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AP Statistics High School Textbooks Students are issued two textbooks and we use both during the course/year. Students are assigned reading and problems from both textbooks. Understandable Statistics. Brase and Brase. 7th edition. Houghton Mifflin Company. ISBN# 0618-20554-3. 2003. Introduction to the Practice of Statistics. Moore, McCabe. 3rd edition. W. H. Freeman and Company. ISBN# 0-7167-3502-4. 1999. Additional Resources I have numerous statistics textbooks that I use to supplement materials/reading as needed. I have downloaded all of the College Board Free Response questions since 1997 and use these problems during the course. Each unit test includes 2-4 Free Response questions applicable to that topic/unit. I have all the 1997/2002 multiple choice questions and use these problems to help students master concepts. I recently purchased the booklet, AP Statistics Module: Sampling and Experimentation: Planning and Conducting a Study. I have a number of review books/manuals that I use and lend to students as applicable including: College Board Statistics – Teacher Guide College Board AP Statistics 2006-2007 Professional Development Workshop Materials Special Focus: Interface McGraw-Hill 5 Steps to a 5: AP Statistics Review Book. Duane C. Hinders D&S Marketing Systems AP Statistics Multiple Choice and Free Response Questions Test Prep Booklet Texas Instruments – Explorations Statistics Handbook for the TI-83 Venture Publishing – Introduction to Statistics with the TI-83 Graphing Calculator. Robert Schneider, George Best. Barron’s – How to Prepare for the AP Statistics Exam. 3rd edition. Martin Sternstein. Activity Based Statistics – Richard Scheaffer. AP Exam All our students are strongly encouraged to take the AP exam in May. Our school will pay for this exam for students that cannot afford the exam fee. page 1 Technology All students are expected to have a TI-83, 83+, 84, 84+ for their use in class and for homework assignments. For students that cannot afford a calculator our school will provide a loaner calculator for that student for the course. All students have access to the two computer labs at our school. The graphing calculator is used everyday in class and students are instructed daily on how to use this technology to help them understand statistical concepts. Students are required to use computer software for their projects during the year. John Bapst uses Fathom Software for AP Statistics. During the course students are exposed to “generic software” outputs and become proficient at reading these outputs. After the AP Exam we use Fathom extensively for their final project. Students are exposed to numerous applets during the course and I have a computer and LCD projector in my classroom. Course Introduction (from our Student Handbook) AP Statistics Prerequisite or Co-requisite: 90% average in Honors Pre-Calculus This is a year long college-level statistics course. Students will be required to do a lot of reading/work on their own. Topics include: Exploring Data, Planning a Study, Probability, and Statistical Inference. Graphing calculators are integral to this course, John Bapst will provide if needed. It is strongly encouraged that all students take the AP Exam in May. Course Objectives By the end of this class students should be able to analyze data to make relevant, intelligent, real world decisions and: 1. Be able to analyze data using numerous graphical/tabular types 2. Be able to analyze data using density/normal curves 3. Understand correlation/causation with data samples 4. Use the LSRL to describe a data set 5. Model and describe non-linear relationships 6. Design an appropriate experiment that is valid and reliable 7. Understand randomness as it is related to probability/data sampling 8. Solve probability problems using both a binomial and geometric distribution 9. Understand sampling distributions as a basis for statistical inference 10. Use confidence intervals and tests of significance to analyze data 11. Understand the difference between a Type I and II error 12. Compare two sample means for statistical inference 13. Use population proportions for statistical inference 14. Use inference/two-way tables to test for goodness of fit 15. Use inference for the regression line and slope of the LSRL 16. To communicate concepts and ideas in a clear manner, using correct statistical vocabulary and notation. 17. Use technology to help solve problems, experiments, interpret results, and verify conclusions. 18. To recognize and develop a thorough plan for collecting data in order to make a valid conjecture. page 2 Throughout the course students are required to communicate their thoughts well, using correct statistical language/knowledge in the context of the problem. Throughout the course, connections are made between the four major themes of the course so students can see how these concepts are interrelated. I want the course to be a continuous learning process, not a number of isolated topics. Inference is talked about on the first day of class, as is the role of controlled experiments. Course Outline Itemized below is a detailed summary of the major topics/concepts covered in each unit/chapter. Since I use two different textbooks, the order of the units does not correspond exactly with the chapters in either textbook. Unit 1: Exploring Data – Numerically and Graphically Univariate Data (2 weeks) Types of data Reading, Interpreting, Analyzing Graphs Graph types including: Pie Charts Bar Graphs Histograms Dot Plots Stem and Leaf Plots/Back to Back Stem and Leaf Cumulative Frequency Graphs Ogives Normal Probability Plots Scatter Plots Connected Scatter plots – Time Plot Box Plots – Regular and Modified Analyzing graphs including SOCS Shape Outliers Center Spread Numerical analysis of data including - Calculating and Interpreting: Mean Median Mode Range-Spread IQR Q1 Q3 Standard Deviation/Variance Mean Absolute Deviation Outliers Unit 2: Density Curves/Normal Curves/Normal Distribution (2 weeks) Density curves – shape/properties page 3 Skewness – left/right Mean/median of density curves Resistance Normal distributions Empirical Rule (1,2,3 Standard Deviations) Chebyshev’s Theorem Percentiles Standardizing Data – Z scores Reading a Z Table Normal/Curve Equation – Points of Inflection Area under a curve – percentile/probability Normal probability plot Normal “looking” data – Assessing Data for Normalcy Unit 3: Bivariate Data – Graphing/Describing (2.5 weeks) Scatterplots Explanatory/Response Variable Correlation – Positive/Negative Interpreting Scatterplots Outliers/Influential Points – The difference between the two Correlation Coefficient (r) – Meaning/Interpreting/Properties of Covariance High correlation does not imply/prove causation The Least Squares Regression Line (LSRL) Properties of the LSRL The components of the LSRL Residuals – Residual Plots – How to interpret residual plots Coefficient of Determination (r2) – How to calculate, meaning of Reading/Interpreting Generic Computer Outputs Unit 4: Linearizing Data – Exponential/Power Models (1.5 weeks) Linearizing non-linear data Review of Rules of Logs/Natural Logs Residuals – Residual Plots – What they mean/how to interpret Extrapolation/Interpolation Lurking Variables/Confounding Variables Correlation does not prove causation 2 way tables – Interpreting Marginal/Conditional Distributions Describing relations between categorical variables Simpson’s Paradox Unit 5: Samples/Experiments/Simulation (3 weeks) Data collection page 4 Bias – How to minimize bias when collecting data Types of bias – Undercoverage/Non-response/Question Wording Sample vs. Population Sampling Methods Convenience Sampling Cluster Sampling Systematic Sampling Random Sampling Simple Random Sampling (SRS) Stratified Random Sample Multi-Stage Random Sample Experimental Design Control Randomization Replication Placebos/Placebo Effect Control Groups/Control Control for lurking and confounding variables Blocking Factors/Levels/Treatments Matched Pairs Observational Studies Surveys Scope of Inference Simulations- Using the calculator random digit tables Reading/Using Random Digit tables Unit 6: Probability (1.5 weeks) Basic Probability Rules/Concepts/Compliment of Randomness/Chance Behavior Independent vs. Dependent Sample Space/Total Events Probability Diagrams/Tress Venn Diagrams With Replacement/Without Replacement Disjoint/Mutually exclusive events Joint Probability Conditional Probability Additional/Multiplication Rules for Probability Bayes Theorem Unit 7: Random Variables (1.5 weeks) Discrete vs. Continuous Variables/Distributions Discrete probability histograms Continuous random variables/distributions/graphs Area under a curve concept/probability page 5 Means/Variances of Random Variables Why variances add and standard deviations don’t Law of large numbers Fallacy of the “Law of Small Numbers” Unit 8: Binomial and Geometric Distributions (1.5 weeks) Binomial Distributions 4 requirements of a binomial setting Binomial Probability Distribution Function Binomial Cumulative Distribution Function TI-83 calculator steps Binomial probability formulas Mean/Standard Deviation of a binomial random variable Geometric Distributions 4 requirements of a geometric setting Geometric probability distribution function TI-83 calculator steps Geometric probability formulas Mean/Standard Deviation of a geometric random variable Unit 9: Sampling Distributions (2 weeks) Introduction to Statistical Inference Samples-Statistics Population – Parameters Sampling Variability – The importance of sample size Sampling Distributions Unbiased Statistics Bias/Variability Sample Proportions Standard Deviation of a sample proportion distribution Rules of thumb for comparing a distribution to a normal distribution Sample Means Standard deviation of a sample mean Central Limit Theorem Sample statistics as unbiased estimator of the population parameter Unit 10: Introduction to Statistical Inference (2.5 weeks) Confidence Intervals – Meaning of/Constructing Margin of Error/Meaning of/How it is calculated Z Score critical values (mention t-score for future chapters) upper/lower Standard error Importance of sample size to minimize error Tests of significance (Hypothesis Tests) Null Hypothesis/Alternate Hypothesis page 6 Z Score to calculate P (Probability Value) Significance Level/Meaning of Checking conditions/assumptions for Hypothesis Testing HAMC = 1. State Hypothesis 2. Check Assumptions 3. Do the Math – Calculate the P Value 4. Conclusion in the context of the problem Confidence Interval vs Hypothesis Tests – How these 2 tests can “tell” us the same information Practical uses/interpretations of hypothesis tests Type I/Type II errors – Real world examples Power of a hypothesis test = (1-Type II error) Unit 11: Inference for Means – T Distributions (2 weeks) T distributions – Family of Curves T table vs. Z table/Reading a T table Degrees of Freedom (again) ZAPTAX – Mr. T is always mean (Z table always for Proportions/T table always for Means) One sample T statistic Standard error Matched Pairs Design Confidence Intervals/Hypothesis Tests for one sample mean Sample size and normalcy Comparing 2 sample means (difference of) Confidence intervals/hypothesis tests for 2 sample means TI-83 steps Choosing d(f) (degrees of freedom) for 2 samples – 3 methods – How/when to use each method Reading/Interpreting generic computer outputs Unit 12: Inference for Proportions (2weeks) Inference for 1 sample proportions Standard deviation of the sample proportion Standard Error Relate proportions to a binomial/setting/distribution When n is large enough, assume normalcy reading a Z table Assumptions/Rules of Thumb Confidence Intervals/Hypothesis Test for 1 sample proportion Calculating sample size Comparing two sample proportions Confidence Intervals/Hypothesis Test for 2 sample proportions (difference of) Pooling for 2 samples TI-83 calculator step Making decisions based upon inference tests page 7 Unit 13: Inference Using Chi-Square (2 weeks) Chi-Square Distributions Degrees of Freedom Reading/Interpreting a Chi-Square Table Chi-Square Goodness of Fit Test TI-83 calculator steps Chi-Square formulas Assumptions when using Chi-Square Tests Chi-Square test for Homogeneity 2 way tables Chi-Square Test for Independence Calculating expected counts Degrees of Freedom – How to calculate Discuss when to use each of these Chi-Square tests Importance of sample size/expected count size Unit 14: Inference of Regression (1.5 weeks) Review scatter plots Predicted LSRL True Regression Line Unbiased estimators for True Slope (β), True Intercept (α), and Standard Deviation (σ) Standard Error about the LSRL Degrees of Freedom Confidence Intervals for the True Slope (β) Hypothesis Testing for the True Slope (β) TI-83 calculator steps Assumptions required for this type of inference Reading/Interpreting generic computer outputs for the Inference for Regression Using inference to make accurate interpretations and predictions with data Unit 15: Review for AP Statistics Exam – (2-3 weeks or as time/schedule permits) Complete the 2002 AP Exam under time constraints in class Review major concepts/themes of the course Review calculator usage Exam strategies/tips Preparing for the AP Statistics Exam AP Statistics Grading Policies/Assessment Homework: Homework is typically assigned every night and will include reading and practice problems. Consistent with our school policies, homework will count as 20% of each quarters final grade. page 8 Quizzes: Quick in-class quizzes will be given on an as needed basis Tests: Major/rigorous exams will be given for each unit/chapter. Exams/quizzes/projects will count as 80% of each quarters final grade. Test Corrections (see attached policy): Students are strongly encouraged to take advantage of my test correction policy for each exam. These are an integral component of the learning process for this course and will help students learn the required material/concepts. AP Statistics Projects (see attached sample project): This course lends itself to some interesting and fun, real world projects. Students will collect and interpret data using the tools/skills learned in this course. A major project is typically assigned for each quarter and this grade will be equivalent to a test grade. Projects must be typed, professional and include graphs/tables/charts as applicable. Students will use Fathom Software to produce these graphs as applicable. Projects typically count as 1-2 test grades in that quarter. AP Statistics Post Exam: Students work on/complete their final, year end inclusive project which ties in the different major themes of the course after the AP Exam. Emphasis on this final project includes connecting the four major themes of the course as well as using Fathom Software. Depending upon time constraints we may continue with ANOVA and/or multiple regression. page 9 Test Corrections High School Test corrections allow you to earn back up to one half of the points you missed on every test. In order to earn the maximum amount of credit, you must do the following things for each question. Identify in writing what your mistakes are. This may include a lack of understanding of the question, operational errors, faulty solving method, or something else. “I was clueless” is not an acceptable answer. Your errors need to be explained. Indicate in writing how to solve the problem. Explain in a few words the process you will use to solve the problem. Work out the problem showing step-by-step detail, arriving at the correct solution. Your solution must be correct in every way. (Fractions reduced, like term combined, radicals rationalized, etc.) No credit is given for an incorrect solution. Label each question and indicate the number of points lost for each question (i.e.: I lost 3 points on question #4) Your corrections must be typed, provided that ALL questions missed are attempted; however, in no instance will a student be given points that would bring their test grade over a score of 99. Research aids you may use to determine the correct solution include your text, other students, teachers, parents, the Internet, or any other source you choose. You may not receive help from a teacher on the day the corrections are due. Work will be neat, clearly labeled, and stapled to the front of your test. TEST CORRECTIONS ARE DUE 1 WEEK FROM THE DAY YOUR TESTS ARE PASSED BACKED TO YOU. THERE ARE NO EXCEPTIONS TO THE DUE DATE. Papers will be handed in at the beginning of class on the due date. If you are absent from school on the due date, the paper must be handed in before first period on your next school day. Do not wait until the next class, as your work will not be accepted. Summary 1. 2. 3. 4. 5. Neat, clear work stapled to the front of the quiz or test. Explanation of what the errors were. A detailed solution leading to the correct answer. Work completed on time. You can only ask the teacher questions on no more than 2 problems, the goal of this exercise is for you to learn how to solve the problem and do the appropriate work/research. page 10 Since test corrections are a privilege, not a right, it is important that you “earn” this privilege. When I pass out an exam I will randomly pick 4-6 homework problems from the chapter that I assigned for homework. As you begin the exam, I will check these homework problems. If you have not done these homework problems and/or do not have them in class with you, you will be “ineligible” to do test corrections for that chapter. I assume that you do your homework every night and keep them in your notebook, so this policy is inherently fair to every student. page 11 AP Statistics Project In this portfolio /project you will collect, interpret, analyze and then present data that is of specific interest to you. You must collect at least 100 data points and present your findings in at least two different types of graphs/charts/tables (of your choice). Your data must be real world, accurate, and easy for someone to verify. You must have an original hypothesis and use your presentations to help “prove or disprove” your original thoughts. As a minimum you must: Graphs/charts/table should be computer/calculator generated or extremely neatly produced. State how you collected your data A discussion of how comfortable you are with your data (Is it good, reliable data?) At least 3 additional things you could do to make your data/presentation better. A detailed discussion (in typed paper format) of what you are trying to prove/show and how you could use your graphs to persuade someone else of your point of view. Due Date: ___________________________ Late portfolios are penalized 15 points off per day late! page 12 Statistics Project (source unknown) This project counts as one test grade and requires that you select a topic to study that will yield numerical data. That is, you will need to find 100 or more distinct data points that you will use in your research. Your proposal should start with a null and alternate hypothesis; something along the lines of “I think that the average number of….” Or “I am interested in trying to determine the average number of…” Minimum requirements for this project are listed below. 1. Explain what it is that you wish to investigate. State your null hypothesis and your alternate hypothesis. Use H0 and Ha format. Justify the choice of <, > or ≠ for Ha. 2. Explain and justify your data collection method, making sure you’ve minimized bias as much as possible. 3. Collect your data and present it appropriately (graphically), using at least 2 different graph types. Include the data, mean, median, range, sample standard deviation, and sample size (n). 4. Choose two different confidence levels. 5. Compute a confidence interval and explain what this interval really means in the context of your project. 6. Find the sample size you would need to take for the margin of error to be half of what you found in your confidence interval. 7. Test your hypothesis and explain the results. Include z – scores and normal distribution graph. 8. Find the p – value for your test. What does this tell you? Explain your reasoning. 9. Write up your findings in a non-technical manner. That is, your explanation should be written as if it would be read by a person who had never taken a statistics course. For example, a report to your friends or a submission to the school newspapers. Project Assigned: ________________________________ Project Due Date: ________________________________ Grading will be based on the attached rubric. Late projects will be deducted 15 points per day late. page 13 Portfolio Assessment Rubric Presentation Organization 0 Portfolio is disorganized; entries are no identified; entries are not neat 1 Portfolio is somewhat organized 2 Portfolio entries are well identified, organized OR neat 3 Portfolio entries are well identified AND neat Accuracy 0 Outcome is not addressed 1 Outcome is partially addressed with many misstatements and errors 2 Outcome is partially addressed or has many misstatements and errors 3 Portfolio entries contain some misstatements, or is lacking in depth 4 Portfolio entries contain very few misstatements and explorations go into detailed analysis Quality 0 Outcome is poorly addressed 1 Portfolio entries show minimal understanding of the concepts which are the focus. Few applications are present 2 Portfolio entries show some understanding of the concepts. Entries are ORIGINAL student work. Some applications are present 3 Portfolio entries are ORIGINAL students work and show thorough understanding of the concepts with applications present 4 Portfolio entries are ORIGINAL student work and show thorough understanding of the concepts with applications present. Evidence of extensions of the concepts have been submitted. Creativity 0 Portfolio has no personal creativity 1 Portfolio has little to no creativity 2 Portfolio has minimal creativity 3 Portfolio shows some creativity in topic presentation 4 Student shows creativity in both examining the topic and its presentation Grammar/Writing Style 0 Writing contains so many grammatical errors it takes away from the paper/portfolio 1 Writing contains many grammatical errors 2 Writing contains few grammatical errors Technical Skills 1 Portfolio addresses only some of the objectives 2 Portfolio addresses most of the objectives 3 Portfolio addresses all of the objectives/outcomes of the assignment page 14