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 AP STATISTICS  M. McCarson, Hillcrest High School, 2005-2006 OVERVIEW The purpose of the Advanced Placement course in Statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data that is collected or studied. Students are exposed to four broad conceptual themes: 1. Exploring data: Observing patterns and departures from patterns 2. Planning a study: Deciding what and how to measure 3. Anticipating patterns: Producing models using probability and simulation 4. Statistical inference: Confirming models, making conclusions The principal text will be The Practice of Statistics by Yates, Moore, and Starnes. Other resources include, but are not limited to, Amsco review for AP Statistics, Schaeffer’s Activity-Based Statistics, Rossman’s Workshop Statistics, Barnett’s Statistics with the TI-83, Barton’s TI-83 Enhanced Statistics, Seymour’s Quantitative Literacy Series. Students need access to a TI-83 or other comparable calculator with statistical components. Students will also need access to the Internet for sample tests, discovery activities, and review notes. We will use Fathom software as necessary throughout the class. CHAPTER 1 – Organizing Data: Looking for Patterns and Departures from Patterns - Aug. 22 – Sept. 2 Define units, variables, quantitative vs. categorical Make graphs – dot (line) plots, histograms, stemplots, time plots Describe graphs giving center, spread, shape, skewness Find numerical summaries – median, mean, mean, standard deviation Make, describe, and compare boxplots Compare distributions and apply to real-world applications CHAPTER 2 – The Normal Distributions – Sept. 6 – Sept. 16 Density Curves – definitions, relationship to median, mean, Empirical Rule Calculate the z-score; calculate the probability (area under curve) Calculate the mean and standard deviation Assess normality using different methods Discuss Chebyshev’s theorem, finding standard deviation Use calculator to find z-scores, area, normality Apply normal distributions to real life applications CHAPTER 3 – Examining Relationships – Sept. 19 – Oct. 4 Define response vs. explanatory, independent vs. dependent variables Collect data and draw and describe scatterplots Define, compute, interpret the correlation coefficient – including cautions Find regression line – interpret slope, intercept; define and use r2; residuals; best fit Observe the effect of influential points on the line of best fit Apply line of best fit to real-world applications CHAPTER 4 - More on Two-Variable Data – Oct. 5 – Oct. 19 Model non-linear data; transform data to find line of best fit; discuss r and r2 Find power, exponential regressions and best fit model Extrapolation, lurking variables, cautions about r, r2, line of best fit Find and describe relations in categorical (two-way tables) data Relate non-linear graphs to real-life applications CHAPTER 5 – Producing Data – Oct. 20 – Nov. 4 Define sample, population, confounding, bias; describe different types of samples Describe cautions about samples Design experiments using control, randomization, replication; random digit table; observation vs. experiment Discuss statistical significance, bias, double-blind, types of experiments Discuss difference between parameters and samples. Simulate experiment using tables, objects (dice), calculators CHAPTER 6 – Probability: The Study of Randomness – Nov. 7 – Nov. 22 Define random, probability, and independent trials; sample spaces; tree diagrams Union, disjoint of data sets; addition rule; conditional probability Tree diagrams for conditional probability Bayes formula; apply to conditional probability Apply probability to games of chance Apply probability to simulations and real life applications. CHAPTER 7 – Random Variables – Nov. 28 – Dec. 9 Define random variable; make, describe, compare discrete and probability distributions Find mean and variance of distributions; develop rules for means and standard deviations Law of large numbers and misconceptions relating to “streaks” Determine when a game of chance is “fair” Apply probability distributions to simulations and real life applications. CHAPTER 8 – The Binomial and Geometric Distributions – Dec. 12 – Jan. 13 Define binomial setting and distributions Find mean and variance of binomial distributions Define geometric setting and distributions; mean; standard deviation Simulations in binomial, geometric settings Compare binomial and geometric to probability distributions CHAPTER 9 – Sampling Distributions – Jan. 18 – Feb. 1 Define parameter; variability; sampling distribution Define, describe, and compare sampling distributions of proportions Means, variances of sample proportion Define and apply the Central Limit Theorem Use simulations to develop sampling distributions Compare sampling distributions to probability distributions CHAPTERS 12 –Confidence Intervals and Test of Significance for Proportions Feb. 2 – Feb. 17 Discuss the meaning of a confidence interval; simulate making a confidence interval Find the sample confidence interval for proportions Find the sample confidence interval for the difference between two proportions Define margin of error, standard error vs. standard deviation Given a specific margin of error, determine appropriate sample size Discuss the logic of significance testing, null and alternative hypothesis, p-values; one and two sided tests; degrees of freedom Perform sample test for a proportion Perform sample test for a difference between two proportions CHAPTERS 12, 11, 10 – TESTS OF SIGNIFICANCE – Feb. 20 – March 10 Discuss and compare the graphs z- and t-distributions Find the sample confidence interval for means Find the sample confidence interval for the difference between two means Define margin of error, standard error vs. standard deviation Given a specific margin of error, determine appropriate sample size Discuss the logic of significance testing, null and alternative hypothesis, p-values; one and two sided tests; degrees of freedom Perform sample test for means Perform sample test for a difference between two means Perform sample test for a set of matched pairs data Compare significance tests to confidence intervals Discuss Type I and Type II errors, robustness, pooled vs. unpooled; concept of power CHAPTER 13 – CHI SQUARE DISTRIBUTIONS – March 13 – March 17 Organize relations in two-way tables Perform chi square tests for goodness of fit, homogeneity of proportions, and independence (one- and two-way tables) Compare chi square tests to two-sided proportion tests Apply chi-square tests to real life applications CHAPTER 14 – Inference for Regression – March 20 – March 31 Determine and recognize situations in which inference for regression lines is not safe Discuss the meaning of slope Perform a test for the inference of the slope of the regression line Read computer printouts to find the slope, intercept, regression line, standard errors and standard error about the line. Review for AP Exam – April 14 – May 1 Use old exams, Amsco book, Barron’s book, textbook supplementary material, projects to review for exam Note: Throughout the year, previously released AP questions will be used as test questions, class discussions; the grading and use of rubrics will be discussed as these examples are used. After the exam: May 3 – May 31 Project: 1) Students will formulate a sample, take a survey and report the results. 2) Students will design an experiment, observe the results, perform a test, and report the results. 3) Students will watch “Magic Town” and/or “Civil Action” to report on use of statistics in the media. 4) Students will work several teacher-made labs involving statistical concepts. |
