dist. to the normal distribution when normal condition is met
(Use shadenorm feature on graphing calculator to analyze normal probability distributions)
7.3 Sample Means
Simulate mean distributions for normal and non-normal original distributions
(Use Rice University sampling distribution applet to explore the sampling dist. of x-bar for a population)
Apply the Central Limit Theorem with its conditions to normalize data sets
(Use the RandNorm feature on graphing calculator to simulate normal distributions to analyze)
Central Limit Theorem Activity - Average word size in textbooks
Sampling Distributions quiz
Take Home Cumulative AP statistics practice test using chapters 1-7 learning targets
Semester I Exam (1 day)
8. Estimating with Confidence (13 days)
8.1 Confidence Intervals: The Basics
Estimate population parameters and margins of error
Analyze the properties of point estimators, including biasedness and variability
Explain the logic and meaning of confidence intervals along with their properties
(Use the confidence interval applet at whfreeman.com to analyze confidence intervals for SRS)
Use the conditions before constructing a confidence interval (random, normal, & independent)
(Use the mean(randnorm) feature on graphing calculator to interpret a confidence level and a confidence interval)
8.2 Estimating a Population Proportion
Meet the conditions of shape, center, and spread
Complete the four step analysis process to find the confidence intervals for proportions
Use the z-critical value when samples are large enough to calculate the margin of error
(Use the 1-PropZint feature on graphing calculator to analyze confidence intervals)
Determine the size of a population necessary to obtain a given margin of error for proportions
8.3 Estimating a Population Mean
Meet the conditions of random, normal, and independent to find confidence intervals for mean
Explain when to use z-critical vs. t-critical values to estimate the confidence intervals for mean
(Use the ZInterval and TInterval features on graphing calculator to analyze confidence intervals)
Determine the size of a population necessary to obtain a given margin of error for means
Know how to use the t-distribution wisely with sample size, normality, skewness, & outliers
Utilize the confidence interval applet to show the relationship between confidence level & interval
M&M confidence interval activity
Estimating with Confidence quiz
Take Home AP statistics practice test using chapter 8 learning targets
9. Testing a Claim (13 days)
9.1 Significance Tests: The Basics
Create a null and alternate hypothesis to test a claim (one-sided and two sided tests)
(Use the test of significance apple at whfreeman.com to analyze hypothesis test for a FT shooter)
Interpret the meaning of the p-value as it relates to the hypothesis statements
(Use fathom software to simulate and analyze significance level test for 400 sets of 50 shots for a FT shooter)
Interpret the meaning of Type I and Type II errors that can occur when testing
(Use the power applet at whfreeman.com to analyze the power and type II error that can occur when testing)
9.2 Tests about a Population Proportion
Are the conditions to do a complete a hypothesis test met (random, normal, independent)
Complete the 4-step (complete, plan, do, conclude) hypothesis test for proportions
(Use Minitab outputs and the 1-propZtest on a graphing calculator to interpret the results of hypothesis tests)
9.3 Tests about a Population Mean
Are the conditions to do a complete a hypothesis test met (random, normal, independent)
Complete the 4-step (complete, plan, do, conclude) hypothesis test for means
When is a t-distribution used instead of a z-distribution for means
Complete the 4-step (complete, plan, do, conclude) hyp test for paired difference of means
(Use Minitab outputs and the Z-test and T-test on graphing calculator to interpret results of hypothesis tests)
Construct an original study to test an existing claim for each one-population hypothesis test
Testing a Claim quiz
Take Home AP statistics practice test using chapter 9 learning targets
10. Comparing Two Populations or Groups (12 days)
10.1 Comparing Two Population Proportions
Find and analyze the mean and standard deviation of the sampling distribution for p1 – p2
(Use Fathom software to analyze the distributions shape, center, and spread for p1, p2, and p1 – p2)
(Use the 2PropZInt on graphing calculator to interpret results for confidence intervals for p1 – p2)
Are the conditions to do a complete a hypothesis test met (random, normal, independent)
Complete the 4-step (complete, plan, do, conclude) hypothesis test for 2 proportions
(Use the 2PropZ-test on graphing calculator to interpret results of hypothesis tests)
10.2 Comparing Two Population Means
Find and analyze the mean and standard deviation of the sampling distribution for x1 – x2
(Use Fathom software to analyze the distributions shape, center, and spread for x1, x2, and x1 – x2)
(Use the 2SampTInt on graphing calculator to interpret results for confidence intervals for x1 – x2)
Are the conditions to do a complete a hypothesis test met (random, normal, independent)
Complete the 4-step (complete, plan, do, conclude) hypothesis test for 2 means
(Use Minitab outputs and the 2SampT-test on graphing calculator to interpret results of hypothesis tests)
Know how to use the t-distribution wisely with sample size, normality, skewness, & outliers
Use the pooled variance for similar variances
Project: Create an advertisement poster by 1st comparing samples from two populations of interest
Comparing Two Populations quiz
Take Home AP statistics practice test using chapter 10 learning targets
Cumulative AP Practice Test with Mid-semester Exam (1 day)
11. Inference for Distributions of Categorical Data (13 days)
11.1 Chi-Square Goodness of Fit Tests
Are the conditions to do a complete a hypothesis test met (random, large n size, independent)
Complete the 4-step chi-square goodness of fit hypothesis test for categorical data
(Use spreadsheets on graphing calculator or Excel to find and analyze Chi-square GOF tests)
Does a distribution match a given, uniform, normal, or binomial pattern
(Use the X2GOF-test on graphing calculator to interpret results from hypothesis tests)
11.2 Inference for Relationships
Are the conditions to do a complete a hypothesis test met (random, large n size, independent)
Complete the 4-step chi-square test for homogeneity for two-way categorical data
(Create matrices on graphing calculator and then use the X2-test to interpret results from hypothesis tests)
Complete the 4-step chi-square test for homogeneity for association/independence
Inference for Distributions of Categorical Data quiz
Take Home AP statistics practice test using chapter 11 learning targets
12. More about Regression (10 days)
12.1 Inference for Linear Regression
Are the conditions for regression inference met (linear, independent, normal, equal variance, random)
(Use fathom software to select 1000 SRS of size n=20 to analyze the sampling distribution of b)
Construct a confidence interval for slope including the standard error
Perform a significance test for slope
(Use the LinregTtest on graphing calculator to interpret the results of hypothesis tests)
12.2 Transforming to Achieve Linearity
Compare and contrast data sets as being linear, power, exponential or logarithmic
(Use fathom software and graphing calculators to compare and contrast these data sets)
Transform data sets into linear sets using powers, exponents and logarithmsor
(Use spreadsheet on graphing calculator to plot original and transformed data sets)
(Use the LinReg feature on graphing calculator to analyze the transformed data sets)
Regression quiz
Take Home Cumulative AP statistics practice test using chapter 1-12 learning targets
Final Review for AP Exam (4 days)
Previously released AP Multiple Choice Exams
Previously released Short Answer AP questions
AP Exam (1 day)
Post AP Exam (approximately 13 days)
Second semester project (on next page)
Chapter 13: Analysis of Variance
Chapter 14: Multiple Regression
. Statistics
Final Project 2nd Semester
Name(s) _________________________________
The purpose of this project is to apply the statistical terminology, tables, graphs, tests, confidence intervals, and
data measurements learned from the entire year (selecting the most appropriate ones for your study). For this
project you will work in a group of 2 or 3 people to create and present a proper inferential statistical study.
For this project your group will need to identify a study of interest; the variables you plan to measure and/or test;
the population(s) you plan to draw conclusions about; and the type of study (i.e. survey, data collection, or
experiment) that was done.
If an experiment is used, provide a written design of your experiment along with the results. If a survey is used,
provide a copy of the questionnaire and a written statement of how the survey was taken along with the results.
If any data was collected via the internet or a printed publication, indicate the sources and/or websites used
along with the results. You should indicate why this study is appropriate to answer your question and what
precautions you will take in order to avoid problems such as: a biased sample, a non-responsive answer, lurking
variables, outliers, etc... You will need to include a final analysis of your study using appropriate statistical
terms, tables, tests and graphs. Also indicate any drawbacks or problems you encountered with your data
collection.
At the end of your project you need to include a written and oral summary with your final conclusions. In
addition, explain what somebody might want to change, if they were to do research on this same topic.
The final project will be submitted as a word processed report along with a visual presentation using the smartboard and/or poster board. Graphs can be created on poster board or computer software to be displayed on the
smart-board so other students can easily read them during the oral presentation. You can store the information
on a CD, to the P-drive, or a jump drive for use on the smart-board.
Student checklist is on the next page…
Use the following outline as a checklist for the project I.
Introduction (4 points)
Ø Explain the purpose of the study
Ø Explain why you were interested in this question
Ø Explain why you chose your statistical design for the study
Ø Explain what you might expect to find from the data prior to any
data collections
(1 pt)
(1 pt)
(1 pt)
(1 pt)
II. Summary of data collection (30 points)
Ø Identify the sample(s) and population(s) of interest for the study
Ø Describe the sampling technique or experimental design used
Include all the individual results from the study and indicate any cautions
used to avoid biasness, lurking variables, outliers, etc…
Ø Use appropriate statistical symbols, techniques, conditions, charts, formulas
and/or graphs to show the results for your study
(3 pts)
(10 pts)
(10 pts)
(A minimum of 2 graphs must be shown – they should be concise, labeled properly, and easy to read)
Ø Correctly interpret and explain the meaning of each graph and
why it was selected (Use appropriate statistical terminology for this)
Ø Include any drawbacks or problems you found with your data collection
III. Final summary (6 points)
Ø What are the final conclusions drawn from your study?
Ø If somebody else were to do this same study, what might
you suggest they do different?
(1 pt)
(5 pts)
(1 pt)
IV. Oral summary presented to the class (average - graded by classmates)
Ø A description of what your study is about and why you chose it
Ø An explanation of how you collected the data or performed your experiment
Ø Include appropriate statistical terminology to describe the results of your findings
Ø Include at least two graphs supporting the results of your findings
(They need to be large enough for the class to see –
Use poster board or graphing software to be displayed on the smart-board)
Ø A final summary of your study
Ø All group members involved in presentation
Ø Overall flow of presentation
DUE DATE _______________
(6 pts)
(10 pts)
TOTAL POINTS = 50
The following sheet will be given for each student to grade each of their classmate’s individual oral
presentation. Their classmates will then receive a grade of the average of their entire peers total on the
oral presentation divided by two for a maximum of 10 points. This total will be counted in step IV.
Oral summary presented to the class.
Student Grading Sheet
for Oral Presentations
Presenter Name(s) ______________________
Fill in the number with the appropriate scale to rate each category from each groups sampling
presentation.
0 Not stated or presented
1 Mentioned, but not presented or described properly
2 Mentioned, and adequately described or presented
3 Outstanding job of presenting properly
Use the 0-3 scale from above
A description of what their study
is about and why they chose it
An explanation of how they
collected the data or performed
their experiment
Include appropriate statistical
terminology to describe the results
of their findings
Include at least two graphs
supporting the results of their
findings
(They need to be large enough for
the class to see)
A final summary of their study
TOTAL POINTS on 0-3 scale
Score
Use each scale as stated below
Were all group members
involved in the presentation
(rank from 0-2)
2 all equally involved
1 all involved, but not equally
0 no teamwork
Overall Quality of
Presentation
Rank on a scale of 0-3
with 3 being outstanding flow
and 0 being no flow
TOTAL POINTS using
these scales
Write comments about the presentation on the back of the sheet. TOTAL POINTS
Score