AP Statistics Syllabus Primary Textbooks: Bock, David E., Paul F. Velleman, and Richard D. Devaux. Stats: Modeling the World. Boston: Pearson/Addison Wesley, 2004. Bock, David E. Teacher s Resource Guide with Lesson Plans. Boston: Pearson/Addison Wesley, 2004. Technology: All students have a TI 84+ graphing calculator for use in class, at home, and on the AP Exam. Students use their graphing calculators extensively throughout the course. All students have access to the internet resource of Agile Mind : AP Statistics. Students complete various guided assessments, self tests, and AP practice tests as assigned throughout the year. Most of the students have internet access at home. In addition, there are computers located throughout campus where students can access Agile Mind. All students have access to the computer lab for 15 class sessions throughout the year. All students have exposure to activstats lessons All students have exposure to various applets on the Internet as part of class lessons Pedagogy: The topic outline provided by the College Board, the primary textbook by Bock, Velleman, and Devaux, and the accompanying resource guide by Bock, serve as the general plan for the course. Resources obtained from the AP Statistics Summer Institute and Agile Mind are used as activities to supplement the textbook Teacher Notes: At the end of the chapters in the Bock book are numerous real world problem situations where students can practice the concepts presented in the chapter. These questions serve as the background and focus for class lessons. The book stresses good communication skills. By the time the school year is over, we will have covered about all of the questions in the book.
From the first week on, we review applicable released AP exam questions. Students work with partners to tackle these questions for practice. In the second semester, students do these AP released questions under timed conditions as quizzes. I find it very practical to let students grade their own responses with a rubric. They use AP scoring guidelines and sample student responses to grade their work. Because statistics is a serious upper level course and students tend to get some senioritis, I try to interject some entertaining activities throughout the year. Some activities I use are Launching Gummy Bears in Space, various M and M lab activities, designing Stats T shirts, and Scavenger Hunt vocabulary activities. These activities seem to energize the students, and their focus on the more serious aspects of the course improves. In order to draw connections between the four conceptual themes of AP Statistics as described in the course and topic outline, students routinely do investigative tasks. Students do two big projects one first semester; one second semester. In each of the investigative tasks, the students examine data, create graphical and numerical displays of data, interpret the data, and write an interpretation of their conclusions in context. The grading of these tasks is based on the AP Rubric system. The components used to grade the tasks are all contained in the resource binder on the page following the task. The sources for the investigative tasks and projects are the Teacher s Resource Guide With Lesson Plans as noted above. Investigative Projects that the students do during a nine month course are as follows: Name of Activity Race and the Death Penalty Dollars for Students Text Chapter Reference Chapter 3, Displaying And Describing Categorical Data Chapter 4, Displaying Quantitative Data Description of Task Write a newspaper article discussing Association between race and death Sentences in the U.S. Write a report comparing amounts of Per student expenditures in eastern and Western states of U.S. Include a visual Display ( stem and leaf). Binde r Page # 3 8 Auto Safety Chapter 5, You work for an insurance co. You 5 13 4 7
Describing Distributions numerically Normal Models Chapter 6, Standard Deviation as a Ruler and Normal Model Have been given the job of reviewing Auto safety records and writing a Report to your boss. Include Appropriate comparative plots and Summary stats; descriptions of injury Ratings for each group of cars; comparison Of injury ratings for the three sizes of cars; Your recommendation to your boss about Your company s policies. 1. Collect data. ( of your interest.) 2. Write brief description of data. Include visual, numeric, verbal. 3. Check the normal model. Use your data mean and std. deviation to create a Normal model. Compare this to your data Distribution explain why model is or is not useful. 6 11 Smoking Chapter 8,Linear Regression 1.Examine data of cigarette consumption and mortality from Heart disease. 2. Write report include appropriate graphs and stats; describe association between cig smoking and heart disease; create linear model; evaluate appropriateness and strength of linear model; interpret slope And y intercept of line; use model to estimate benefits of reaching goal of cutting cig smoking in half over next decade. 8 11 Olympic Long Jumps Alligators Chapter 9,Regression Wisdom Chapter 10, Reexpressing Data ESP Chapter 11, Understanding Randomness Backhoes and Forklifts GROUP PROJECT Chapter 13 Experiments Chapters 1 13 Examine data for gold medal distances. Write a report Including: appropriate graphical and numeric analyses; discuss trend in long jump performances based on an appropriate linear model. Explain the decisions you made in creating your model with analysis of gaps in data and departures from trend; predict distance that will win Gold medal in long jump in 2008 Given a set of data ( from College Board s Teacher s Guide 1997), create a linear model; discuss accuracy of model; try again to create a stronger predictive model; explain why new one is better; assess how well your model would work for wildlife scientists. Test claim that your friend has ESP. Use simulation. Write a report in which you explain your procedure do at least 20 trials, and write your conclusion. Design an experiment by specifying the procedure a company should use to test 20 new machines to see if a defect has been fixed. You are to describe the design of your experiment; outline it with a diagram; explain and perform your randomization procedure, showing the assignments; Outline steps you take to reduce possibility of bias. Explain how you decide if the defect has been fixed. Conduct a survey, study, or experiment, or do a simulation. Present your findings to the class and submit a written report. Students are given a list to chose from, or they can make up their own ( with teacher approval) Students are evaluated using a list on page 13 16. 9 7 10 7 11 7 13 9 13 15
Simulated Coins Chapter 18 Sampling distribution models Chapter 21 More about Tests Investigate sampling distribution and model for proportion of heads that may show up when a coin is tossed repeatedly. Toss coins or do a simulation. 18 6 Life after High School Examine data collected by a polling organization about senior plans for after high school. ( Motivation of study did 9/11 have an impact on future plans of high school seniors?) Answer the following questions: 1. What is the minimum sample size needed for a 90% confidence level and a 4% margin of error? 2. Determine a 90% confidence interval for the percentage of seniors who plan to go to college this year. 3. do the data suggest that the percentage of seniors who enlist in the military is different this year compared to the 4.5% of high school seniors from the 90 s? Test an appropriate hypothesis and reach conclusion. 4. What happens to your conclusion if you find out that half of the undecided and non response people eventually enlist. Would that cause you to change your conclusion? 5. Explain in context a Type I, Type II error would be here. 21 6 SAT Performance Chapter 23 Inferences about Means What is the mean SAT score for this high school. (information ) How do these students measure against the rest of the state? Is there a significant difference between Verbal and Math scores for these students> Nationally, males tend to have higher Math scores; is that true here? 23 9 You are to draw a sample of students explain your method of sample Use your sample to create a 95% confidence interval for mean SAT Based on confidence interval, compare your sample results with statewide mean score. Prepare a written report that includes evidence of your work and conclusions. SAT Performance Chapter 25 Paired samples, Blocks Continue with the same sample used before. Determine whether your sample provides stat evidence that Verbal and Math scores differ for students at this high school. Determine whether your sample provides stat evidence that males have higher Math scores than females at this school. Write a report that describes demonstrations of the procedures you used and your conclusions. 25 7 97 AP Stat Scores Chapter 26 Comparing counts Write a report assessing the success the first group of AP Stats students with respect to the following : How did their stat scores compare to the national results How do AP stat students do compared to BC calc Do these results show that these males and females may perform 26 11
differently on the AP stats exam Be sure you test your hypotheses, and show the types of tests your do, show calculations, results, and state your conclusions. Final Project All Chapters Requirements: 1.Choose a good question to investigate. 2. Design an appropriate study or experiment. 3. Collect good data; they may come from a survey, observational study, experiment, or other sources such as publications or the internet. 4. Summarize data using appropriate graphs, summary stats and verbal description. 5. Make inferences based on your data. 6. State your conclusions. 7. Present your research to the class 8. Submit a complete written report. PS 7 An additional activity which helps students tie all the themes of statistics together is an ongoing one, which begins the very first week of class. I distribute the AP course and topic outline, along with formula charts, and tables to students. Students keep these pages at the front of their binder for reference throughout the year. One of the class activities the first week is to go through the AP outline and formula charts to introduce students to the scope of study included in the course. As students finish investigative tasks and various assignments through the year, they cross reference these activities back to their AP outline. By the beginning of the 5 th six weeks, their AP outline has numerous notes and references back to examples contained in their binders. As a final part of AP exam review, students are required to maintain a Free Response review binder in which they are required to complete free response questions ( not previously done in class) for the past 6 years ( form A and form B). Students classify these questions as to what category and theme of statistics they best fit into, and make notes on their outlines.
As often as I can, I try to relate whatever activity we are doing in stats to the real world. Students are asked to bring in articles and graphs from magazines and newspapers about studies, experiments, polls. Students, through class discussions about these articles, share interesting ideas and analyze studies noting the good statistics or misleading statistics that they read about or hear about on the news. The following is the Course TimeLine used for this course: Text Chapter Title of Chapter Objectives of Chapter ( as provided in textbook) Sample Activities used 1 Stats Starts Here Intro to course Why do we care about stats? (power point, notes) 2 Data Intro students to data, vocabulary, and TI tips (power point, notes) 3 Displaying and Describing Categorical Data 4 Displaying Quantitative Data 5 Describing Distributions Numerically 6 Standard Deviation As a Ruler Describe and compare distributions of data; Introduce idea of independence Examine and describe a variety of visual displays including histograms, stem and leaf plots, dotplots, timeplots. Select an appropriate measure of center and spread, based on the distribution. Know basic properties of mean, median. Understand meaning of standard deviation. Understand effects of adding and multiplying a constant. Standardize data for the purpose of comparison Understand that the standard deviation is a ruler for comparison of data. Recognize when a normal model is appropriate Course Outline Reference IIA,B 1 IIA,B 1 IA,B,C,,E 3 IA,B,C,E 4 IA,B,C,E 5 IA,B,C,E III C Class Periods 5 1 6 Review 1 6 Review Review of Chapters 1 6 IA,B,C,E IIIC 1 6 1 6 Test IA,B,C,E, 1 IIIC 7 Scatterplots, Association, Look at associations between quantitative variables Draw scatterplots, look for patterns. ID 3 1
And Correlation Describe association in direction, form, scatter Find correlation if linear association. Emphasize correct vocabulary when describing Associations. 8 Linear Regression Define residuals; show how they lead to line of best fit. Understand that correlation describes regression between standardized scores. Find equation of best fit line from summary stats, from data using calculator, and by reading computer output. Interpret slope, y intercept, and value of r squared in context. 9 Regression Wisdom Look at scatterplots when pattern changes.. Look at effects of extrapolation, outliers, influential points, use of means ( or other summaries) rather than all data. Look at effect of mistakenly inferring cause and effect. Practice more linear regression and potential problems that arise. ID 8 ID 4 10 Re Expressing Data Model curved relationships between two variables. Re express using ladder of powers. Re express using logarithmic approach. ID 6 7 10 7 10 Review Review of Chapters 7 10 ID 1 7 10 7 10 Test Test on Chapters 7 10 ID 1 11 Understanding Recognize random outcomes in real world situations IIIA 4 Randomness Perform a simulation by generating random numbers using sources of random values i.e. dice, tables. Describe a simulation so others can repeat it. 12 Sample Surveys Study vocabulary of sampling Distinguish between types of bias Understand that randomization helps guard against bias. Know how to draw a random sample from a random number table. Plan and conduct a sample survey. ( Random Rectangle Activity) IIA,B,C,D 5 13 13 Experiments Experiments (continued) :Learn 4 basic principles of experiment design: control, randomize, replicate, block Recognize factors, treatments, and response variables in experiments Understand value of blinding and placebos when dealing in certain experiments. Design a completely randomized experiment. IIC,D IIC,D 4
Design an experiment in which blocking is used to reduce variation. (Gummy Bears in Space Activity) (1998 AP Q 3, 2001 AP Q4) (1999 AP Q 3, 2002 AP Q 2) 11 13 11 13 Review 1 11 13 11 13 Test 1 14 From Recognize random outcomes in real world situations IIIA 3 Randomness to Probability Be able to state Law of Large Numbers Know basic rules and definitions of probability Understand difference between independent events and disjoint events. Know how to use the Complement Rule to make probabilities simpler. 15 Probability Rules Know how and when to apply probability rules. Understand concept of conditional probability and know how to make and use a tree diagram as a problem solving tool. Understand concept of independence. IIIA,B 4 16 Random Variables Be able to recognize random variables. Find the probability model for a random variable. Find the expected value and variance of a random variable. Know how to determine new mean and standard deviation after adding or multiplying a constant. Interpret the meaning of expected value and standard deviation of a random variable in context. IIIA,B 4 17 Probability Models Know how to tell if a situation involves Bernoulli trials. Know conditions for using a geometric, binomial, or normal model. Calculate geometric probabilities. Calculate binomial probabilities. IIIA 4 14 17 14 7 Review 1 14 17 14 17 Test 1 18 Sampling Distribution Models Understand the connection between variability of a statistic and sample size. Understand that the Central Limit Theorem provides the sampling distribution model of the mean for large samples regardless of the underlying population. IIID 4 19 Confidence Intervals for Proportions Understand that the margin of error of a confidence interval for a proportion changes with the sample size and confidence level. IVA 4
20 Testing Hypotheses about Proportions Know how to examine data for conditions that would make inference invalid. Construct and interpret a one proportion z interval. State null and alternative hypotheses for a one proportion z test. Know conditions that must be met in order to use a one proportion z test Distinguish between a one tail and two test test. Perform a one proportion z test, and interpret results. 21 More about Tests Understand concepts of alpha level, statistic significance, Type I and Type II errors, and the Power of the test. Interpret the meaning of a P value in everyday language. Know that we don t accept null hypothesis; instead, we fail to reject null hypothesis. 22 Comparing Two Proportions State the null and alternative hypothesis for testing difference between two population proportions. Know how to examine data for violations of conditions that would make inference about population invalid. Construct a confidence interval for difference between two proportions. Perform and interpret a two proportion z test for difference in proportions. IVB 2 IVB 2 IVB 2 18 22 18 22 Review 1 18 22 18 22 Test 1 23 Inferences about Means Know assumptions required for t tests and t based confidence intervals. Compute and interpret a t test for population mean using a statistics software package or work from summary statistics for a sample. Compute and interpret a confidence t interval for the population mean using a statistics package summary statistics for a sample. Interpret the meaning of the confidence interval for a population mean. IVA 3 24 Comparing Means 25 Paired Samples and Blocks Recognize situations that are conducive to a two sample t test for difference between means of two independent groups. Recognize when a pooled t procedure is appropriate. Perform and interpret a two sample t test using a statistics package or calculator. Recognize whether a design that compares two groups is paired or not. Find a paired confidence interval. Perform and interpret a paired t test. IVB 2 IVA,B 2
22 25 22 25 Review 1 22 25 22 25 Test 26 Comparing Counts 27 Inferences for Regression Recognize when a test of goodness of fit, homogeneity, or test of independence is appropriate. Perform and interpret chi square tests using statistics software or calculator. Test the standard hypothesis that the true regression slope is zero. State the null and alternative hypotheses. Construct and interpret a confidence interval for the mean of predicted y values and prediction interval for y based on summary statistics. Be able to interpret computer output for regression. Interpret meaning of true regression slope in words. IVB 6 IVB 4 26 27 26 27 Review 1 26 27 26 27 Test 1 Review for AP Exam, Practice Exam,Test 20