Primary Textbook AP Statistics Syllabus Charles R. McClenahan, Ph.D. Santa Fe High School Watkins, Ann E., Richard L. Scheaffer, George W. Cobb. Statistics in Action: Understanding a World of Data. Emeryville, CA: Key Curriculum Press, 2004. Technology All students have a TI-83+, TI-84+, or TI-89 graphing calculator for use in class, at home, and on the AP Exam. Students will learn how to use graphing calculators to analyze and display data. They will use graphing calculators throughout the course. Students will have access to personal computers in the classroom. They will learn to use software including, but not limited to, Microsoft Excel to display and analyze data, including regression analyses, performing simulations, and generating graphs. Course Description The course will rely heavily on the use of hands-on activities. These include experiments, simulations, and analyses of case studies. Important statistical concepts will be introduced using these activities. Graphical displays of the data from these activities will form a crucial part of this course. These displays will include, but not be limited to, the following: dotplots, stemplots, back-to-back stemplots, histograms, bar charts, boxplots, parallel boxplots, scatter plots, and frequency plots. Course Outline The course will be organized by chapters in the primary textbook. The activities and goals for each chapter heading are listed below their respective chapter heading. Chapters 1 through 11 will be completed before the date of the AP Exam. Moreover, there will be sufficient time before the AP Exam for students to review for the exam. After the AP Exam the students will explore case studies presented in Chapter 12. The students will also have time to complete their term projects.
Chapter 1 A Case Study of Statistics in Action (6 days) o Simulation: By Chance or by Design? o Discrimination in the Workplace: Data Exploration o Discrimination in the Workplace: Inference Chapter 2 Exploring Distributions (14 days) o Estimating Distance Using Feet and Meters o Comparing Hand spans o Exploring a Distribution Generated by Tossing Coins o Make and interpret plots for displaying univariate data: dot plot, histogram, stemplot, and boxplot. o Compute and interpret measures of center: mean and median. o Compute and interpret measures of spread: interquartile range and standard deviation. o Examine the effects of a linear transformation of the data on measures of center and spread. o Understand the use of normal density curves as models for data distributions. o Calculate probabilities connected with the normal distribution using standard units (z-scores) and a table of the standard normal distribution. Chapter 3 Relationships Between Two Quantitative Variables (15 days) o Find the Acceleration of Frictionless Pucks Down Ramps with Different Inclines o Pinching Pages and Measuring Thickness o Was Leonardo Correct? o Near and Far: Estimating Distances and Performing a Regression Analysis o Finding the Areas of Equilateral Triangles o Copper Flippers: Exponential Decay o Make a scatterplot and determine what its shape tells about the relationship between the two variables. o Find and interpret the equation of the least squares regression line. o Find and interpret the correlation coefficient o Use diagnostic tools such as residual plots to determine whether the linear regression line is appropriate or a transformation is needed first. -2-
o Make a transformation that expresses a curved relationship as a linear one. o Learn to create graphical displays using Microsoft Excel. Chapter 4 Sample Surveys and Experiments (13 days) o Time In the Hospital o Random Rectangles o Randomization and its Effect o Bears in Space o Understand that population parameters can be estimated by looking at a properly chosen sample from that population. o Learn the basic terminology of sampling and sample surveys. o Learn how to recognize common sources of bias from methods of selecting the sample and from the method of getting the response. o Learn the characteristics of the most common types of sampling, including simple random sample, stratified random sample, cluster sample, and systematic sample with random start. o Understand that cause and effect can be established only with a randomized controlled experiment, not with an observational study. o Understand why each characteristic of a well-designed experiment (randomization of treatments to subjects, replication, and control or comparison group) is crucial. o Learn the common experimental designs (completely randomized, randomized block). o Understand within-treatment variability versus between-treatment variability, and how blocked designs can minimize the former. Chapter 5 Sampling Distributions (17 days) o Return of the Random Rectangles o Cents and Center o Buckle Up o The Sum and Difference of Two Rolls of a Die o Take random samples of a fixed size n from a population by using a table of random digits. o Use the four-step guide (model, sample and summary, repetition, and distribution) to construct sampling distributions. o See that all summary statistics have sampling distributions and to explore a variety of these distributions. -3-
o Know the shape, mean, and standard error of the sampling distributions of the sample mean and the sample proportion the two most commonly used summary statistics. o Understand the relationship between the sampling distribution of the sample mean and the sample total. o Use the idea of a range of reasonably likely values to make a decision based on sampling distributions. o Know the shape, mean, and standard error of the sampling distribution of a sum and a difference of sample values. Chapter 6 Probability Models (12 days) o Spinning Pennies o Exploring "or" o More on "or" o Independence With Real Data o Build a reasonable probability model for a simple situation based on either data of symmetry (equally likely) arguments. o See how the Law of Large Numbers relates data to probability o Understand the general Addition Rule for probability and how it simplifies when events are mutually exclusive. o Understand and calculate conditional probabilities for discrete events. o Understand the general Multiplication Rule for probability and how it simplifies when events are independent. o Learn to use a graphing calculator and spreadsheet program on a PC to perform a simulation. Chapter 7 Probability Distributions (7 days) o Can People Identify the Tap Water? o Waiting for Type A Blood o Expected Value of a Geometric Distribution o Use the terminology of probability distributions and learn how to compute their expected values and standard deviations. o Use the expected value to make decisions. o Recognize and apply the binomial probability model. o Recognize and apply the geometric probability model. -4-
Chapter 8 Inference for Proportions (18 days) o Determining Eye Dominance o Constructing a Chart of Reasonably Likely Outcomes o The Capture Rate o Spinning and Flipping Pennies o Brown Plain and Peanut M&M's o Differences When there Is No Difference o Understand the concept of a confidence interval for estimating the proportion of success in a binomial distribution. o Construct such a confidence interval and interpret the results. o Use a test of significance to decide whether you should reject the claim that a sample was drawn from a binomial population with a specified proportion of success. o Construct and interpret a confidence interval for the difference between the proportion of success in one population and the proportion of success in another population. o Use a test of significance to decide whether you should reject the claim that a sample was drawn from two binomial populations that have the same proportion of success. Chapter 9 Inference for Means (26 days) o What Makes Strong Evidence? o The Effect of Estimating the Standard Deviation o The Effect of Skewness on Confidence Intervals o The Strength of Evidence o Handspans o Understand the concept of a confidence interval for estimating a population mean, compute a confidence interval, and interpret the results. o Perform a test of significance for deciding whether it is reasonable to reject a claim that a sample was drawn from a population with a specified mean. o Produce and interpret a confidence interval for the difference between the mean of one population and the mean of another population. o Perform a test of significance for deciding whether it is reasonable to reject a claim that two samples were drawn from two populations that have the same mean. -5-
Chapter 10 Chi-Square Tests (10 days) o Generating the Chi-Square Distribution o Independent or Not? o Recognize, conduct, and understand the chi-square test for goodness-of-fit and to see that it is an extension of a significance test on a single proportion. o Recognize, conduct, and understand the chi-square test for homogeneity and to see that it is an extension of the significance test of equality of two population proportions. o Recognize, conduct, and understand the chi-square test of independence and to see that the notion of statistical independence of two variables measured on the same subjects is new, that this test is not an extension of any that have come before, even though it looks similar to the test for homogeneity. o See connections between analysis of counts and interpretations of the results based on sample proportions. o Learn to use a graphing calculator and spreadsheet program on a PC to calculate chi-square. Chapter 11 Inference for Regression (7 days) o How Fast Do Kids Grow? o What Effects Variation in b 1? o Phone Numbers and Names o Recognize that the regression line as computed in Chapter 3 sometimes must be considered an estimate of a true, underlying linear model. o Recognize that the slope of a regression line fitted from sample data will vary from sample to sample. o Recognize that the formula for the standard error of this slope reflects the fact that having a wider spread in the values of x and smaller spread in the distances of y from the regression line decreases the variability of the slope. o Construct and interpret a confidence interval for the slope. o Perform a test of significance for the slope. o Check the conditions that are needed before doing inference for a slope. o Transform data to better meet the conditions for inference. o Learn to use a graphing calculator and spreadsheet program on a PC to determine a least squares regression line. -6-
Review for AP Exam (6 days) Chapter 12 Case Studies (6 days) o Review the statistical techniques the students have learned. o Examine situations that are somewhat more complicated than those found in most of the examples and problems in the textbook. o Be introduced to some slightly more advanced ideas in statistical inference. o Find out what happened with Robert Martin and Westvaco. Final Project In lieu of a final exam, students will complete a final project. Students will design, perform and report a statistical study, experiment, or survey. By performing this project, students will gain strong experience in developing statistical studies and making sound connections and judgments between the design and the results of an experiment. Moreover, students will learn that the most important part of any study is to clearly, concisely, and accurately report the results. Unless you are given special permission to do otherwise, you will work in pairs. 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. Proposal You must first prepare a written proposal. In this proposal, you will present the following: Describe the question you wish to investigate. Diagram and explain the design of your observational study, survey, or experiment. Include all steps taken to reduce confounding and bias. Describe how you will conduct this study. Be specific about how you will set up and perform all steps. Explain the criteria you will use to draw conclusions. Include any assumptions you will need to make. Collecting and Analyzing Data Collect your data as you described in your proposal. Then analyze your data as following: -7-
Critically examine the information you collected. Do you find any potential problems? Analyze the data you collected 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? Report Your report must include the following: Tables and graphical presentations, as appropriate for your study. All graphs must be clearly labeled to indicate what data are displayed. A description of any deviations you made from your initial description of the data collection process. A description of any bias present, even after your attempts to eliminate it. An appropriate inference procedure, used to answer the initial question you posed, along with an interpretation of the result. Conclusions you are able to draw from this procedure. List of all the specific duties of each partner. Each partner is expected to contribute equally to this project. Your report must have the following attributes: 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. All graphs must be generated using computer software, such as Microsoft Excel. Do not use or show Calculator-Speak. (For example: I then used LinReg L1, L3 to find the equation. ) All outside sources of information must be correctly attributed and referenced. References will use the format of the American Psychological Association. (You can find a tutorial on their web site, http://www.apastyle.org/learn/tutorials/basicstutorial.aspx.) -8-
Presentation You must present your results to the class. Both partners must participate in the presentation. Your presentation must include the same items as the written report. Graphs must be large enough for the entire class to see. Presentation graphs may be neatly hand-drawn. -9-