AP Statistics: Syllabus 4

Transcription

1 AP Statistics: Syllabus 4 Syllabus v Scoring Components Page(s) SC The course provides instruction in exploring data. 5 7 SC The course provides instruction in sampling. 4 SC3 The course provides instruction in experimentation. 4 SC4 The course provides instruction in anticipating patterns. 8 SC5 The course provides instruction in statistical inference. 9 0 SC6 The course draws connections between all aspects of the statistical process including design, 3 analysis, and conclusions. SC7 The course teaches students how to communicate methods, results and interpretations using the vocabulary of statistics. SC8 The course teaches students how to use graphing calculators to enhance the development of statistical understanding through exploring data, assessing models, and/or analyzing data. SC9 The course teaches students how to use graphing calculators, tables, or computer software to 8 enhance the development of statistical understanding through performing simulations. SC0 The course demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploring data, analyzing data, and/or assessing models.

2 Syllabus v Pedagogy The primary text provides the general layout of the course. Students are required to read the chapters in the textbook before the topics are discussed in class so that class time can be devoted to more discussion, investigation, and activities, with less time spent lecturing. Students will gain proficiency on accuracy and communication of statistical concepts throughout the course, to include effectively communicating how methods, results, and interpretations of data for any given experiment are valid. They learn that writing complete responses using appropriate justifications is a critical aspect of gaining statistical proficiency. This is emphasized on all homework assignments; write-ups from activities, investigations, and experiments; and especially on student assessments. One method that has been successful in enhancing these skills is having students review each other s responses on AP Statistics released free-response questions. Working in groups of three, they use rubrics to score responses. Some class time is spent discussing any differences in their scores, helping students learn what constitutes an effective response. On most assignments, quizzes, and exams, students are expected to use an appropriate graphing calculator. I use a graphing calculator with an overhead display as well as a projection unit for class demonstrations. Each chapter in the main text has a section on calculator use to give students instruction and practice using the statistical capabilities of their calculators. On some assignments and activities, students use Minitab to analyze data. Every networked computer throughout our building (in the IMC, computer labs, and classrooms) has access to Minitab. [SC8 & SC0] It is important to note that approximately two weeks (0 to 4 ) of every trimester is spent in the computer lab. Course Projects Course projects are in the form of extended formal writing assignments. As a consequence, form and technical adequacy are enforced. These assignments are given throughout the year. The main purpose of these course projects is for students to gain strong experiences in developing statistical studies and making sound judgments and connections between the design and the results of an experiment. Two examples are given below. Example Chapter (data collection and experimental design): In small groups, students write up the helicopter experiment in the second chapter. The point of the experiment is that students are clearly able to describe their experimental-design process from design to collection of data to descriptive report of their results. [SC7] Students design, execute, and write a group project. Exemplary reports are discussed in class. SC8 The course teaches students how to use graphing calculators to enhance the development of statistical understanding through exploring data, assessing models, and/or analyzing data. SC0 The course demonstrates the use of computers and/ or computer output to enhance the development of statistical understanding through exploring data, analyzing data, and/or assessing models. SC7 The course teaches students how to communicate methods, results and interpretations using the vocabulary of statistics.

3 Syllabus v Example Chapter 3 (graphical methods of describing data): Students produce graphical displays using data that they have collected or existing data they have located. This activity usually produces interesting examples that can be referenced throughout the chapter. These data are used to introduce Minitab s data entry and graphing capability. Later in the year, as we progress through inference, students are responsible for increasingly longer (individual) projects involving data collection and analysis. Their writing is evaluated with increasing rigor as their skills are honed, and more attention is given to the necessity of putting their project in a larger scientific context. As a culminating project, students will design an experiment or survey, plan a sampling procedure, gather data, use descriptive and inferential statistics, interpret their results in context, and present their results. This project requires that students engage in all stages of the research process. [SC6] SC6 The course draws connections between all aspects of the statistical process including design, analysis, and conclusions. Course Materials Primary Text Peck, Roxy, Chris Olsen, and Jay Devore. Introduction to Statistics and Data Analysis, nd ed. Belmont, Calif.: Brooks/Cole, 005. References and Resource Materials ABS = Scheaffer, Richard, Ann Watkins, Jeffrey Witmer, and Mrudulla Gnanadesikan. Activity-Based Statistics: Instructor Resources, nd ed. Emeryville, Calif.: Key College, 004. B = Bohan, James. AP Statistics: Preparing for the Advanced Placement Examination. New York: Amsco, 000. FF = Erickson, Tim. Fifty Fathoms: Statistics Demonstrations for Deeper Understanding. Oakland, Calif.: EEPS Media, 00. FR = Selected AP Statistics Exam free-response questions are used throughout the course. GCE = Graphing calculator exercises H = Hinders, Duane. 5 Steps to a 5: AP Statistics. New York: McGraw-Hill, 004. OTH = Other resource materials: newspapers, select journals, and the World Wide Web (including NCSSM Statistics Leadership Institute material). Students often use data sets they have collected. RJC = Ryan, Barbara F., Brian L. Joiner, and Jonathan Cryer. Minitab Handbook, 5th ed. Belmont, Calif.: Brooks/Cole, 005. SGU = Peck, Roxy, et. al. Statistics: A Guide to the Unknown. Belmont, Calif.: Thomson Brooks/Cole,

4 Syllabus v Chapter : The Role of Statistics Chapter : The Data Analysis Process and Collecting Data Sensibly [SC & SC3] 3 3 Course Overview Policies and Expectations Variability Data Analysis Bar Charts Dotplots Planning and Conducting a Study Sampling Random Rectangles Activity Observation and Experimentation Designing Surveys Helicopter Experiment Chapter Review Chapter Test I A.. Center and spread. Clusters and gaps II A. Overview of methods of data collection II B. Planning and conducting surveys II C. Planning and conducting experiments II D. Generalizability of results and types of conclusions that can be drawn Chapter Section : Three Reasons to Study Statistics Section : The Nature and Role of Variability Section 3: Statistics and Data Analysis Section 4: Types of Data and Some Simple Graphical Displays OTH: A current newspaper article is assigned in class to illustrate the pervasive nature of the course s content. Chapter Section : The Data Analysis Process Section : Sampling GCE: Generating random integers Section 3: Statistics Studies: Observation and Experimentation GCE: Randomization Section 4: Simple Comparative Experiments Section 5: More on Experimental Design Section 6: More on Observational Studies: Designing Surveys Section 7: Communicating and ABS: Random Rectangles Activity SGU: The Anatomy of a Pre-election Poll, Evaluating School Choice Programs OTH: Paper Helicopter Experimental Design Activity (adapted from NCSSM Statistics Leadership Institute materials) FR: 999 FR#3, 000 FR#5, 00 #4, 00 #, 00(B) #3, 003 #4, 004 #, 006 #, 006 #5, 006(B) #5 SC The course provides instruction in sampling. SC3 The course provides instruction in experimentation. 4

5 Syllabus v Chapter 3: Graphical Methods for Describing Data [SC] Bar Charts and Pie Charts Stem-and-Leaf Displays Frequency Distribution and Histograms Displaying Bivariate Numerical Data Communicating and Interpreting the Results of Statistical Analyses Chapter 3 Test I A.. Center and spread. Clusters and gaps I A. Cumulative frequency plot Chapter 3 Section : Displaying Categorical Data: Comparative Bar Charts and Pie Charts GCE: Using lists on the calculator Section : Displaying Numerical Data: Stem-and-Leaf Displays GCE: Setting the window on the calculator FR: 997 FR# Section 3: Displaying Numerical Data: Frequency Distributions and Histograms GCE: Scaling and drawing histograms Section 4: Displaying Bivariate Numerical Data Section 5: Communicating and FR: 997 FR#, 000 # LAB: Introduction to Minitab (RJC) FR: 00(B) #5 SC The course provides instruction in exploring data. 5

6 Syllabus v Chapter 4: Numerical Models for Describing Data [SC] Describing Variability in a Data Set Summarizing a Data Set: Boxplots Interpreting Center and Variability I B. 4. Using boxplots I A. 3. Outliers and other unusual features 4. Shape I B.. Measuring center: median, mean. Measuring spread: range, interquartile range, standard deviation 3. Measuring position 5. The effect of changing units I C. Comparing distributions of univariate data Chapter 4 Section : Describing the Center of a Data Set Section : Describing Variability in a Data Set GCE: Quartiles Section 3: Summarizing a Data Set: Boxplots (five number summary) GCE: Boxplots Section 4: Interpreting Center and Variability: Chebyshev s Rule, the Empirical Rule, and z-scores GCE: z-scores Section 5: Communicating and OTH: Students graph, find measures of center, and measures of variability for data sets that they have collected. OTH: Students match boxplots, histograms, and summary statistics in an activity adapted from ABS. FR: 004 #, 005 #, 005(B) # SC The course provides instruction in exploring data. Communicating and Interpreting the Results of Statistical Analyses Chapter 4 Review Chapter 4 Test I E.. Frequency tables and bar charts 4. Comparing distributions using bar charts 6

7 Syllabus v Chapter 5: Summarizing Bivariate Data [SC] Correlation Review: Correlation Game Using Fathom to Find the Line of Best Fit Fitting a Line to Bivariate Data Exercise for Understanding the Meaning of r Assessing the Fit of a Line (Anscombe Activity) Nonlinear Relationships and Transformations Chapter 5 Review Chapter 5 Test I D.. Analyzing patterns in scatterplots. Correlation and linearity 3. Least squares regression line I D. 4. Residual plots, outliers, and influential points I D. 5. Transformations to achieve linearity Chapter 5 Section : Correlation GCE: Linear regression on the calculator Section : Linear Regression: Fitting a Line to Bivariate Data Section 3: Assessing the Fit of a Line GCE: Residuals Section 4: Nonlinear Relationships and Transformations FR: 999 FR#, 000 FR# Section 5: Communicating and OTH: Students play the correlation game, a Web applet on matching correlation coefficients and scatterplots. FF: Students use a Fathom demonstration for fitting a line to bivariate data. SGU: Monitoring tiger prey abundance in the Russian Far East OTH: Students complete a worksheet for understanding the meaning of r WSC: Students complete a worksheet adapted from this text using the Anscombe data sets FR: 000 FR#, 999 FR# LAB: More on Minitab (RJC) SC The course provides instruction in exploring data. 7

8 Syllabus v Chapter 6: Probability [SC4 & SC9] Chance Experiments and Events Definition of Probability Basic Properties of Probability Review Conditional Probability. Interpreting probability. Law of Large Numbers 3. Addition rule, multiplication rule I E.. Marginal and joint frequencies 3. Conditional relative frequencies and association 3. Conditional probability Chapter 6 Section : Chance Experiments and Events Section : Definition of Probability GCE: Simulating Independent Events Section 3: Basic Properties of Probability Section 4: Conditional Probability Section 5: Independence Section 6: Some General Probability Rules Section 7: Estimating Probabilities Empirically and Using Simulation OTH: Students complete some activities using playing cards adapted from a presentation at the 006 Annual NCTM Conference. FR: 999 #4, 00 #3 SC4 The course provides instruction in anticipating patterns. SC9 The course teaches students how to use graphing calculators, tables, or computer software to enhance the development of statistical understanding through performing simulations. 3 Independence General Probability Rules Review Estimating Probabilities Empirically/ Using Simulation Chapter 6 Review Chapter 6 Test 3. Independence 5. Simulation of random behavior 8

9 Syllabus v Chapter 7: Random Variables and Probability Distributions [SC5] 3 Random Variables Probability Distributions for Discrete Random Variables Probability Distribution for Continuous Random Variables Mean and Standard Deviation of a Random Variable (RV) Binomial and Geometric Distributions Normal Distributions Checking for Normality and Normalizing Transformations Using the Normal Distribution to imate a Discrete Distribution 4. Discrete random variables 6. Mean and standard deviation of RV, and linear transformation of an RV III B. Combining independent RVs 4. Binomial and geometric RVs III C. The normal distribution Chapter 7 Section : Random Variables GCE: Discrete probability distributions Section : Probability Distributions for Discrete Random Variables GCE: Binomial probability calculations Section 3: Probability Distributions for Continuous Random Variables GCE: Geometric probability calculations Section 4: Mean and Standard Deviation of a Random Variable FR: 005 #, 005(B) #, 006 #3 Section 5: The Binomial and Geometric Distributions Section 6: Normal Distributions GCE: The normal approximation to the binomial Section 7: Checking for Normality and Normalizing Transformations Section 8: Using the Normal Distribution to imate a Discrete Distribution FF: Demonstrations on normally-distributed data, transforming the mean and standard deviation, adding uniform random variables, and binomial distributions FR: 00 #, 00 #3, 00(B) #, 003 #3, 004 #3, 004 #4 SC5 The course provides instruction in statistical inference. Chapter 7 Review Chapter 7 Test 9

10 Syllabus v Chapter 8: Sampling Variability and Sampling Distributions Chapter 9: Estimation Using a Single Sample [SC5] Statistics and Sampling Variability The Sampling Distribution of a Sample Mean The Sampling Distribution of a Sample Proportion Simulation of Sampling Distributions Test Point Estimation Large-Sample Confidence Interval for a Population Proportion Confidence Interval for a Population Mean Communicating and Interpreting the Results of Statistical Analyses Chapter 9 Review III D.. Sampling distribution of the sample mean 3. The central limit theorem III D.. Sampling distribution of the sample proportion III D. 6. Simulation of sampling distributions III D. 7. t-distribution IV A.. 4.; 6. Estimation (point estimators and confidence intervals) Chapter 8 Section : Statistics and Sampling Variability Section : The Sampling Distribution of a Sample Mean GCE: The sampling distribution of the mean Section 3: The Sampling Distribution of a Sample Proportion FF: Demonstrations on sampling distributions and sample size, the central limit theorem, standard error and standard deviation, what is standard error, and the distribution of sample proportions FR: 998 # Chapter 9 Section : Point Estimation Section : Large-Sample Confidence Interval for a Population Proportion GCE: Confidence interval for a population proportion Section 3: Confidence Interval for a Population Mean GCE: Confidence interval for a population mean Section 4: Communicating and FF: Demonstrations on confidence intervals of proportions, capturing with confidence intervals, where does that root (p( p)) come from, why np>0 is a good rule of thumb, how the width of the confidence interval depends on N, exploring confidence intervals, and capturing the mean with confidence intervals OTH: Students use a Web applet to further explore confidence intervals. FR: 00(B) #4, 004(B) #, 005 #5 SC5 The course provides instruction in statistical inference. 0

11 Syllabus v Chapter 0: Hypothesis Testing Using a Single Sample Hypotheses and Test Procedures Errors in Hypothesis Testing Large-Sample Hypothesis Tests for a Population Proportion Hypothesis Tests for a Population Mean Power and Probability of Type II Error Communicating and Interpreting the Results of Statistical Analyses. Logic of hypothesis testing. Large sample test for a proportion 4. Test for a mean. Concepts of Type I and Type II Errors; concept of power Chapter 0 Section : Hypotheses and Test Procedures Section : Errors in Hypothesis Testing Section 3: Large-Sample Hypothesis Tests for a Population Proportion GCE: Hypothesis test for a population proportion Section 4: Hypothesis Tests for a Population Mean GCE: Hypothesis test for a population mean Section 5: Power and the Probability of Type II Error Section 6: Communicating and FF: Demonstration on equivalence of tests and estimates, distribution of p values, power, and power and sample size LAB: More Minitab (RJC) FR: 003 #, 004(B) #3, 005 #4 Chapter 0 Review Chapter 0 Test

12 Syllabus v Chapter : Comparing Two Populations or Treatments Inferences Concerning the Difference Between Means Using Independent Samples Inferences Concerning the Difference Between Means Using Paired Samples Large-Sample Inferences Concerning a Difference Between Two Proportions Distribution-Free Procedures for Inferences Using Independent Samples Chapter Review Chapter Test III D. 5. Sampling distribution of a difference between two independent-sample means IV A. 7. Large-sample confidence interval for a difference between two means 5. Test for difference between two independent means IV A. 7. Large-sample confidence interval for a difference between two means (paired) 5. Test for difference between two means (paired) III D. 4. Sampling distribution of a difference between two independent-sample proportions. IV A. 5. Large-sample confidence interval for a difference between two proportions 3. Large-sample test for a difference between proportions Chapter Section : Inferences Concerning the Difference Between Two Population or Treatment Means Using Independent Samples GCE: Inferences about differences in independent means FR: 006 #4 Section : Inferences Concerning the Difference Between Two Population or Treatment Means Using Paired Samples GCE: Inferences about differences in means with paired samples Section 3: Large-Sample Inferences Concerning a Difference Between Two Population or Treatment Proportions GCE: Inferences for differences in proportions FR: 006(B) # Section 4: Distribution-Free Procedures for Inferences Using Independent Samples Section 5: Communicating and Interpreting the Results of Statistical Analyses OTH: Students complete activities using independent samples and other activities using paired samples, adapted from various sources. LAB: More Minitab (RJC) FR: 998 #4, 000 #4, 00 #5, 003(B) #3, 003(B) #4, 004(B) #3, 004(B) #4, 005(B) #5, 005(B) #4, 006(B) #3, 006(B) #4

13 Syllabus v Chapter : The Analysis of Categorical Data and Goodness-of-Fit Tests 4 Chi-Square Tests for Univariate Categorical Data Tests for Homogeneity and Independence in a Two-Way Table Chapter Review Chapter Test III D. 8. Chi-square distribution 6. Chi-square test for goodness-of-fit 6. Chi-square test for homogeneity of proportions and independence Chapter Section : Chi-Square Tests for Univariate Categorical Data GCE: The goodness-of-fit test Section : Tests for Homogeneity and Independence in a Two-Way Table GCE: Homogeneity and independence Section 3: Communicating and OTH: Students complete activities (using M&Ms) to complete chi-square tests for univariate data, homogeneity, and independence. LAB: more Minitab (RJC) FR: 998 #3, 999 #, 003 #5, 003(B) #5 3

14 Syllabus v Chapter 3: Simple Linear Regression and Correlation: Inferential Methods As needed Simple Linear Regression Model Inferences About the Slope of the Population Regression Line Checking Model Adequacy Chapter 3 Review Chapter 3 Test Preparing for the AP Exam IV A. 8. Confidence interval for the slope of a least-squares regression line 7. Test for the slope of a least-squares regression line Chapter 3 Section : The Simple Linear Regression Model Section : Inferences About the Slope of the Population Regression Line Section 3: Checking Model Adequacy FR: 999 #, 00(B) #, 00 #4, 003(B) #, 004(B) #, 005 #3, 005(B) #5, 006 # Section 4: Inferences Based on the Estimated Regression Line Section 5: Inferences About the Population Correlation Coefficient Section 6: Communicating and Preparing for the AP Exam Students complete a practice examination (H and/or B) Scoring of the exam is discussed After the AP Exam Chapter 4: Multiple Regression Analysis Section : Multiple Regression Models Section : Fitting a Model and Assessing Its Utility Section 3: Inferences Based on an Estimated Model Section 4: Other Issues in Multiple Regression Section 5: Communicating and OTH: Students complete an activity adapted from ABS (gummy bears in space). LAB: Students utilize Minitab (RJC) to analyze the data from their activity and then use Microsoft Office to produce the write-up. 4