Unit 1 – Exploring and Understanding Data (25 Days)



AP Statistics Syllabus for AP Audit

Lindsey Box

Union High School

Tulsa, Oklahoma

Brief Description of Course

AP Statistics is a year-long introductory course for students who have successfully completed Algebra II and wish to complete studies equivalent to a one-semester, introductory, non-calculus based college course in statistics. The purpose of this AP course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Through demonstration, hands-on activities, and classroom discussions, students acquire proficient experience in understanding the importance of verbal and written communications of statistical concepts. Students will explore and analyze data using graphical and numerical techniques. Students will also use probability and statistical inferences to develop an appropriate model for data collected. AP Statistics can be taken alone or in conjunction with another math course.

Primary Textbook

Bock, David E., Paul F. Velleman and Richard D. DeVeaux. Stats: Modeling the World. 3rd edition; Boston: Pearson/Addison-Wesley, 2010.

Technology

Students are expected to have at least a TI83 to use for all homework and assessments throughout the course. Classroom sets are available for use in class. In the classroom, a TI-SmartView with a Promethean Interactive White Board and a document camera are used regularly. A variety of online Java applets, Minitab, Powerpoint, and websites are used to illustrate course content. Students are also exposed to computer output from Minitab, JMP, and Fathom when applicable.

Homework

Students will be given an assignment sheet for each unit. Some of the problems on the assignment sheet will be completed in class with a partner. The purpose of these exercises will be to give students the opportunity to discuss statistics with other students as well as provide examples for that chapter. The remaining problems, as noted on the assignment sheet in bold, are the problems that will be turned in for a grade. These exercises comprise the most representative problems for that chapter and must show all required work and be written in complete sentences.

Problem of the Day

Each day, when students arrive to class, they begin working on the problem of the day that is displayed on the Smartboard. When students arrive to class, they are to sit down and start working on that day’s problem of the day. Students must explain/justify their answer.

AP Questions

Students will be given an AP Question Packet containing the released AP Statistics free response questions. Students will also be provided a schedule at the beginning of each semester entailing when each AP Free Response problem is due. AP questions will be graded using the AP rubrics. AP style multiple choice questions will also be assigned for each unit. Students are randomly assigned to partners and each pair will have 25 minutes to answer 10 to 15 multiple choice questions.

Quizzes/Tests

Both chapter and cumulative quizzes are given regularly throughout the course. Quizzes will typically be given once per chapter and will count as one-third of a test grade. Quizzes may be made up of multiple choice and/or free response style questions.

Tests will be given after each unit of material covered and contain both multiple choice and free response questions. The multiple choice portion of the test will comprise 40% of the score and the free response portion will comprise the remaining 60%. Unit tests are designed to emulate the AP Exam given in May.

Projects

Throughout the year, students will be required to complete and present several projects involving topics discussed in class. Many course projects are in the form of extended writing assignments and will be assessed based on the clarity of communication in addition to the mathematics presented. Some projects will require the use of computer software.

Unit 1 – Exploring and Understanding Data (25 Days)

|Number of Days |Chapter/Topic/Activity/Assignments |AP Statistics Course Topic Outline |

|1 day | | |

| |Chapter 1 – Stats Starts Here | |

| | | |

| |Topics covered: | |

| |Introduction to Statistics, Data, and Variation. | |

| | | |

| |Assignments: | |

| |Read: Read Chapter 1 | |

|2 days | | |

| |Chapter 2 – Data | |

| | | |

| |Topics covered: | |

| |Analyzing Data – Who, What, When, Where, Why, How | |

| |Categorical vs. Quantitative Variables | |

| |TI: Entering data and working with data lists | |

| | | |

| |Assignments: | |

| |Read Chapter 2 | |

| |Pg. 16 #1, 9, 12 | |

|3 days | |I. Exploring Data |

| |Chapter 3 – Displaying and Describing Categorical Data |E. Exploring categorical data |

| | |1.Frequency tables and bar |

| |Topics covered: |charts |

| |Frequency and Relative Frequency Tables |2.Marginal and joint |

| |Distributions of Categorical Variables |frequencies for two-way tables |

| |Importance of the Area Principle |3.Conditional relative |

| |Bar and Pie Charts |frequencies and association |

| |Contingency Tables |paring distributions |

| |Marginal and Conditional Distributions |using bar charts |

| |Independence of Categorical Variables | |

| |Segmented Bar Charts | |

| |Simpson’s Paradox | |

| | | |

| |Webpages/Articles: | |

| | | |

| | | |

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| | | |

| | | |

| | | |

| |Projects/Lab Activities: | |

| |Write and design a newspaper article summarizing data given for Race and the Death Penalty. Use | |

| |appropriate graphical displays. | |

| |Analyzing Bad Graphs - Find a graph in a newspaper, magazine, or on the internet that is an | |

| |example of a violation of the area principle. Explain how the graph is misleading and what should | |

| |be changed to improve it. | |

| | | |

| |Assignments: | |

| |Read Chapter 3 | |

| |Pg. 38 #6-8, 11-17, 19, 21, 23, 28, 30 | |

| |Smoking and Education worksheet | |

|3 days | |I. Exploring Data |

| |Chapter 4 – Displaying and Summarizing Quantitative Data |A. Constructing and interpreting |

| | |graphical displays of distributions of |

| |Topics covered: |univariate data (boxplot, stemplot, histogram, |

| |Distributions of Quantitative Variables |cumulative frequency plot) |

| |Frequency and Relative Frequency Histograms |1. Center and spread |

| |Stem-and-Leaf Displays |2. Clusters and gaps |

| |Dotplots |3. Outliers and other |

| |Describing a Distribution in terms of shape, outliers, center, and spread (SOCS) |Unusual features |

| |Shape: Modality, Uniformity, Symmetry, Skewness, Unusual Observations, Gaps, and Clusters |4. Shape |

| |Center and Spread in General Terms |C. Comparing distributions of |

| |Comparing Distributions |univariate data (dotplots, |

| |Timeplots |back-to-back stemplots, parallel boxplots) |

| |TI: Creating a Histogram |Comparing center and |

| | |spread within group, between group variation |

| |Applets: |Comparing clusters and |

| |Effects of Bin Width on Histograms |gaps |

| | |Comparing outliers and |

| |Assignments: |other unusual features |

| |Read Chapter 4 |Comparing shapes |

| |Pg. 72 #9-11, 14, 18, 26, 30, 48 | |

| |Investigative Task: Dollars for Students | |

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| | | |

|5 days | |I. Exploring Data |

| |Chapter 5 – Summary Statistics |A. Constructing and interpreting |

| | |graphical displays of distributions of |

| |Topics covered: |univariate data (boxplot, stemplot, histogram, |

| |Measures of Central Tendency (Mean, Median, Mode, and Midrange) |cumulative frequency plot) |

| |Measures of Spread (Range, IQR, Variance, Standard Deviation) |1. Center and spread |

| |Five Number Summary |2. Clusters and gaps |

| |Quartiles/Percentiles |3. Outliers and other |

| |Calculating Outlier “Fences” |unusual features |

| |Boxplots |4.Shape |

| |Comparing Multiple Datasets |B. Summarizing distributions of |

| |Resistance vs. Non-resistance to Extreme Values |univariate data |

| |Cumulative Frequency Graphs |Measuring center: median |

| |TI: Creating a Boxplot, Finding the Five Number Summary, Calculating the Mean and Standard |and mean |

| |Deviation |Measuring spread: range, |

| | |interquartile range, standard deviation |

| |Video: |Measuring position: |

| |TED Talk: Religion and Babies |quartiles, percentiles, standardized scores |

| | |(z-scores) |

| | |4. Using boxplots |

| |Projects/Lab Activities: |C. Comparing distributions of |

| |Auto Safety Investigative Task – Students analyze and compare auto safety records among small, |univariate data (dotplots, back-to-back |

| |mid-size, and large vehicles using graphical and numerical measures in order to draw a conclusion |stemplots, parallel boxplots) |

| |concerning insurance policies. |paring center and |

| | |spread within group, between group variation |

| |Assignments: |paring clusters and |

| |Read Chapter 5 |gaps |

| |Pg. 95 #5-10, 15, 16, 21, 35, 36 |paring outliers and |

| |Mooseburgers vs. McTofu boxplot comparison activity |other unusual features |

| | |paring shapes |

|6 days | |I. Exploring Data |

| |Chapter 6 – The Standard Deviation as a Ruler and the Normal Model |B. Summarizing distributions |

| | |of univariate data |

| |Topics covered: |3. Measuring position: |

| |Introduction to Standardized Scores (z-scores) |quartiles, percentiles, standardized scores |

| |Shifting Data by Adding or Subtracting a Constant Value |(z-scores) |

| |Rescaling Data by Multiplying or Dividing by a Constant Value |5. The effect of changing |

| |Normal Models |units on summary measures |

| |Parameters vs. Statistics | |

| |Standard Normal Model | |

| |Empirical Rule (68-95-99.7 Rule) |III. Anticipating Patterns |

| |Tables of Normal percentiles to calculate probabilities for a Normal Model and to find z-scores |C. The normal distribution |

| |for a given percentile. |1. Properties of the normal |

| |Assessing Normality |distribution |

| |Normal Probability Plots |2. Using tables of the |

| |TI: Finding Normal Probabilities, Finding z-scores for a given percentile, Creating a Normal |normal distribution |

| |Probability Plot |3. The normal distribution |

| | |as a model for |

| |Assignments: |measurements |

| |Read Chapter 6 | |

| |Pg. 129 #8-16, 25, 26, 38, 40, 42 | |

| |Normal Models Investigative Task | |

|5 days |Unit Assessments | |

| |Quiz – Chapter 2/3 | |

| |Quiz – Chapter 4/5 | |

| |Unit 1 Vocab Crossword Puzzle | |

| |Unit 1 Review | |

| |Unit 1 Multiple Choice Test | |

| |Unit 1 Free Response Test | |

Unit 2A – Exploring Relationships Between Variables (11 days)

|Number of Days |Chapter/Topic/Activity/Assignments |AP Statistics Course Topic Outline |

|2 days | |I. Exploring Data |

| |Chapter 7 – Scatterplots, Association, and Correlation |D. Exploring bivariate data |

| | |1. Analyzing patterns in |

| |Topics covered: |scatterplots |

| |Introduction to Bivariate Data |2. Correlation and linearity |

| |Creating a Scatterplot | |

| |Describing a Scatterplot in terms of Direction, Form, Strength, and Unusual Observations | |

| |Explanatory vs. Response Variables | |

| |Calculating Correlation | |

| |Conditions Required for Correlation | |

| |Properties for Correlation | |

| |Correlation Tables | |

| |Correlation vs. Association | |

| |Lurking Variables and Causation | |

| |TI: Creating a Scatterplot, Calculating Correlation | |

| | | |

| | | |

| |Webpages/Articles: | |

| | | |

| | | |

| |Assignments: | |

| |Read Chapter 7 | |

| |Pg. 164 #3-8, 10-12, 16, 18, 20, 23-26, 32, 33, 26, 40 | |

|5 days | |I. Exploring Data |

| |Chapter 8 – Linear Regression |D. Exploring bivariate data |

| | |1. Analyzing patterns in |

| |Topics covered: |scatterplots |

| |Linear Models |2. Correlation and linearity |

| |Predicted Values |3. Least-squares regression |

| |Line of Best Fit |lines |

| |Regression to the Mean |Residual plots, outliers, |

| |Least Squares Regression Line (LSRL) |and influential points |

| |Finding the Slope and Y-intercept of the LSRL using Summary Statistics | |

| |Interpreting the Slope and Y-Intercept of the LSRL | |

| |Calculating and Interpreting Residual Values | |

| |Creating and Interpreting a Residual Plot | |

| |Understanding and Interpreting the Coefficient of Determination | |

| |Assumptions and Conditions for the Linear Regression Model | |

| |Reading Computer Output for Regression | |

| |TI: Finding the LSRL, Adding a Line to a Graph of Data points, Creating a Residual Plot | |

| | | |

| |Projects/Lab Activities: | |

| |Height vs. Foot Length Lab – Students will gather data about the class heights and foot lengths in| |

| |order to analyze and interpret the data as a review of the chapter’s content. | |

| | | |

| |Assignments: | |

| |Read Chapter 8 | |

| |Pg. 192 #1-6, 8, 10-12, 16, 18, 20, 22 | |

| |Distance & Price worksheet | |

| |Smoking and Coronary Heart Disease Investigative Task | |

|4 days |Unit Assessments | |

| |Quiz – Chapter 7 | |

| |Unit 2A Review | |

| |Unit 2A Multiple Choice Test | |

| |Unit 2A Free Response Test | |

Unit 2B – Exploring Relationships Between Variables (8 Days)

|Number of Days |Chapter/Topic/Activity/Assignments |AP Statistics Course Topic Outline |

|2 days | |I. Exploring Data |

| |Chapter 9 – Regression Wisdom |D. Exploring bivariate data |

| | |3.Least-squares regression |

| |Topics covered: |lines |

| |Abuses of Regression |4.Residual plots, outliers, |

| |Exploring Subsets of Data |and influential points |

| |Non-linear datasets | |

| |Dangers of Extrapolation | |

| |Examining Outliers in Regression Models | |

| |Lurking Variables and Causation | |

| |Working with Summary Values | |

| | | |

| |Articles: | |

| |Women may outsprint men by 2156 – Article illustrating extrapolation in the news | |

| | | |

| | | |

| |Assignments: | |

| |Read Chapter 9 | |

| |Pg. 215 #1-3, 9, 12 | |

| |Graduating Class worksheet | |

| |The Wandering Point activity | |

|4 days | |I. Exploring Data |

| |Chapter 10 – Re-expressing Data: It’s Easier Than You Think |D. Exploring bivariate data |

| | |3. Least-squares regression |

| |Topics covered: |lines |

| |Linear vs. Non-linear growth |Residual plots, outliers, |

| |Re-expressing data sets |and influential points |

| |Using the Ladder of Powers |5. Transformations to |

| |Using logarithms to straighten scatterplots, including the Exponential, Logarithmic, and Power |achieve linearity: logarithmic and power |

| |models. |transformations |

| |TI: Using logarithms to re-express data, Creating residual plots | |

| | | |

| |Projects/Lab Activities: | |

| |Alligators Investigative Task – Students will analyze non-linear bivariate data regarding the | |

| |length and weights of alligators in order to make the best prediction of weight for an alligator | |

| |of a given length. Students must also weigh the pros and cons of possible influential outliers. | |

| | | |

| |Assignments: | |

| |Read Chapter 10 | |

| |Pg. 239 #5, 6, 15, 16 | |

|2 days |Unit Assessments | |

| |Unit 2B Review | |

| |Unit 2B Test | |

Unit 3 – Gathering Data (18 Days)

|Number of Days |Chapter/Topic/Activity/Assignments |AP Statistics Course Topic Outline |

|3 days | |III. Anticipating Patterns |

| |Chapter 11 – Understanding Randomness |A. Probability |

| | |5. Simulation of random |

| |Topics covered: |behavior and probability distributions |

| |Understanding the Concept of Randomness | |

| |How the Mind is Not Random | |

| |Pseudorandom Numbers | |

| |Tables of Random Digits | |

| |Conducting a Simulation | |

| |Components of a Simulation (outcomes, trials, response variables) | |

| |TI: Seeding the Random Number Generator, Generating Random Numbers | |

| | | |

| |Video: | |

| |Numberphile video: Random Numbers | |

| | | |

| | | |

| |Projects/Lab Activities: | |

| |Simulation Project – Students will create their own scenario that can be modeled by a probability | |

| |simulation and present their problem and solution in poster format. | |

| |ESP Investigative Task – Students will design a simulation to test a friend’s claim of having ESP.| |

| |Streaky Behavior Lab – Students will explore real randomness vs. perceived randomness by examining| |

| |coin flips to determine the length of a “streak” of heads in a real coin flip sequence. | |

| | | |

| |Assignments: | |

| |Read Chapter 11 | |

| |Pg. 265 #5-7, 19 | |

| |Dart Simulation worksheet | |

| 4 days | |II. Sampling and Experimentation: |

| |Chapter 12 –Sample Surveys |Planning and conducting a study |

| | |A. Overview of methods of data |

| |Topics covered: |collection |

| |Sample Statistics vs. Population Parameters |1.Census |

| |The Good and the Bad of Polling |2.Sample survey |

| |Why Randomization is Important in Sampling |B. Planning and conducting |

| |How Sample Size Plays a Role in Sampling |surveys |

| |Taking a Census |Characteristics of a well- |

| |Sampling Frame |designed and well-conducted survey |

| |Sampling Variability |Populations, samples, and |

| |Statistical Sampling Methods: Simple Random Sampling, Stratified Random Sampling, Cluster |random selection |

| |Sampling, Multistage Sampling, Systematic Sampling |3. Sources of bias in |

| |Nonstatistical Sampling Methods – Voluntary Response Sampling, Convenience Sampling |sampling and surveys |

| |Bias in Sampling – Voluntary Response Bias, Sampling from a Bad Sampling Frame, Undercoverage, |4. Sampling methods, |

| |Overcoverage, Nonresponse Bias, Response Bias, Poorly Worded Questions |including simple random sampling, stratified |

| |Projects/Lab Activities: |random sampling, and cluster sampling. |

| |JellyBlubbers – Students will attempt to estimate the average length of the JellyBlubber colony |D. Generalizability of results and |

| |using a variety of sampling methods. They will compare the accuracy of the methods. |types of conclusions that can be drawn from |

| |Video: |observational studies, experiments and surveys |

| |Opinion Polls and the 2012 Presidential Election | |

| | |

| |olls-random-sampling | |

| | | |

| |Article: | |

| |How Polls are Conducted by Gallup | |

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| | | |

| | | |

| |Assignments: | |

| |Read Chapter 12 | |

| |Pg. 288 #1-4, 7-10, 15-18, 20, 22, 25-28 | |

| |Describe the Bias worksheet | |

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|6 days | |II. Sampling and Experimentation: Planning and |

| |Chapter 13 – Experiments |conducting a study |

| | |Overview of methods of data collection |

| |Topics covered: |3. Experiment |

| |Observational Studies vs. Experiments |4. Observational study |

| |Types of Observational Studies – Retrospective vs. Prospective |C. Planning and conducting |

| |Elements of an Experiment |experiments |

| |Experimental Units, Subjects, and Participants |Characteristics of a well- |

| |Explanatory Variables, Factors, Levels, and Treatments |designed and well- |

| |Response Variables |conducted experiment |

| |Principles of Experimental Design (Control, Randomization, Replication, and Blocking) |2. Treatments, control |

| |Completely Randomized Experimental Designs |groups, experimental units, random assignments |

| |Idea of Statistical Significance |and replication |

| |Control Treatments and Control Groups |3. Sources of bias and |

| |Blinding (Single and Double Blind) |confounding, including placebo effect and |

| |Placebo and Placebo Effect |blinding |

| |Randomized Block Experimental Designs |4. Completely randomize |

| |Matched Pairs Designs |design |

| |Idea of Confounded Variables |5. Randomized block design, |

| | |including matched pairs design |

| | |D. Generalizability of results and |

| |Projects/Lab Activities: |types of conclusions that can be drawn from |

| |Experimental Design Task – Students will locate an article describing an experimental study, then |observational studies, experiments and surveys |

| |answer several questions concerning the study. | |

| |Gummy Bears in Space – Students will conduct and analyze an experiment of launching gummy bears | |

| |and measuring the distance. | |

| | | |

| |Video: | |

| |Experiments, Observational Studies, and Drawing Conclusions | |

| | | |

| | | |

| |Assignments: | |

| |Read Chapter 13 | |

| |Pg. 312 #6-8, 12, 22, 24, 26, 33 | |

|5 days |Unit Assessments | |

| |Quiz – Chapter 11 | |

| |Quiz – Chapter 12 | |

| |Unit 3 Review | |

| |Unit 3 Multiple Choice Test | |

| |Unit 3 Free Response Test | |

Unit 4A – Randomness and Probability (12 days)

|Number of Days |Chapter/Topic/Activity/Assignments |AP Statistics Course Topic Outline |

|3 days | |III. Anticipating Patterns |

| |Chapter 14 – From Randomness to Probability |A. Probability |

| | |1. Interpreting probability, |

| |Topics covered: |including long-run relative frequency |

| |Difference between randomness and chaos |interpretations. |

| |Probability as a Long Run Relative Frequency |2. “Law of Large Numbers” |

| |Language of Probability – Trials, Outcomes, and Events, Sample Space |concept |

| |Fundamental Counting Rule |3. Addition rule, |

| |General Idea of Independence |multiplication rule, conditional probability, |

| |Law of Large Numbers |and independence |

| |Basic Rules of Probability | |

| |Complement Rule | |

| |Addition Rule for Disjoint Events | |

| |Multiplication Rule for Independent Events | |

| |Union and Intersection of Two Events | |

| |Introduction to Venn Diagrams | |

| | | |

| |Video: | |

| |Brain Games: Risk | |

| | | |

| |Projects/Lab Activities: | |

| |Law of Large Numbers – Students will roll a single die 100 times and calculate the simulated | |

| |chance of each outcome. We will compile the results from all students to explore how the outcomes | |

| |relate to the theoretical probabilities of each outcome. | |

| | | |

| |Assignments: | |

| |Read Chapter 14 | |

| |Pg. 338 #1, 2, 6-8, 11, 12, 19-24, 31, 32 | |

| |Wheel of Savings worksheet | |

| |Sum of Two Dice probability worksheet | |

|5 days | |III. Anticipating Patterns |

| |Chapter 15 – Probability Rules |A. Probability |

| | |1. Interpreting probability, |

| |Topics covered: |including long-run relative frequency |

| |Probability for Equally Likely Events |interpretations. |

| |General Addition Rule |2. “Law of Large Numbers” |

| |Conditional Probability |concept |

| |General Multiplication Rule |3. Addition rule, |

| |Formal Idea of Independence |multiplication rule, conditional probability, |

| |Independent Events vs. Disjoint Events (Revisited) |and independence |

| |Drawing with and without Replacement | |

| |Making a Picture – Venn Diagrams, Probability Tables, and Tree Diagrams | |

| |Introduction to Bayes’ Rule | |

| | | |

| |Video: | |

| |Numberphile video: Monty Hall Problem | |

| | | |

| | | |

| |Projects/Lab Activities: | |

| |Let’s Make a Deal game – Students will be participants in a classroom version of the game show | |

| |Let’s Make a Deal. They will be presented with the Monty Hall problem and decide which strategy | |

| |works best: stick or switch? | |

| | | |

| |Assignments: | |

| |Read Chapter 15 | |

| |Pg. 361 #1-10, 42, 45, 46 | |

| |Venn Diagram worksheet | |

| |Drug Testing and Bayes’ Rule worksheet using tree diagrams | |

|4 days | | |

| |Unit Assessments | |

| |Quiz – Chapter 14 | |

| |Quiz – Chapter 15 | |

| |Unit 4A Review | |

| |Unit 4A Test | |

|3 days |Semester Review and Exam | |

Unit 4B –Randomness and Probability (13 days)

|Number of Days |Chapter/Topic/Activity/Assignments |AP Statistics Course Topic Outline |

|4 days | | |

| |Chapter 16 – Random Variables |III. Anticipating Patterns |

| | |A. Probability |

| |Topics covered: |4. Discrete random variables |

| |Random Variables |and their probability distribution, including |

| |Discrete and Continuous Random Variables |binomial and geometric |

| |Creating a Probability Model for Discrete Variables |6. Mean (expected value) and |

| |Expected Values of Random Variables |standard deviation of a random variable, and |

| |Variance and Standard Deviation of Random Variables |linear transformation of a random variable |

| |Linear Transformations of Random Variables |B. Combining independent |

| |Combining Independent Random Variables |random variables |

| |Combining Normal Random Variables |Notion of independence |

| |TI: Calculating Mean and Standard Deviation for Probability Models |versus dependence |

| | |2. Mean and standard |

| |Projects/Lab Activities: |deviation for sums and differences of |

| |Casino Lab – Students will run trials of well-known casino games and record the results. They will|independent random variables. |

| |calculate the expected value for each of the games. | |

| | | |

| |Assignments: | |

| |Read Chapter 16 | |

| |Pg. 383 #1-6, 9-16, 20, 22, 24-27, 33-36, 42 | |

|5 days | | |

| |Chapter 17 – Probability Models |III. Anticipating Patterns |

| | |A. Probability |

| |Topics covered: |4. Discrete random |

| |Properties of Bernoulli Trials |variables and their probability distribution, |

| |Properties of the Geometric Model |including binomial and geometric |

| |Calculating Geometric Probabilities |5. Simulation of random |

| |Calculating the Expected Value and Standard Deviation for a Geometric Model |behavior and probability distributions |

| |Properties of the Binomial Model |6. Mean (expected value) |

| |Calculating Binomial Probabilities |and standard deviation of a random variable, and|

| |Calculating the Expected Value and Standard Deviation for a Binomial Model |linear transformation of a random variable |

| |Simulating Binomial and Geometric Probability Models |B. Combining independent random variables |

| |Normal Approximation to the Binomial Model |1. Notion of independence |

| |TI: Calculating Geometric Probabilities, Calculating Binomial Probabilities |versus dependence |

| | |2. Mean and standard |

| |Assignments: |deviation for sums and differences of |

| |Read Chapter |independent random variables. |

| |Pg. 401 #2-5, 8, 10, 12, 15-17, 19, 21, 26, 30 | |

|4 days | | |

| |Unit Assessments | |

| |Quiz – Chapter 16 | |

| |Unit 4B Review Activity – Probability Around the World | |

| |Unit 4B Test | |

Unit 5 – From the Data at Hand to the World at Large (32 days)

|Number of Days |Chapter/Topic/Activity/Assignments |AP Statistics Course Topic Outline |

|6 days |Chapter 18 – Sampling Distribution Models | |

| |Topics covered: |III. Anticipating Patterns. |

| |Simulating a Sampling Distribution Model |D. Sampling distributions |

| |Sampling Variability |1. Sampling distribution |

| |Describing the Sampling Distribution Models for Sample Proportions in terms of Center, Spread, and |of a sample proportion |

| |Shape |2. Sampling distribution |

| |Assumptions and Conditions for the Sampling Distribution Model of Sample Proportions |of a sample mean |

| |Calculating Probabilities Based on the Sampling Distribution Model of Sample Proportions |3. Central Limit Theorem |

| |Describing the Sampling Distribution Models for Sample Means in terms of Center, Spread, and Shape |6. Simulation of |

| |Central Limit Theorem |sampling distributions |

| |Assumptions and Conditions for the Sampling Distribution Model of Sample Means | |

| |Calculating Probabilities Based on the Sampling Distribution Model of Sample Means | |

| |Law of Diminishing Returns | |

| |Standard Error of the Sampling Distribution Model | |

| | | |

| |Lab Activity: | |

| |Flipping Coins Lab – Using a penny, students will flip the coin 25 times, recording the proportion | |

| |of heads and repeat this several times. By combining the data, the class will explore the sampling | |

| |distribution for sample proportions. | |

| | | |

| |Applets: | |

| |Convergence of the Sum of Dice to Normality | |

| |Central Limit Theorem for Means | |

| | | |

| |Projects: | |

| |Simulated Coins Investigative Task – Students will explore and describe the sampling distribution | |

| |for sample proportions using a random number generator to simulate the flipping of a fair coin. | |

| | | |

| |Assignments: | |

| |Read Chapter 18 | |

| |Pg. 432 #2, 4-6, 8-13, 16-20, 30, 44, 46-48, 50, 52, 54 | |

|5 days | | |

| |Chapter 19 – Confidence Intervals for Proportions |IV. Statistical Inference |

| | |Estimation (point estimators and confidence |

| |Topics covered: |intervals) |

| |Sampling Variability |Estimating population parameters and margins |

| |Estimating Population Parameters |of error |

| |Point Estimates |Properties of point estimators, including |

| |Margin of Error |unbiasedness and variability |

| |Interpreting Confidence Levels | |

| |Critical Values of z* |Logic of confidence intervals, meaning of |

| |Creating a One-Proportion Z-Interval |confidence level and confidence intervals, and|

| |Interpreting Confidence Intervals |properties of confidence intervals |

| |Assumptions and Conditions for a One-Proportion Z-Interval |Large sample confidence interval for a |

| |Calculating Minimum Sample Size for a given Margin of Error |proportion |

| |TI: Calculating a One-Proportion Z-Interval | |

| | | |

| |Projects/Lab Activities: | |

| |Skittles Lab – Using a bag of Skittles, students will sample with replacement, recording the | |

| |proportion of red skittles in 30 draws, and create a confidence interval to estimate the proportion | |

| |of red skittles. Students will graph their CI on the chart paper on the board to illustrate the | |

| |concepts of sampling variability and confidence level. | |

| |Capture/Recapture | |

| | | |

| |Applets: | |

| |Understanding Confidence applets/confidenceinterval.html | |

| |Assignments: | |

| |Read Chapter 19 | |

| |Pg. 455 #2, 4, 6, 8-12, 24, 28, 35, 36 | |

| | | |

|5 days | |IV. Statistical Inference |

| |Chapter 20 – Testing Hypotheses About Proportions |B. Test of significance |

| | |1. Logic of significance |

| |Topics covered: |testing, null and alternative hypotheses;|

| |Logic of a Hypothesis Test |p-values; one- and two-sided tests |

| |Null vs. Alternate Hypotheses |3. Large sample test for |

| |Idea of Rejecting vs. Retaining the Null Hypothesis |a proportion |

| |Conducting a One-Proportion Z-Test | |

| |Calculating a Probability Value (P-Value) | |

| |Assumptions and Conditions for a One-Proportion Z-Test | |

| |One-sided vs. Two-sided Hypothesis Tests | |

| |Drawing Conclusions from our Data | |

| |How Hypothesis Tests and Confidence Intervals are Related | |

| |TI: Calculating a One-Proportion Z-Test | |

| | | |

| |Assignments: | |

| |Read Chapter 20 | |

| |Pg. 476 #1, 2, 4-18, 20-24 | |

|4 days | | |

| |Chapter 21 – More About Tests |IV. Statistical Inference |

| | |B. Test of significance |

| |Topics covered: |1. Logic of significance |

| |P-values as a Conditional Probability |testing, null and alternative hypotheses; |

| |Making a Decision based on an Alpha Level |p-values; one- and two-sided tests |

| |Critical Values for a Hypothesis Test |2. Concepts of Type I |

| |Comparing a Hypothesis Test to a Confidence Interval |and Type II errors and concept of power |

| |Type I and Type II Errors | |

| |Power of the Test | |

| |The Relationship between Alpha, Beta, and Power | |

| |Effect Size | |

| | | |

| |Applets: | |

| |Relationship Between Type I Errors, Type II Errors, and the Power of the Test | |

| | | |

| | | |

| |Projects/Lab Activities: | |

| |Making a Decision Project – Students will create an original scenario, identifying the null and | |

| |alternate hypotheses and then describing the Type I error, Type II error and Power of the test in | |

| |the context of their scenario. | |

| |Life After High School Investigative Task | |

| | | |

| | | |

| |Assignments: | |

| |Read Chapter 21 | |

| |Pg. 499 #1-4, 7-14 | |

|4 days | |III. Anticipating Patterns. |

| |Chapter 22 – Comparing Two Proportions |D. Sampling distributions |

| |Topics covered: |4. Sampling distribution |

| |Sampling Distribution Model for the Difference Between Two Independent Proportions |of a difference between two independent sample|

| |Assumptions and Conditions for Two-Proportion Inference |proportions |

| |Creating a Two-Proportion Z-Interval | |

| |Idea of Pooling |IV. Statistical Inference |

| |Conducting a Two-Proportion Z-Test |Estimation (point |

| |Relationship between an Interval and a Test |estimators and confidence intervals) |

| |TI: Calculating a Two-Proportion Z-Interval, Calculating a Two-Proportion Z-Test |5. Large sample |

| | |confidence interval for a difference between |

| |Assignments: |two proportions |

| |Read Chapter 22 |B. Test of significance |

| |Pg. 519 #1-14, 16, 18, 19, 21, 22 |4. Large sample test for |

| | |a difference between two proportions |

| | | |

|8 days |Unit Assessments | |

| |Quiz – Chapter 18 | |

| |Quiz – Chapter 19 | |

| |Quiz – Chapter 20 | |

| |Quiz – Chapter 22 | |

| |Unit 5 Lab Activity – Pass the Pigs Lab – Students will gather data using the game “Pass the Pigs”, | |

| |then analyze the data, using all of the inference techniques from Unit 5. | |

| |Unit 5 Review | |

| |Unit 5 Multiple Choice Test | |

| |Unit 5 Free Response Test | |

Unit 6 –Learning About the World (10 days)

|Number of Days |Chapter/Topic/Activity/Assignments |AP Statistics Course Topic Outline |

|3 days | |III. Anticipating Patterns. . |

| |Chapter 23 – Inferences About Means |D. Sampling distributions |

| | |7. t-distribution |

| |Topics covered: | |

| |Standard Error of the Sample Mean |IV. Statistical Inference |

| |T-distribution |Estimation (point estimators and confidence |

| |Degrees of Freedom |intervals) |

| |When to Use the Z-distribution vs. the T-distribution |Estimating population |

| |Assumptions and Conditions for Inference for Means |parameters and margins of error |

| |Calculating a One-Sample T-Interval for Means | |

| |Interpreting a Confidence Interval for Means |2. Properties of point |

| |Normal Probability Plots Revisited |estimators, including unbiasedness and |

| |Conducting a One-Sample T-Test for Means |variability |

| |Drawing a Conclusion Based on a Test for Means |6.Confidence interval for a |

| |Relationships between Intervals and Tests |mean |

| |Calculating a Minimum Sample Size for a Given Margin of Error |B. Test of significance |

| |TI: Calculating probabilities for the T-distribution, Calculating a One-Sample T-Interval, |5. Test for a mean |

| |Calculating a One-Sample T-Test | |

| | | |

| |Projects/Lab Activities: | |

| |JellyBlubber Lab – Students will gather data by taking an SRS of JellyBlubbers in order to | |

| |estimate the true mean length of the colony by creating a confidence interval for the mean. | |

| |Students will then chart the intervals on a class graph to illustrate the meaning of 95% | |

| |confidence. | |

| | | |

| |Assignments: | |

| |Read Chapter 23 | |

| |Pg. 554 #1, 2, 7-12, 17-20, 23-28 | |

|2 days | | |

| |Chapter 24 – Comparing Means |III. Anticipating Patterns |

| | |D. Sampling distributions |

| |Topics covered: |5. Sampling distribution of a |

| |Sampling Distribution Model for the Difference Between Two Independent Means |difference between two independent sample means|

| |When to Use the Z-distribution vs. the T-distribution | |

| |Assumptions and Conditions for Two-Sample Inference for Unpaired Means | |

| |Creating a Two-Sample T-Interval for Unpaired Means |IV. Statistical Inference |

| |Idea of Pooling |Estimation (point estimators and confidence |

| |Conducting a Two-Sample T-Test for Unpaired Means |intervals) |

| |Relationship between an Interval and a Test |7. Confidence interval for a |

| |TI: Calculating a Two-Sample T-Interval for Unpaired Means, Calculating a Two-Sample T-Test for |difference between two means (unpaired and |

| |Unpaired Means |paired) |

| | |B. Test of significance |

| |Assignments: |6. Test for a difference |

| |Read Chapter 24 |between two means (unpaired and paired) |

| |Pg. 579 #1-10, 26, 27 | |

|3 days | | |

| |Chapter 25 – Paired Samples and Blocks |IV. Statistical Inference |

| | |Estimation (point estimator |

| |Topics covered: |and confidence intervals) |

| |Paired Data vs. Independent Samples |7. Confidence interval for a |

| |Assumptions and Conditions for Inference for Paired Means |difference between two means (unpaired and |

| |Creating a Matched-Pairs T-Interval for Means |paired) |

| |Conducting a Matched-Pairs T-Test for Means |B. Test of significance |

| |TI: Creating a Matched-Pairs T-Interval for Means, Conducting a Matched-Pairs T-Test for Means |6. Test for a difference |

| | |between two means (unpaired and paired) |

| |Lab Activities: | |

| |Timing Your Reaction Lab – Students will gather data using a Reaction Timer and a yardstick for | |

| |their dominant and non-dominant hands and analyze the data using 2-sample inference methods for | |

| |independent samples (males vs. females) and dependent samples (dominant vs. non-dominant) | |

| | | |

| |Assignments: | |

| |Read Chapter 25 | |

| |Pg. 602 #1-8, 11, 12, 14, 15, 20, 21 | |

|2 days |Unit Assessments | |

| |Unit 6 Review | |

| |Unit 6 Test | |

Unit 7 –Inference When Variables Are Related (10 days)

|Number of Days |Chapter/Topic/Activity/Assignments |AP Statistics Course Topic Outline |

|5 days | | |

| |Chapter 26 – Comparing Counts |III. Anticipating Patterns. . |

| | |D. Sampling distributions |

| |Topics covered: |8. Chi-square distribution |

| |Chi-Square Distribution | |

| |Chi-Square Test of Goodness of Fit |IV. Statistical Inference |

| |Assumptions and Conditions for Chi-Square Tests |B. Test of significance |

| |Expected Counts vs. Observed Counts |7. Chi-square test for |

| |Chi-Square Test of Homogeneity |goodness of fit, homogeneity of proportions and|

| |Chi-Square Test of Independence |independence (one- and two-way tables) |

| |TI: Calculating a Chi-Square Test for Goodness of Fit, Calculating a Chi-Square Test for a Table | |

| | | |

| |Lab Activities: | |

| |Chi Square M&Ms Lab – Students will gather data on Plain and Peanut Butter M&Ms in order to | |

| |illustrate the difference between Chi Square Tests for Goodness of Fit, Independence, and | |

| |Homogeneity | |

| | | |

| |Assignments: | |

| |Read Chapter 26 | |

| |Pg. 642 #1-6, 9-15, 17-20 | |

|3 days |Chapter 27 – Inferences for Regression |IV. Statistical Inference |

| | |Estimation (point estimators |

| |Topics covered: |and confidence intervals) |

| |Idealized Regression Model |8. Confidence interval for |

| |Assumptions and Conditions for Inference for Regression |the slope of a least- squares regression line |

| |Sampling Distribution Model for the Slope of the Regression Line |B. Test of significance |

| |Constructing a T-Interval for the Slope of the LSRL |8. Test for the slope of a |

| |Conducting a T-Test for the Slope of the LSRL |least-squares regression line |

| |Reading Computer Output | |

| |TI: Calculating a T-Interval for the Slope, Calculating a T-Test for the Slope | |

| | | |

| |Assignments: | |

| |Read Chapter 27 | |

| |Pg. 672 #1-4, 7-10, 13-17, 19, 21 | |

|2 days |Unit Assessments | |

| |Unit 7 Review | |

| |Unit 7 Test | |

Unit 8 –AP Exam Review (12 days)

|Number of Days |Chapter/Topic/Activity/Assignments |AP Statistics Course Topic Outline |

|11 days | | |

| |Review for AP Exam | |

| | | |

| |Topics covered: | |

| |Mock AP Exam using 2002 Released Multiple Choice and most recently released Free Response | |

| |Practice Multiple Choice Questions from AP Review Books | |

| |Item Analysis of Practice Exams | |

| |Practice Investigative Tasks from previously released Free Response | |

| |Review sessions after school for each unit of material covered | |

| |Topic Outline with detailed review | |

|1 day |AP Exam | |

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