AP STATISTICS
AP STATISTICS
Course Syllabus
Eric Haight
Franklin High School
900 N. Resler
El Paso, TX 79912
emhaight@
AP STATISTICS
Course Overview
AP Statistics is the high school equivalent of a one semester, introductory college statistics course. Participating students have completed Algebra II, most of them have completed Precalculus and some take AP Calculus concurrently with AP Statistics.
In this course, students develop strategies for collecting, organizing, analyzing, and drawing conclusions from data. Students design, administer, and tabulate results from surveys and experiments. Probability and simulations aid students in constructing models for chance phenomena. Sampling distributions provide the logical structure for confidence intervals and hypothesis tests.
Teaching Strategies – Pedagogy
The primary text, Introduction to Statistics & Data Analysis by Peck/Olsen/Devore, (referred to below as POD), provides the general layout of the course as well as being the primary source of homework assignments. Students are strongly encouraged to read the chapters in the textbook and answer vocabulary terminology, before the topics are discussed in class, so that class time can be devoted to more discussion, practice, investigation, and activities with less time spent class note taking and lecturing. As much as possible, class time is utilized working on activities and investigations from a variety of sources.
These activities and investigations are taken from the textbook, Activity-Based Statistics, and materials gathered from AP Summer Institutes, Statistics Workshops, NCTM Conferences, and great ideas from contributors to the AP Statistics Electronic Discussion Group.
Students are encouraged from the beginning of the course to write complete responses in their homework, quizzes, and tests, on write-ups from the activities and investigations, and especially on released AP Statistics free response questions. Throughout the course, students practice released free response questions, and grading each other’s responses using released rubrics.
Techonological support
Students always use a TI83+, graphing calculator, with statistical programs, computer statistical software, such as Fathom, and internet web-based java applets. Each POD chapter has a section on calculator use, to give students instruction and practice using the statistical capabilities of their calculators. On some assignments and activities, students are required to use Spreadsheets and/or the Fathom Statistics program to analyze data. . For all assignments computers are available in our Math Lab. Students also take Online Quizzes to practice multiple-choice questions. We also use as often as possible, the series of videos Against All Odds, to emphasize the important concepts covered in the course.
Assessment
Students are assigned homework primarily from the textbook. Other sources are used to provide extra practice or enrichment. Students are expected to plan on about an hour of work for each hour of class in this course. Generally, textbook assignments are due the following class day, whereas free response questions and write-ups from activities and investigations are collected a few days after they have been assigned. Chapter tests are weighted 50 percent of their six week grade, quizzes, projects, and homework make the other 50 percent. Each six weeks grade represents 30 percent of the semester grade. The final exam represents 10 percent.
All quizzes and tests are announced well in advance. Quizzes are given on a regular basis to keep students from falling behind in their work. At the end of each chapter, assessment is performed with the Chapter Test.
Review for the AP Exam
Students practice Free Response Questions throughout the course, and sometimes these are included as part of the Chapter Tests. Towards the end of the course they receive an AMSCO’s AP Statistics Book and a suggested review plan. In the last 2-3 weeks they practice Multiple Choice Tests as well as “in class” timed Free Response Questions. We also organize a mock “timed exam”, to help the students distribute their time accordingly during their real AP Exam.
Course Materials
Primary Text: Statistics & Data Analysis by Peck/Olsen/Devore (POD), 2nd. Edition, 2007, Brooks/Cole Thomson Learning, (POD).
Workshop Statistics, Discovery with Data and the Graphing Calculator by Rossman/Von Oehsen, Springer.
Teaching Mathematics with FathomTM , Dynamic Data TM , Software, by Key Curriculum Press.
AP Released Exams
How to Prepare for the AP Statistics Advanced Placement Examination by Sternstein, Barron’s Educational Series, Inc.
AMSCO’S AP Statistics, Preparing for the Advanced Placement Examination by James F. Bohan.
Course Projects
The course projects are in the form of extended assignments. As a consequence, form and technical adequacy are enforced.
Examples of projects are:
- Collection of data and descriptive analysis.
- Analysis of a significant data set using the computer.
- Design of an observational study or experiment.
- Design and development of an experiment using the inferential analysis.
All these projects are presented as a formal report typed, with all or most of the graphics and analysis done in the computer. As time permits after the AP exam, students additionally make an oral power point presentation to the class on their final project.
Course Content and Timeline
Semester 1
* The time given is an approximation.
| |
|Chapter 1: The Role of Statistics (3 class periods)* |
|1.1 and 1.2 Three Reasons to Study Statistics |
|The Nature and Role of Variability |
|1.3 Statistics and Data Analysis |
|1.4 Types of Data and Some Simple Graphical Displays |
|Activity: A current newspaper article is assigned to illustrate the pervasive nature of the course’s content |
|Chapter 2: The Data Analysis Process and Collecting Data Sensibly (3 weeks)* |
|2.1 The Data Analysis Process - How are data produced - Observational studies vs. experiments; populations vs. samples; sampling vs. |
|census; bad sampling: voluntary response & convenience. |
|2.2 Obtaining good samples Simple random sample (SRS); stratified sampling; cluster sampling, systematic sampling, multi-stage sampling |
|Skill: Using a random digits table and a calculator to help choose random samples |
|2.3 Statistics Studies: Observation and Experimentation |
|2.4 Basics of experimental design subjects, factors, treatments, explanatory & response variables, placebo effect, blinding; completely|
|randomized design (CRD) |
|Principles of experimental design: control, random assignment, replication |
|Activity: Students participate in a double blind experiment. |
|2.4 and 2.5 More advanced experimental designs Multi-factor experiments; block designs; why block?; difference between blocking and |
|stratifying. |
|2.4 and 2.5 Matched pairs designs - A special form of blocking!; cross-over designs |
|Activity: Students participate in a matched pairs experiment & analyze data. |
|2.6 Designing and implementing surveys Questions: wording, type, order; administration methods; concerns – undercoverage, nonresponse, |
|bias |
|2.7 Communicating and Interpreting the Results of Statistical Analyses |
|Activity: Students do the Random Rectangles, adapted from a Summer Workshop. |
|Free Response Questions from AP Exams: 1999(3), 2000(5), 2001(4), 2002(2), 2002(B)(3), 2003(4), 2004(2), 2006(1), 2006(5), 2006B(5) |
|Chapter 3: Graphical Methods for Describing Data (2 weeks)* |
|3.1 Displaying Categorical Data: Comparative Bar Charts and Pie Charts |
|Skill: Using lists on the calculator |
|3.2 Dotplots & Stemplots Constructing & interpreting graphical displays; Shape, Outliers, Center, Spread; splitting stems; back-to-back|
|stemplots |
|3.3 Histograms Constructing & describing; frequency and relative frequency |
|Skill: Making histograms on the calculator |
|3.4 Timeplots Seasonal variation, trends, cycles, time series, Bivariate Data |
|3.5 Communicating and Interpreting the Results of Statistical Analyses |
|Free Response Questions from AP Exams: 1997(2) 2000(1) 2002-B(5) |
|Activity: Matching boxplots, histograms, summary statistics |
|Chapter 4: Numerical Methods for Describing Data ( 2 weeks)* |
|4.1 Describing the Center of a Data Set |
|Skill: Computing numerical summaries on the calculator |
|4.2 : Describing Variability in a Data Set |
|4.3 Boxplots & changing units of measurement. Five number summary Outlier determination-1.5IQR analysis; parallel boxplots |
|Skill: Constructing and analyzing boxplots, modified boxplots, outliers, on the calculator |
|4.4 Interpreting Center and Variability: Chebyshev’s Rule, the Empirical Rule, and z Scores rule |
|Skill: Determining z-scores using the calculator. |
|4.5 Communicating and Interpreting the Results of Statistical Analyses. |
|Free Response Questions from AP Exams: 2004(1), 2005(1), 2005(B)(1) |
|Chapter 5: Summarizing Bivariate Data ( 4 weeks)* |
|5.1 Scatterplots: constructing and interpreting Direction, shape, strength (and outliers), Correlation |
|Skill: Making scatterplots and linear regression on the calculator |
|5.1 Correlation: calculations & properties defining correlation; what affects correlation? |
|Activity: Guess the correlation game (java applet) |
|5.2 Least squares regression line (LSRL) least squares principle; interpreting the slope and y-intercept in context; prediction vs. |
|extrapolation |
|Skill: Finding the LSRL on the calculator |
|Activity: Java applet on minimizing sum of squared error |
|5.2 Properties of the LSRL [pic]; [pic] on LSRL |
|Activity: Computer activity using the program Fathom to explore LSRL, outliers and influential points, and residual plots. |
|5.3 Analyzing model quality: residuals & [pic] residual plots – constructing & interpreting; [pic]– calculation & interpretation |
|Skill: Computing residuals & making residual plots on the calculator |
|5.3 Cautions about correlation & regression Lurking variables; causation. common response, and confounding |
|5.4 General transformations to achieve linearity powers and logs |
|Skill: Transformations and regression models on the calculator |
|5.5 Exponential models Exponential growth; log x and log y transformation Power models . |
|Choosing the best model residuals and [pic] |
|Skill: PwrReg and ExpReg on the calculator (note differences in residuals) |
|Free Response Questions from AP Exams: 2000(1), 1999(1). |
|Chapter 6: Probability (3 weeks)* |
|6.1 and 6.2 Basic probability concepts. Probability as long-run relative frequency; randomness; legitimate probability models; sample |
|spaces, outcomes, events |
|Activities: Dies, spinners; experimental vs. theoretical probability |
|6.3 Basic probability rules Addition rule for disjoint events; complement rule; Venn diagrams – union and intersection; general |
|addition rule |
|6.4 Conditional probability General multiplication rule & tree diagrams |
|6.5 Independence & the multiplication rule. Definition of independent; multiplication rule for independent events |
|6.6 Some General Probability Rules |
|6.7 Estimating Probabilities Empirically and Using Simulation |
|Free Response Questions from AP Exams: 1999(4), 2001(3) |
Semester 2
|Chapter 7: Random Variables and Probability Distributions (3 weeks)* |
|7.1 Discrete random variables Properties; graphs; mean and variance |
|7.2 Probability Distributions for Discrete Random Variables |
|Continuous random variables Uniform and Normal distributions |
|7.3 Probability Distributions for Continuous Random Variables |
|7.4 Mean and Standard Deviation of a Random Variable |
|7.5 The Binomial and Geometric Distributions |
|Skill: Binomial distributions on the calculator |
|7.6 Normal Distributions, The normal approximation to the binomial |
|7.7 Checking for Normality and Normalizing Transformations |
|Free Response Questions from AP Exams: 2001(2), 2002(3), 2002(B)(2), 2003(3), 2004(3), 2004(4) |
|Chapter 8: Sampling Variability and Sampling Distributions (2 weeks)* |
|8.1 What is a sampling distribution? Moving towards inference; definition of sampling distribution; bias and variability |
|8.2 Sampling distributions of [pic] Mean and standard deviation of sampling distribution; normal approximation and rules of thumb |
|Activity: Use of the computer: Reese's Pieces Java Applet |
|8.3 Sampling distributions of [pic] Mean and standard deviation of sampling distribution; Central Limit Theorem (CLT) |
|Activity: Pennies ages and the CLT Sampling Activity |
|Calculations involving [pic] Normal population distribution vs. CLT |
|Chapter 9: Estimation Using a Single Sample – Confidence Intervals (3 weeks)* |
|9.1 Point Estimation |
|9.2 Large-Sample confidence Interval for a Population Proportion |
|Skill: Confidence interval for a population proportion using calculators |
|9.3 Confidence Interval for a Population Mean |
|Skill: Confidence interval for a population mean using calculators |
|9.4 Communicating and Interpreting the Results of Statistical Analyses |
|Free Response Questions from AP Exams: 2002(B)(4), 2004(B)(2), 2005(5) |
|Chapter 10: Hypothesis Testing Using a Single Sample (3 weeks)* |
|10.1 Hypotheses and Test Procedures |
|10.2 Errors in Hypothesis Testing |
|10.3 Large-Sample Hypothesis Tests for a Population Proportion |
|10.4 Hypothesis Tests for a Population Mean. What do we do if [pic]is unknown? t-distributions and the t-table for significance tests |
|and confidence intervals |
|Skill: Hypothesis test for a population mean using the calculator |
|10.5 Type I & II errors, Power Type I and II error in context. |
|10.6 Communicating and Interpreting the Results of Statistical Analyses. Technical details One-tailed vs. two-tailed tests; P-values |
|vs. fixed significance levels; cautions and warnings. |
|Activity: Calculator program that connects these three concepts |
|Free Response Questions from AP Exams: 2003(2), 2004(B)(3), 2005(4) |
|Chapter 11: Comparing Two Populations or Treatments (3 weeks)* |
|11.1 Inferences Concerning the Difference Between Two Populations or Treatment Means, using Independent Samples. |
|Skill: Inferences about differences in independent means, using the calculator. |
|11.2 Inferences Concerning the difference Between Two Populations or Treatment Means using Paired Samples. |
|Skill: Inferences about differences in means with paired samples. |
| 11.3 Large Sample Inferences Concerning a Difference Between Two Population or Treatment Proportions. |
|Skill: Inferences for Differences in Proportions using the calculator. |
|Free Response Questions from AP Exams: 1998(4), 2000(4), 2002(5), 2003(B)(3 and 4), 2004(B)(3 and 4), 2005(B)(4 and 5), 2006(B)(3 and |
|4). |
| Chapter 12: The Analysis of Categorical Data and Goodness-of-Fit Tests (1 week)* |
| 12.1 Chi-Square Tests for Univariate Categorical Data. The chi-square family of curves. |
|Activity: M&M color distributions – Goodness-of-fit Test. |
|12.2 Chi-square tests for Homogeneity and Independence in a two-way table. |
|Skill: Homogeneity and Independence Chi-square test on the calculator. |
| 12.3 Communicating and Interpreting the Results of Statistical Analysis and Computer output. |
|Free Response Questions from AP Exams: 1998(3), 1999(2), 2003(5) 2003(B)(5). |
|Chapter 13: Simple Linear Regression and Correlation: Inferential Methods ( 1 week)* |
|13.1 The Simple Linear Regression Model. |
|Activity: Investigating Old Faithful eruption data. |
|13.2 Inferences About the Slope of the Population Regression Line. |
|Skill: Regression inference on the calculator. |
|13.3 Checking Model Adequacy – Interpreting computer output. |
| Free Response Questions from AP Exams: 1999(1), 2002(B)(1), 2002(4), 2003(B)(2), 2004(B)(1), 2005(3), 2005(B)(5), 2006(2). |
Review for the Advanced Placement Examination - (10 class periods, including a full practice AP exam)
* Mock Grading Sessions
* Practice Multiple Choice Questions
* Practice AP Free Response Questions
* Practice and Review in the AMSCO’s AP Statistics Book.
AFTER THE AP EXAM: Students complete a Case Study Project, alone or in teams, on a topic of their choosing. In this project they apply most of what they have learned in the course. Both a written analysis and a brief oral power point presentation are required for this project. If time is allowed, we introduce Analysis of Variance.
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