AP Statistics Syllabus – Revised June 2011 Course Number 1210320 Text: Stats Modeling the World, Bock, Velleman, De Veaux, 2010. Problem assignment references in the syllabus are to the corresponding section in the text. Course Design: The primary text provides the general design for this course. Students are required to read the chapters from the textbook before the topics are discussed in class so that students are more familiar with the topic and more time can be devoted to investigative activities and less time on lectures. Each student will be assigned a TI graphing calculator at the beginning of the year and it will be their property until the last day of class. If a student elects to use some other calculator, like the TI-Nspire or TI-89 they are responsible for being able to use it in a statistical setting. In all cases, students will be required to do all calculations (w/o graphing calculator function) until they have a good understanding what is involved in the calculation. Once that student has mastered the concepts involved in the calculation they will be instructed on how to do the same calculations using the TI-84 function and from that point on the students are free to answer questions with or w/o a graphing calculator. There will be several occasions throughout the year in which students will do activities involving computer generated reports. These activities will require students to be able to interpret the results and communicate their finding in a written report. The emphasis on all homework, classwork, and activity reports will be on the student’s ability to arrive at the correct conclusion along with communicating their results in appropriate statistical language. Hopefully, by the end of this course, students will realize that writing complete responses using appropriate justifications is a critical aspect of gaining statistical proficiency. Students will be assigned an investigative task for most chapters. These tasks will require the students to use, apply and analyze the topics they have learned in that chapter in a new setting. Student progress will be assessed using the standard chapter quizzes, unit tests, along with grades for homework, activity reports and there will be two major projects. Their midterm grade will be a comprehensive report on the material we covered in the first half of the year (one or two variable descriptive statistics) and the second major report will be their final grade and this report should be on the material we covered in the second half of the year (Inferential Statistics). Midterm and Final Project: Students will collect data or design and conduct an experiment to investigate a topic of their choosing. The written report should include a title and the following sections; o Introduction: Describe your topic to the reader and your motivation for picking this topic. o Methodology: How did you gather your data or how the experiment was conducted? o State all resources. o Results: Present the data in table or graph form in such a way that conclusions can easily be made. Make sure graphs are labeled appropriately. o Conclusions: State your conclusions in appropriate statistical terms or what conclusions can be drawn from your experiment. State any unusual finding that might cause concern. What was learned from this project? o Students will be given examples of excellent reports from past students along will reports that were considered unacceptable, so that students will have a better idea of what is expected of them. Students will be graded based on a rubric that they will have before the report is graded. Primary Textbook References and Resource Material (Noted with the following letters in the Course outline) Bock, Velleman, De Veaux, Stats Modeling the World. 3rd edition. Boston: Addison-Wesley, 2010. (BVD) Yates, Daniel, Moore, David, and Starnes, Daren. The Practice of Statistics. 2nd edition. New York: W.H.Freeman and Co., 2003. (YMS) V Annenber/CPB. Against All Odds: Inside Statistics. 26-30 minute video clips. Washington D.C.: The Annenburg/CPB Collection. 1989 Videocassettes www.learner.org Note: not all videos listed are shown during class time. Often students take the video home to review for a class or test. TI Texas Instrument TI-84 graphing calculator. Printed Test Bank and Resource Guide (TB) / Golden Binder (GB) are the ancillary materials provided by the texts BVD, YMS respectively. Both have a wide variety of activity exercises in which the students are encouraged to explore some phenomena and come to some type of statistical conclusion about what is happening. These activities will give students practice in communicating methods, results and interpretations using the vocabulary of statistics along with drawing connections between all aspects of the statistical process, including design, analysis and conclusions. Study Island: http://www.studyisland.com/ (SI) AP The College Board AP Statistics released exam problems will be used throughout the course with a heavier emphasis as we get closer to the AP exam. Homework problems Will be assigned from the Primary textbook unless otherwise noted. All questions will be answered in complete sentences and all conclusions will be written in context of the problem. Homework problems that involve the graphing calculator must first be set up with an appropriate equation and then the final answer can be recorded. ADDITIONAL TOPICS 1. Significant familiarity with the TI-84, shortcuts and special functions. 2. Additional work on simulations beyond the scope of the text. 3. Biographies of mathematicians who have contributed to the study of statistics. 4. Students will be given a weekly AP test practice problem. More intensive work on practice AP exams is done just before the exam. Curriculum and Pacing Guide Mathematics: AP Statistics Unit 1: Exploring and Understanding Data In this unit we cover data displays and summaries. Many students will recognize some of the material from middle and high school, so our emphasis is on statistical thinking. Of course, we define terms and provide examples. But we also discuss why methods presented are used, and what we hope to learn from them. These are concepts that appear throughout the course. Even more important than what to look for in a histogram or how to summarize the spread of a distribution is the underlying lesson that there are reasons for displaying and summarizing data. These reasons inform and motivate the entire course. Essential Questions: Why is statistics important? What is the nature of the data? Describe the type of graph that would be most appropriate for different data sets, and justify the choice. What are common distribution shapes and describe at least one characteristic of each. How can you quickly order data and, at the same time, reveal the distribution shape? What are commonly used measures of central tendency? What information do they provide? How do variance and standard deviation measure data spread? Why is this important? Given a boxplot, determine the five number summary and explain what is revealed about the spread of the data? Analyze the effects of adding/subtracting, multiplying/dividing on the mean and variance of a data set. What are some characteristics of a normal distribution? What does the empirical rule tell you about data spread about the mean? Can you compare apples and oranges? What is a standard normal distribution? What is a standard z score? How do you convert any normal distribution to a standard normal distribution? Days Chapter Topic 0 1 1 2 What is Statistics? - TB Class Survey 1-5, 1-6 Data 4 3 6 4 Displaying and Describing Categorical Data - TB WS 3-7 - (SI) Categorical Data Displaying and Summarizing Quantitative Data - Refer to YMS Ch 1 #6for constructing bar graph and circle graph - Refer to YMS Ch 1 # 14 for constructing a histogram - Supplementary material YMS Ch 1 #32 and 34 ; Resistant & Nonresistant - (SI) Central Tendency & Spread - (SI) Dotplots Concepts & Terms Assignment Read Ch. 1 pgs. 2-6 Data, Data table, Case, Population, Sample, Variable, Units, Categorical Variable, Quantitative Variable Frequency table, Relative frequency table, Distribution, Area principal, Bar Chart, Pie Chart, Categorical data condition, Contingency table, Marginal distribution, Conditional distribution, Independence, Independence, Segmented bar chart, Simpson’s paradox Distribution, Histogram, Gap, Stem-and-leaf display, Dotplot, Shape, Center, Spread, Mode, Unimodal, Bimodal, Uniform, Symmetric, Tails, Skewed, Outliers, Median, Range, Quartile, Interquartile range, Percentile, 5Number Summary, Mean, Resistant, Variance, Standard deviation Pgs.16-18 #2, 4, 8, 10, 14, 16, 26 D1:Pgs. 38-39 #6, 8-10, 12-16 even D2:Pgs. 39-40 #18-24 even D3:Pg. 41 #26-30 even D4:Pgs. 42-43 #32-38 even TB Investigative Task: “Race and the Death Penalty” D1: GB Quiz 1.1A for #1 do a bar graph and a circle graph; #2 do a histogram and a split stem plot. No description necessary. D2:GB Quiz 1.1A For both questions, describe the distribution. D3:Pgs.72-73 #6-14 even D4:Pgs. 73-75 #16-28 even D5:Pgs. 75-76 #30-42 even D6:Pgs 77-78 #48 TB Investigative Task “Dollars for Students” - 4 (SI) Stemplots (SI) Histogram (SI) Cumulative Frequency Plots Understanding and Comparing Distribution TB WS 5-5 - (SI) Boxplots 5 4 6 The Standard Deviation as a Ruler and the Normal Model - TB Class Example 6-4 2 1 21 Review Test Total Boxplot, Outlier, Far Outlier, Comparing distribution, Comparing boxplots, Timeplot Standardizing, Standardized value, Shifting, Rescaling, Normal model, Parameter, Statistic, Z-score D1:GB Quiz 1.2 B or C D2: Pgs.95-96 #6-12 even D3: Pgs. 97-100: #14, 16, 20, 24, 28 D4; Pg. 101 #34, 36 TB Investigative Task “Auto Safety”, “SUV Insurance” D1 & 2:Pgs. 129-130 #222 even D3: Pg. 131 #26-30 even D4: Pgs. 132-133 #38-42 even TB Investigative Task “Normal Model” Total Days: 21 Unit 2: Exploring Relationships between Variables In this unit we expand on the idea of considering a second variable. Chapters7, 8, and 9 discuss relationships between two quantitative variables, introducing scatterplots, correlation, and regression. The discussion is sophisticated and rich in new concepts and points of view, even though there is not mention of inference. We’ll see these methods (and inference for them) again in Chapter 27. Essential Questions: • How can a scatter plot be used to describe the association between quantitative variables in terms of form, strength, and direction? • Tell how to compute the correlation coefficient and what does it reveal about the strength of the linear relationship between two random variables? • What is the least-squares criterion? How do you find the equation of the least-squares line? • Explain the significance of the residual plot in an analysis of the least squares regression model. • What is the coefficient of determination, and what does it tell you about the explained variation of y in a random sample of data pairs (x,y)? • How would the slope of the least squares regression line be interpreted? • What procedure should be used, if any, when a nonlinear scatterplot is encountered? Days Chapter Topic Concepts & Terms Assignment 3 7 Scatterplots, Association, and Correlation - TB Class Example 7-3 & 7-7 - (SI) Scatterplots Scatterplots, Association, Outlier, Response variable, Explanatory variable, X-variable, Y-variable, Correlation Coefficient 4 8 Linear Regression - TB WS 7-7 Goes with Ch. 7&8 - TB Class Example 8-5 - TB WS 8-9 - (SI) Scatterplots Model, Linear model, Predicted value, Residuals, Least squares, Regression to the mean, Regression line, Line of best fit, Slope, Intercept, Standard deviation of the residuals, R2 D1: Pgs.164-165 #2-10 even D:2 Pgs. 165-167 #12-26 even D:3 Pg. 168 # 32 & 34 D4: Pg. 169 #36 D1: Pgs. 192-193 #2-10 even D2: Pg. 193 # 12-22 even D3: Pgs. 194-195 #24-32 even D4: Pgs. 195-196 # 34 & 36 4 9 4 10 2 1 18 Review Test Total Regression Wisdom - TB Class Example 9-3 - TB Class Activity 9-5 & 9-6 - TB WS 27-9 (SI) Scatterplots Re-expressing Data: Get it Straight - TB Class examples 10-3, 10-4, 10-5 - TB WS 10-7 - GB Quiz 4.1 A, B, or C - (SI) Scatterplots Extrapolation, Outlier, Leverage, Influential point, Lurking variable Re-expression, Ladder of Powers, Linear Transformation, exponential growth model, Power law model TB Investigative Task “Smoking” D1: Pgs. 214-215 #2-8 even D2: Pg. 216 #12-16 even D3: Pgs. 217-218 #20, 22 D4: Pgs. 218-219 #24, 26 Pg. 208 Just checking TB Investigative Task “Olympic Long Jumps” D1: Pg. 239 #2, 4 D2: Pgs. 239-241 #6-12 even D3: Pg. 241 #14 D4: Pg. 242 #18, 20 Total Days: 39 Unit 3: Gathering Data We’ve been examining data, noting patterns and relationships, and finding models to describe them. Now we address where these data come from. The essential insight in gathering data for statistical analysis is the central role of randomness. We sample randomly or assign subjects to treatments at random. We randomize to minimize biases and to reduce the influence of effects we cannot control.. Even more important, we randomize to make it possible to use statistical inference methods that can extend our understanding beyond the data at hand to the world at large. In this unit we discuss randomness, apply it to gathering data, formalize it with probability, and then connect it to the summaries and models of the first two parts with inference. Essential Questions: • How can a random sample be obtained? • What is the difference between a random sample and a simple random sample? • What are the other types of sampling techniques? Discuss the advantages and disadvantages of each type. • What types of bias can be encountered and why is it important to reduce bias? • Discuss the different types of random sampling designs and when it is appropriate to use each design. • Describe the difference between an observational study and an experiment? • Discuss the value of a control group. • What is the correct procedure for designing an experiment? Days Chapter Topic Concepts & Terms Assignment 2 11 Understanding Randomness - GB Quiz 5.1 B #3 - GB Quiz 5.3 C #3 - TB Class examples 11-4 &11-5 Random, Generating random numbers, Simulation, Simulation component, Trial, Response variable D1: Pg. 265 #2-10 even D2: Pg. 265 #12-16 even Population, Sample, Sample survey, Bias, Randomization, Sample size, Census, Population parameter, Statistic, Sample statistic, Representative, Simple random sample (SRS), Sampling frame, Sampling variability, Stratified random sample, Cluster sample, Multistage sample, Systematic sample, Pilot, Voluntary response bias Observational study, Retrospective study, Experiment, Random assignment, Factor, Response, Experimental units, Level, Treatment, Principles of experimental design, Statistically significant, Control group, Blinding, Simple-blind, Doubleblind, Placebo, Placebo effect, Blocking, Matching, Designs, Confounding D1: Pg. 288 #2-10 even D2: Pg. 289 #12-20 all D3: Pg. 290 #22-30 even D4: Pgs. 290-291 #32-36 even 4 12 Sample Surveys - TB Class examples 12-3, 12-4, 12-5 - GB Quiz 5.1 B #1,2 - (SI) Data Collection - (SI) Surveys 4 13 Experiments and Observational Studies - TB Class examples 13-4, 13-5, 13-6, 13-7 - (SI) Data Collection - (SI) Experiments 1 1 12 Total Days: 51 Review Test Total TB Investigative Task “ESP” D1: Pg. 312-313 #2-10 even D2: Pg. 313 #14-18 even D3: Pg. 313-314 #20-26 even D4: Pg. 315 #36-40 even TB Investigative Task “Backhoes and Forklifts” Unit 4: Randomness and Probability In this unit we introduce the formal concepts of probability and distribution. These concepts have been informally discussed all along. In chapters 14 and 15, we lay the foundations for probability and discuss how it works through conditional probabilities and tree diagrams. Chapters 16 and 17 discuss random variables and probability models. Together, these four chapters lay the foundation that will allow students to understand statistical inference. Essential Questions: • How can the basic definitions and rules of probability be used? • How can counting techniques and tree diagrams be used to solve probability problems? • What is a random variable? How do you compute µ and σ for a discrete random variable? • How can the binomial probability distribution be used to compute the probability of n successes? • How can the geometric probability distribution be used to compute the probability of success on the nth trial. • How can µ and σ be computed for the binomial and geometric distributions? • How can the probabilities of standardized events be computed? Days 4 Chapter 14 Topic From Randomness to Probability - TB Class Examples 14-4, 14-5 - (SI) Independent and Dependent Variables 4 15 Probability Rules - TB Class Examples 15-3, 15-4, 15-5 - (SI) Probability Concepts & Terms Random phenomenon, Trial, Outcome, Event, Sample space, Law of large numbers, Independence (informally), Probability, Empirical probability, Theoretical probability, Personal probability, The Probability Assignment Rule, Complement rule, Disjoint (mutually exclusive), Addition rule, Legitimate probability assignment, Multiplication rule, Independence assumption General addition rule, Conditional probability, General multiplication rule, Independence (used formally), Tree diagram 5 16 Random Variables - TB Class Examples 16-3, 16-4, 16-5, 16-6, 16-7, 16-8 - (SI) Random Variables & Probability Distributions Random variable, Discrete random variable, Continuous random variable, Probability model, Expected value, Variance, Standard deviation, Changing a random variable by a constant, Adding or subtracting random variables Assignment D1: Pg. 338 #2-10 even D2: Pg. 338-339 #12-20 D3: Pgs. 339-340 #22, 26-30 even D4: Pgs. 340-341 #32-36 even D1: Pgs. 361-362 #2-6 even D2: Pg. 362 #8-12 even D3: Pgs. 362-363 #16-20 even D4: Pgs. 363-364 #22, 24, 34, 38 D1: Pg. 383 #2-8 even D2: Pgs. 383-384 #10-18 even D3: Pg. 384 #20-24 even D4: Pgs. 384-385 #26-30 even D5: Pg. 385 #38,40 6 17 2 1 22 Review Test Total Probability Models - TB Class Examples 17-3, 17-4 Bernoulli trials, Geometric probability model, 10% condition, Success/Failure condition D1: Pg. 401 #2-8 even D2: Pg. 402 #10-18 even D3: Pgs. 402-403 #20-26 even D4: Pg. 403 #32, 34 D5: Pg. 403 #36 D6: Pg. 399 Just Checking Total: 73 days Unit 5: From the Data at Hand to the World at Large In this unit we come to statistical inference. Problems of statistical inference require us to draw a sample of observations from a larger population. Conclusions about the population proportions can be obtained from sample data by the use of statistical estimates and tests of significance. Essential Questions: • What is a probability sampling distribution? • How do sampling distributions assist statisticians in making good decisions for a population? • What is the relationship between sample size and margin of error? • How can the proportion p of successes in a binomial experiment be estimated given the number of successes and sample size? How does the normal approximation fit into this process? • When given incomplete (sample) information, how can it be decided whether to accept or reject a proposal? • What procedure should be used to estimate a population proportion? • Describe the difference between a critical value and a test statistic? • What is the significance of the standard error? • What is the P-value of a statistical test? What does this measurement have to do with performance reliability? • How can a statistical test be constructed for the proportion p of successes in a binomial experiment? • How do we use sample data to compare proportions from two independent populations? • Identify the conditions necessary to perform a confidence interval and hypothesis test for a population proportion. • Discuss the ramifications of a Type I or Type II error. Days Chapter Topic Concepts & Terms Assignment 5 18 Sampling Distribution Models - TB Class Examples 18-6 through 18-11 - (SI) Sampling Distributions Sampling distribution model, Sampling variability/Sampling error, Sampling distribution, Model for a proportion, Central Limit Theorem, Sampling distribution model for a mean D1: Pgs. 432-433 #2-6 even D2: Pg. 433 #8-12 even D3: Pg. 434 #16-20 even D4: Pg. 434 #28 Pg. 436 #32 D5: Pg. 436 #34, #42 4 19 5 20 4 21 Confidence Intervals for Proportions - Inference Toolbox YMS Pg. 548 - TB Class Examples 19-3, 19-4, 19-5 - (SI) Sampling Distributions - (SI) Estimation Testing Hypotheses about Proportions - Inference Toolbox YMS Pg. 471 - TB Class Examples 20-5, 20-6, 20-7 - (SI) Sampling Distributions - (SI) Tests of Significance More About Tests and Intervals - TB Class Examples 21-3, 21-4 - (SI) Tests of Significance Standard error, Confidence interval, One-proportion z-interval, Margin of error, Critical value TB Investigative Task “Simulated Coins” D1: Pg. 455 #2-6 even D2: Pgs. 455-456 #8-14 even D3: Pgs. 456-457 #16-22 even D4: Pgs. 457-458 #24, 30, 32 Null Hypothesis, Alternative hypothesis, Two-tailed alternative, One-tailed alternative, P-value, One-proportion z-test D1: Pgs. 476-477, #2-8 even D2: Pg. 477 #10-14 even D3: Pg. 478 #16-20 even D4: Pg. 478 #22-26 even D5: Pg. 479 #28-32 even Alpha level, Statistically significant, Significance level, Type I error, Type II error, Power, Effect size D1: Pgs. 499-500 #2-12 even D2: Pgs. 500-501 #14-18 even D3: Pg. 502 #24, 26 D4: Pg. 503 #34 TB Investigative Task “Life After High School?” 4 22 2 1 25 Review Test Total Total Days: 98 Comparing Two Proportions - TB Class Examples - 22-3 through 22-6 - (SI) Sampling - Distributions - (SI) Estimation - (SI) Tests of Significance Variances of independent random variables add, Sampling distribution of the difference between two proportions, Twoproportion z-interval, Pooling, Two-proportion z-test D1: Pg. 519 #2-6 even D2: Pgs. 519-520 #8-12 even D3: Pgs. 520-521 #16, 18 D4: Pg. 521 #20, 22 Unit 6: Learning About the World In this unit we will continue to use the same inference procedures as in unit 5. However now we will draw conclusions about the population mean from sample data by the use of statistical estimates and tests of significance. Essential Questions: • Why is the Central Limit Theorem so important in our study about inference for the mean? • What distributions can the CLT be applied to, and how can this be accomplished? • When confronted with incomplete (sample) information, how can a decision be made whether to accept or reject a proposal? • What procedure should be used to estimate a population mean? • Describe the difference between a critical value and a test statistic? • What is the significance of the standard error? • What is the P-value of a statistical test? What does this measurement have to do with performance reliability? • How can a statistical test for µ be constructed? Does it make a difference whether σ is known or unknown? • What are the statistical advantages of paired data values? How can statistical tests be constructed? • How can means be compared from two independent populations when σ is unknown for each population? • Identify the conditions necessary to perform a confidence interval and hypothesis test for a population mean. Days 4 Chapter 23 4 24 3 25 Topic Inference About Means - TB Class Examples 23-4, 23-5, 23-7 - (SI) Sampling Distributions - (SI) Estimation - (SI) Tests of Significance Comparing Means - TB Class Examples 24-3, 24-4, 24-5 - (SI) Sampling Distributions - (SI) Estimation - (SI) Tests of Significance Paired Samples and Blocks - TB Class Examples 25-3, 25-4 - (SI) Sampling Distributions - (SI) Estimation - (SI) Tests of Significance Concepts & Terms T distribution, Degrees of freedom (df), One-sample t-interval for the mean, One-sample t-test for the mean Two-sample t methods, Twosample t-interval for the difference between means, Two-sample t-test for the difference between means, Pooling, Pooled t-methods Paired data, Paired t-test, Paired-t confidence interval Assignment D1: Pg. 554 #2-8 even D2: Pgs. 555-556 #10-16 even D3: Pg. 556 #18, 20 D4: Pg. 557 #30, 32 TB Investigative Task “SAT Performance” D1: Pgs. 578-580 #2-8 even D2: Pgs. 580-581 #10, 12, 14 D3: Pg. 582 #16, 18 D4:Pg. 585 #36 D1: Pgs. 602-603 #2-8 even D2: Pgs. 603-604 #10-16 even D3: Pgs. 605-606 #20, 24 TB Investigative Task “SAT Performance Part II” 2 1 14 Review Test Total Total Days: 112 Unit 7: Inference When Variables Are Related This unit is about understanding and modeling relationships between variables. In chapter 26, we look at categorical data with χ2 models. In chapter 27, the subject is inference for regression models. Essential Questions: • How can it be determined whether the observed counts in a frequency distribution or contingency table are consistent with a proposed model? • How can it be determined whether two or more observed distributions could have arisen from populations with the same model? • How can it be decided if two distributions are independent? • How can a correlation coefficient be tested? • What is the standard error of estimate? How do you compute it, and where is it used? • How can a confidence interval for a least-squares prediction be computed? • The slope of the least-squares regression line represents rate of growth. How can it be determined if the rate of growth is statistically significant? Days 8 Chapter 26 2 27 2 1 13 Review Test Total Total Days: 125 Topic Comparing Counts - TB Class Examples 26-5, 26-6, 26-7 - (SI) Tests of Significance Inferences for Regression - TB Class Examples 27-4, 27-5, 27-6, 27-7 - (SI) Tests of Significance Concepts & Terms Chi-square model, Cell, Chi-square statistic, Chi-square test of goodness-of-fit, Chi-square test of homogeneity, Chi-square test of independence, Chi-square component, Standardized residual, To-way table, Contingency table Conditions for inference, in regression , Residual standard deviation, t-test for the regression slope, Confidence interval for the Regression slope (β) Assignment D1: Pgs. 642-643 #2-6 even D2: Pg. 643 #8, 10 D3: Pgs. 644-645 #12-18 even D4: Pg. 645 #20-24 even D5: Pg. #26-30 even D6: Pg. 647 #32-36 even D7: Pg. 648 #38, 40 D8: Pg. 648 #42 TB Investigative Task “97 AP Stat Scores” D1: Pgs. 673-674 #2-8 even D2: Pgs. 675-676 #12-18 even SUPPLEMENTAL WORK: TEST PREPARATION AND STRATEGIES Days 10 Chapter 10 20 Total Total Days: 145 Topic Multiple Choice Questions in a timed setting - (SI) Multiple Choice Free Response questions in a timed setting - (SI) Free Response Concepts & Terms In-class practice In-class practice Assignment
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