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Advanced Placement Statistics – S. Walter - BCHS Syllabus 2016 Primary Textbook: Yates, Daniel, Moore, David, and Daren Starnes. The Practice of Statistics, fifth edition. New York: W.H. Freeman and Company, 2008. Technology: o All students will use a TI-84 graphing calculator for all work required. o All students will be exposed to Minitab computer output in sample problems and during classroom demonstration. Students will have some assignments that require use of Minitab software or interpretation of Minitab output. The following outline contains the course objectives as described by The College Board coupled with the corresponding chapter that covers the objectives. Preliminary Chapter: What Is Statistics? Introduction Data Production: Where Do You Get Good Data? Data Analysis: Making Sense of Data Probability: What are the Chances? Statistical Inference: Drawing Conclusions from Data Statistical Thinking and You Chapter 1: Exploring Data (2.5 Weeks) 1.1 Displaying Distributions with Graphs Variables: Categorical and quantitative Dotplots and histograms Interpreting histograms Outliers Center, Shape and Spread Symmetric and skewed distributions Stemplots Time Plots 1.2 Describing Distributions with Numbers Measuring Center: the mean Measuring Center: the median Comparing the mean and the median Measuring Spread: the quartiles (IQR and outliers) The five-number summary and boxplots (modified boxplots) Measuring Spread: the standard deviation Chapter 2: The Normal Distributions (2 Weeks) 2.1 Density Curves and the Normal Distributions Density Curves The median and mean of a density curve Normal Distributions (inflection points) The 68-95-99.7 Rule 2.2 Standard Normal Calculations The standard normal distribution Standardized observations Normal distribution calculations The standard normal table Finding normal proportions Finding a value given a proportion Assessing normality (histogram, boxplot, normal probability plot) Chapter 3: Examining Relationships (2.5 Weeks) 3.1 Scatterplots Response variable, explanatory variable Scatterplots Interpreting scatterplots (direction, form, strength) Positive association, negative association Linear relationship Adding categorical variables to scatterplots 3.2 Correlation The correlation r Facts about correlation 3.3 Least-Squares Regression Regression Line Mathematical model The least-squares regression line Equation of the least-squares regression line Facts about least-squares regression Slope of the least-squares regression line Coefficient of Determination Residuals / Residual plots Influential observations and outliers in regression Chapter 4: More on Two-Variable Data (2 Weeks) 4.1 Modeling Nonlinear Data Modeling nonlinear data Exponential and power functions Algebraic properties of logarithms Exponential growth and decay Linear growth and exponential growth Residuals again Power Regression 4.2 Interpreting Correlation and Regression Extrapolation Lurking Variables Using averaged data Association is not causation Causation, common response, confounding Associaton doesn’t imply causation 4.3 Relations in Categorical Data Marginal Distributions Two way tables Describing relationships Simpson’s Paradox Chapter 5: Producing Data (3 Weeks) 5.1 Designing Samples Sampling Voluntary Response Sample Experiment Confounding Statistical Inference Population, Sample Sample design Convenience Sampling Bias Simple Random Samples Random Digits Choosing an SRS Probability Sample Stratified Random Sample Multistage Sample Design Cautions about sample surveys Undercoverage and Nonresponse Response Bias Wording of Questions Inference about the population 5.2 Designing Experiments Observational Study –vs- Experiment Experimental Units, Subjects, Treatment, Factor, Level Comparative experiments Placebo effect Control Group Completely Randomized experiments Matching Randomization Completely Randomized design The Logic of Experimental Design Statistical significance Principles of Experimental Design: control, randomization, replication Cautions about experimentation (hidden bias) Double Blind experiment Block design Matched pairs design 5.3 Simulating Experiments Simulation Assigning of digits to represent outcomes Simulate many repetitions Simulations with calculator or computer Chapter 6: Probability: The Study of Randomness (2 Weeks) 6.1 Randomness The idea and language of probability Randomness and probability: Random phenomenon Thinking about randomness The uses of probability Independence 6.2 Probability Models Sample Space Tree diagram Multiplication Principle With and without replacement Intuitive probability: event Probability Rules Complement Disjoint Addition Rule Assigning probabilities: finite number of outcomes Assigning probabilities: equally likely outcomes Independence and the Multiplication Rule Applying the probability rules 6.3 More About Probability Rules of Probability: Complement, Addition, Multiplication General Addition Rule: Union and Disjoint sets Venn Diagrams Conditional Probability Joint Probability: General Multiplication Rule Definition of Conditional Probability Intersection Tree Diagrams with several stages Independent Events Chapter 7: Random Variables (1.5 Weeks) 7.1 Discrete and Continuous Random Variables Random variable Discrete Random variable Probability histogram Continuous random variable Normal distributions as probability distributions 7.2 Means and Variances of Random Variables The mean of a random variable Expected Value Statistical estimation and the law of large numbers The Law of small numbers How large is a large number? Rules for means The variance of a random variable Rules for variances Mid Term Exam Chapters 1 - 7 Chapter 8: The Binomial and Geometric Distributions (1.5 Weeks) 8.1 The Binomial Distribution The Binomial Setting Binomial Distribution Finding binomial probabilities Cumulative distribution functions Binomial formulas Binomial coefficient Binomial probability Simulating binomial experiments Binomial mean and standard deviation 8.2 The Geometric Distribution The Geometric setting Rules for calculating geometric probabilities Exploring geometric distributions with TI-83 The expected value and other noteworthy properties of the geometric random Variable Probability of more than “n” trials Chapter 9: Sampling Distributions (2 Weeks) 9.1 Sampling Distributions Parameter and Statistic Sampling variability Sampling distribution Describing sampling distributions The bias of a statistic Unbiased statistic The variability of a statistic 9.2 Sample Proportions Population proportion Sample proportion The sampling distribution of p hat Rule of Thumb 1 Rule of Thumb 2 9.3 Sample Means Parameters and statistics The mean and standard deviation of x Sampling distribution of a sample mean Central Limit Theorem The Law of Large Numbers revisited Chapter 10: Introduction to Inference (3 Weeks) 10.1 Estimating with Confidence Statistical Confidence Confidence Interval Margin of error Confidence Level Critical values Confidence Interval for a population mean How confidence intervals behave Choosing the sample size for desired margin of error Some cautions 10.2 Estimating a Population Mean Conditions for Inference about a Population Mean Standard Error The t Distributions Degrees of freedom One-sample t confidence interval Paired t procedures Robustness of t procedures 10.3 Estimating a Population Proportion Conditions for inference about a proportion A confidence interval for a population proportion Putting it all together: The inference toolbox Choosing the sample size Chapter 11: Testing a Claim (2 Weeks) 11.1 Significance Tests: The Basics Stating the null and alternative hypotheses Conditions for significance tests Test statistics P-values Statistical significance Interpreting Results in Context 11.2 Carrying Out Significance Tests Z test for a population mean Tests from confidence intervals Confidence intervals and two-sided tests 11.3 Use and Abuse of Tests Choosing a level of significance Statistical significance and practical importance Don’t ignore lack of significance Statistical inference is not valid for all sets of data Beware of multiple analyses 11.4 Using Inference to Make Decisions Type I and Type II Errors Error probabilities Significance and Type I error Power and Type II error Increasing the power Chapter 12: Significance Tests in Practice (2 Weeks) 12.1 Tests About a Population Mean The one-sample t statistic and the t distribution Determining p values The one-sample t test More about the one-sample t test: robustness and power 12.2 Tests About a Population Proportion The one-proportion z test Chapter 13 Comparing Two Population Parameters (1 Week) 13.1 Comparing Two Means Conditions for comparing two means The two-sample z statistic The two-sample t procedures Robustness again 13.2 Comparing Two Proportions Two-sample problems: proportions The sampling distribution of p1 – p2 Confidence interval for comparing two proportions Significance tests for p1 – p2 Significance test for comparing two proportions Chapter 14: Inference for Distributions of Categorical Variables: ChiSquare Procedures (1 Week) 14.1 Test for Goodness of Fit Chi square One-way table Expected count The Chi-Square goodness of fit test Properties of the Chi-Square distributions 14.2 Inference for Two-Way Tables Conditional distributions The problem of multiple comparisons Two-way tables Stating Hypotheses Computing Expected Cell Counts The X2 test for homogeneity of populations The X2 statistic and its p-value The X2 test of association/independence Chapter 15: Inference for Regression (1 Week) The regression model Conditions for the regression model Checking the regression conditions Estimating the parameters Confidence intervals for the regression slope Testing the hypothesis of no linear relationship Practice Final Exam Chapters 1 – 15 1st Semester Project: (after Chapter 5) Students will design a survey that will explore response bias. Since we have explored different types of bias, students will choose the type of bias that they want to confirm. A proposal of the initial question, (how bias will be determined), how subjects will be selected and a graphical display of the results will be required. Some examples of projects students have chosen: Does gender influence the response to whether girls/boys are better at sports? (person asking question – 1 male and other female) Would you date a girl taller than you? (one person asking question is much taller than other) Do you think cheerleaders are ditsy? (one person asking question is a cheerleader; other person is not) Can wording of the question play a role in the response of the survey? Students will submit a written analysis as well as present the projects in the form of an imovie to the class. The class will have the opportunity to ask questions concerning what worked and what did not work in the activity. 2nd Semester Project: After the AP exam is completed, students will design their own hypothesis test. They will determine the null and alternative hypothesis, decide the sampling method and perform the experiment. Examples of types of questions the students can ask: Is gender independent of choice of color of M & M? Does a bag of skittles match the proportion of colors that are supposed to be in the bag? Is gender related to horsepower and model of a car? Is age related to Piaget type questions? (which glass is more full? Which line is longer?) Are the ACT scores of the senior class higher than the state average? Students will submit a design for approval, as well as the method of data collection. A written analysis, including the positive and negatives of the project, will also be required. Students will also submit an imovie , power point presentation, or a podcast displaying the results in a graphical manner.