AP Statistics Leanne Hankins Martinsville High School Course Description: AP Statistics involves the study of four main areas: exploratory analysis; planning a study; probability; and statistical inference. According to the College Board, upon entering this course students are expected to have mathematical maturity and quantitative reasoning ability. Mathematical maturity can be defined as a complete working knowledge of the graphical and algebraic concepts through Math Analysis, including linear, quadratic, exponential, and logarithmic functions. In contrast to many other math courses, this course will require reading of the text. AP statistics is taught as an activity based course in which students actively construct their own understanding of concepts and techniques of statistics. Primary Textbook, References and Resource Materials (Noted with the following letters in the Course Outline) B Bock, Vellum & DeVeaux. Stats: Modeling the World. Edition, Pearson Education, Inc., 2007. Y Yates, Moore & Starnes. The Practice of Statistics. Edition, W.H. Freeman and Company, 2008 TI Texas Instruments Nspire (used with Nspire & 84 faceplates) handheld device FRQ Selected AP Statistcs Exam Free Response Questions are used throughout the course W Worksheets for reinforcement, introduction of concepts or review O Other resource materials used in the classroom come from articles in Newspapers, journals, and the internet. Students often bring in data sets they collect or download from the internet. HW Homework problems assigned from the Bock, Vellum & DeVeaux textbook. Some problems listed are worked in class as discussion problems Course Projects: Course projects are in the form of extended formal writing assignments. As a consequence, form and technical adequacy are enforced. These assignments are given throughout the year. The main purpose of these course projects is for students to gain a strong experience in developing statistical studies and making sound connections and judgments between the design and the results of an experiment. Part (/3 of project grade) You will revisit the information you collected in your experimental design project. Analyze the data you collected in each project using an appropriate test for inference. Were your original results valid? Were all necessary assumptions for each test met? What can you reasonably conclude from your data? Part 2 (2/3 of project grade) You may work alone or with a partner. If you work with a partner, this project will count as two quiz grades. If you work alone, you may choose to count this project as two quiz grades or a test grade. The first task is to decide on an appropriate and interesting question to investigate. Part of answering the question must involve a hypothesis test, confidence interval, and/or regression. You may collect your data via an observational study, a survey, or an experiment. If you choose a study, you must obtain your data through firsthand sources. School surveys must be preapproved by the administration, and must be done representatively. You must use at least 40 pieces of data. Collect your data as you described in your initial report.
If you worked in a pair, include a list of all the specific duties each partner completed. Each partner is expected to contribute equally to this project. Format and Style It must be word-processed. Use an application such as Equation Editor or Math Type for mathematical expressions, equations, and symbols. It must have a cover page that includes all pertinent information. All symbols you use must be defined in context. All formulas must be shown and set up. Graphs and tables must be neat, labeled, and accurate. Graphs may be either hand-drawn or computer-generated. Do not use or show Calculator-Speak. (For example: I then used LinReg L, L3 to find the equation. ) Summer Assignment: Read Chapters (Stats Starts Here) and 2(Data) and complete 5 problems from pg 6 (-26). Course Pacing: Chapter 3: Displaying and Describing Categorical Data Approximate Topics Course overview I. A. Cumulative Policies and Expectations frequency plot Discuss Summer Assignment. Center and spread 2. Clusters and Gaps Rules of Data Analysis Frequency Tables Bar Charts Pie Charts Segmented Bar Charts Contingency Tables Conditional Distributions Examining Contingency tables 2 Review Quiz Project Assigned Read Chapters & 2 5 problems from pg 6-8 pg 36 (-44) Chapter 4: Displaying Quantitative Data Histograms Stem-and-Leaf Displays Dotplots Think Before You Draw, Again Shape Center and Spread Displaying Quantitative Data Comparing Distributions Comparing Infant Deaths Timeplots: Order, Please! I. A.. Center and spread 2. Clusters and Gaps pg. 63 (-42)
Re-expressing Skewed Data to Improve Symmetry Review Quiz 2 Review - Chapters -4 Test Chapters -4 Chapter 5: Describing Distributions Numerically Finding the Center: The Median I.B. Spread 2. Measuring spread Spread: The Interquartile Range 4. Using boxplots pg. 90 (-50) 5 Number Summary Rock Concert Deaths: making Boxplots Comparing Groups with Boxplots Comparing Groups: Summarizing Symmetric Distributions The Formula For Averages (Say it in Greek) Mean or Median? What About Spread? The Standard Deviation Thinking About Variation Shape, Center and Spread Summarizing Distribution: Step- By-Step Chapter 6: Standard Deviation as a Ruler and the Normal Model The Standard Deviation as a ruler I.B. Standardizing with Z-scores 2. Standard deviation Shifting Data 3. Z-scores Rescaling Data Back to Z-scores Working with Standardized Variables: When is a Z-score BIG? The 68-95-99.7 Rule The First Three Rules for Working with Normal Models Working with the 68-9599.7 Rule: pg. 23 (-50) pg. 3 (-40) as Unit Review
Finding Normal Percentages by Hand Finding Normal Percentage Using Technology Working with Normal Models : From percentages to Scores: Z in Reverse Working with Normal Models II: Step-by-Step More Working with Normal Models: How Does a Normal Probability Plot Work? Review Quiz 2 Review Chapters 5 & 6 Test Ch 5 & 6 Project due Chapter 7: Scatterplots, Association, and Correlation Approximate Topics Looking at Scatterplots I. D. Scatterplot Details. Scatterplots Roles of Variables 2. Correlation 4. Residual plots Correlation Correlation Conditions Looking at Associations: Step-By- Step Correlation Properties Correlation Tables Straightening Scatterplots Project 2 assigned 5 problems from pg. 60 (-36) Chapter 8: Linear Regression The Linear Model Residuals Best Fit Means Least Squares Correlation and the Line How Big Can Predicted Values Get? The Regression Line in Real Units I.D. 2 Linearity 3. Regression lines 4. Residual plots pg. 89 (-50)
Calculating a Regression Equation: Residuals Revisited R2 The Variation Accounted For How Big Should R2 Be? A Tale of Two Regressions Regressions: Reality Check: Is the Regression Reasonable? Review Quiz 2 Review Ch 7 &8 Test Ch 7 & 8 Chapter 9: Regression Wisdom Shifting Residual for Groups Subsets Getting the Bends I.D. pg. 23 (-28) Extrapolation: Reaching Beyond the Data Predicting the Future Outliers, Leverage and Influence Lurking Variables and Causation Working with Summary Values Chapter 0: Re-expressing Data: Get It Straight Straightening Relationships Everybody Does It Goals of Re-expression The Ladder of Powers Re-expressing to Straightening a Scatterplot: Plan B: Attack of the Logarithms Multiple Benefits Why Not Just User a Curve pg. 20 (-3) pg. 245 (-43) as Unit Review Review Quiz 2 Review Ch 9 & 0 Test Ch 9 & 0 Project 2 due Chapter : Understanding Randomness
It s Not Easy Being Random Practical Randomness A Simulation 2 Simulation: Project 3 assigned pg. 267 (-36) Chapter 2: Sample Surveys Idea : Examine a Part of the Whole Idea 2: Randomize Idea 3: It s the Sample Size pg. 289 (-32) Does a Census Make Sense? Population and Parameters Simple Random Samples Stratified Sampling Cluster and Multistage Sampling Systematic Samples Sampling: Who s Who? or, How to Sample Badly Chapter 3: Experiments and Observational Studies Observational Studies Randomized, Comparative Experiments The Four Principals of Experimental Design Diagrams Designing and Experiment: Step- By-Step Does the Difference Make a Difference? Experiments and Samples Control Treatments Blinding pg. 33 (-43) pg. 39 (-44) as Unit Review
Placebos Blocking Adding More Factors Confounding Lurking or Confounding Review Quiz 2 Review Ch -3 Test Ch -3 Project 3 due Chapter 4: Randomness to Probability Dealing with Random Phenomena Probability The Law of Large Numbers Project 4 assigned Probability pg. 339 (-36) Equally Likely Outcomes Personal Probability Formal Probability Putting Rules to Work Probability: Chapter 5: Probability Rules The First Three Rules of Probability Using the General Additional Rule: It Depends The General Multiplication Rule pg. 363 (-46) Independence Independent Disjoint Depending on Independence Tables and Conditional Probability Are the Disjoint? Independent?: Drawing Without Replacement Tree Diagrams Reversing the Conditioning Review Quiz
2 Review Ch 4 & 5 Test Ch 4 & 5 Chapter 6: Random Variables Expected Value: Center First Center, Now Spread Expected Values and Standard Deviations for Discrete Random Variables: Step=By-Step More About Means and Variances Hitting the Road: pg. 38 (-40) Continuous Random Variables Packaging Stereos: Chapter 7: Probability Models Searching for Tiger The Geometric Model Independence Working on the Geometric Model: pg. 398 (-36) The Binomial Model Working with the Binomial Model: pg. 403 (-42) as The Normal Model to the Rescue Unit Review Continuous Random Variables Review Quiz 2 Review Ch 6 & 7 Test Ch 6 & 7 Project 4 Due Chapter 8: Sampling Distribution Models Modeling the Distribution of Sample Proportions How Go Is the Normal Model A Sampling Distribution Model for a Proportion Working with Sampling Distribution Models for Proportions: Project 5 assigned pg. 428 (-42)
What About Quantitative Data? Simulating the Sampling Distribution of a Mean The Fundamental Theorem of Statistics The Real World and the Model World But What is Normal? Working with the Sampling Distribution Model for the Mean: Standard Error Sampling Distribution Models Chapter 9: Confidence Intervals for Proportions A Confidence Interval What Does 95% Confidence Really Mean Margin of Error: Certainty vs. Precision Critical Values A Confidence Interval for a Proportion pg. 446 (-38) Chapter 20: Testing Hypothesis about Proportions Hypothesis Testing Hypotheses A Trial as a Hypothesis Test What to Do with an Innocent Defendant The Reasoning of Hypothesis Testing Alternate Alternatives Testing a Hypothesis: Step-By- Step P-Values and Decisions: What to pg. 469 (-30)
Tell About Hypothesis Testing Tests and Intervals: A Better Confidence Interval a for Proportions Review Quiz 2 Review Ch 8-20 Test Ch 8-20 Chapter 2: More About Tests Zero In on the Null Another One-Proportion Z-Test: How to Think About P-values Alpha Levels What Not To Say About Significance 8 problems from pg. 49 (-28) Critical Values Again Confidence Intervals and Hypothesis Test Wear that Seatbelt: Making Errors Power A Picture is Worth Reducing Both Type I and Type II Errors Chapter 22: Comparing Two Proportions Another Ruler The Standard Deviation of the Difference Between Two Proportions The Sampling Distribution A Proportion Z-interval: Step- By-Step Will I Snore When I m 64? Everyone Into the Pool Compared to What? A Two-Proportion Z-Test: Step- 8 problems from pg. 507 (-30) pg. 53 (-38) as Unit Review
By-Step Review Quiz 2 Review Ch 2 & 22 Test Ch 2 & 22 Project 5 Due Chapter 23: Inferences About Means Getting Started Gosset s t What Does This Mean For Means? Finding t-values By Hand A One-Sample t-interval for the Mean: Project 6 assigned pg. 54 (-36) More Cautions About Interpreting Confidence Intervals Make a Picture, Make a Picture, Make a Picture A Test for the Mean A One-Sample t-test for the Mean: Significance and Importance Intervals and Tests Sample Size Degrees of Freedom Chapter 24: Comparing Means Plot the Data Comparing Two Means A Two-Sample t-interval: Step- By-Step Another One Just Like the Other One? Testing the Difference Between Two Means A Test for the Difference Between Two Means pg. 567 (-34)
A Two-Sample t-test for the Difference Between Two Means: Back Into the Pool The Pooled t-test Is the Pool All Wet? Why Not Test the Assumption That the Variances are Equal? Is There Ever a Time When Assuming Equal Variances Makes Sense? Turkey s Quick Test Chapter 25: Paired Samples and Blocks Paired Data A Paired t-test: Confidence Intervals for Matched Pairs A Paired t-interval: pg. 586 (-30) Project 5 assigned pg. 597 (-36) for Unit Review Review Quiz 2 Review Ch 23-25 Test Ch 23-25 Project 6 Due Chapter 26: Comparing Counts Goodness-of-Fit Calculations One-Sided or Two-Sided? A Chi-Squared Test for Goodness-of-Fit The Chi-Squared Calculation But I Believe the Model Comparing Observed Distributions pg. 628 (-34)
Calculations A Chi-Square Test for Homogeneity: Examining Residuals Independence A Chi-Square Test for Independence: Chi-Square and Causation Chapter 27: Inferences for Regression The Population and the Sample Which Comes First: the Conditions or the Residuals pg. 659 (-36) Regression Inference: Step-By- Step Intuition About Regression Inference Standard Error for the Slope Project 5 assigned What About the Intercept? Regression Inference Another Example pg. 672 (-30) A Regression Slope t-test: Step- By-Step Standard Errors for Predicting Values Confidence Intervals for Predicting Values Review Quiz 2 Review Ch 26 & 27 Test Ch 26 & 27 Review for AP Exam Notes: