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Standards Curriculum Map Bourbon County Schools Level: High School Grade and/or Course: AP Statistics Updated: May 2012 Days Unit/Topic Standards Days 125 Unit 1: Exploring and Understanding Data I. Exploring Data: Describing patterns and departures from patterns A. Constructing and interpreting graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot) 1.Center and spread 2.Clusters and gaps 3.Outliers and other unusual features 4.Shape B. Summarizing distributions of univariate data 1.Measuring center: median, mean 2.Measuring spread: range, interquartile range, standard deviation 3.Measuring position: quartiles, percentiles, standardized scores (z-scores) 4.Using boxplots 5.The effect of changing units on summary measures C._Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots) 1.Comparing center and spread: within group, between group variation 2.Comparing clusters and gaps 3.Comparing outliers and other unusual features 4.Comparing shapes E.Exploring categorical data 1.Frequency tables and bar charts 2.Marginal and joint frequencies for two-way tables 3.Conditional relative frequencies and association e.g. = Example only Activities AP Multiple Choice Bellringers FRQ Practice Data Collection Common assessment Learning Targets (“I Can” Statements) • I can identify the individuals and variables in a set of data. • I can identify each variable as categorical or quantitative. • I can make and interpret bar graphs, pie charts, dot plots, stem plots, and histograms of distributions of a categorical variable. • I can look for overall patterns and skewness in a distribution given in any of the above forms. • I can give appropriate numerical measures of center tendency and dispersion. • I can recognize outliers. • I can compare distributions using graphical methods. • I can use a graphing calculator to obtain summary statistics, to include the 5-number summary. Vocabulary Categorical Variable Quantitative Variable Population Sample Bar Chart Pie Chart Marginal Distribution Conditional Distribution Dotplot Stemplot Histogram Shape Center Spread Skewed Outliers Mode Symmetric Mean Median Range IQR Percentile Variance Standard Deviation Boxplot Normal model Parameter Statistic z-score 1 4. Comparing distributions using bar charts Days Unit/Topic Days 26-45 Unit 2: Regression Standards I. Exploring Data: Describing patterns and departures from patterns Activities AP Multiple Choice • I can know that areas under a density curve represent proportions. • I can approximate median and mean on a density curve. • I can recognize the shape and significant characteristics of a normal distribution, including the 68-95-99.7 rule. • I can find and interpret the standardized value (z-score) of an observation. • I can find proportions above or below a stated measurement given relevant measures of central tendency and dispersion or between two measures. • I can determine whether a distribution Approaches normality. • I can find marginal distributions from a two-way table. • I can describe the relationship between two categorical variables using percents. • I can recognize and explain Simpson’s paradox. Learning Targets (“I Can” Statements) • I can identify variables as quantitative or Vocabulary Scatterplot Association 2 D.Exploring bivariate data 1.Analyzing patterns in scatterplots 2.Correlation and linearity 3.Least-squares regression line 4.Residual plots, outliers and influential points Days Unit/Topic Days 46-65 Unit 3: Collecting Data Common Core Standards II.Sampling and Experimentation: Planning and conducting a study A.Overview of methods of data collection 1.Census 2.Sample survey 3.Experiment Bellringers FRQ Practice Data Collection Common assessment Activities AP Multiple Choice Bellringers FRQ Practice Data Collection Common assessment categorical. • I can identify explanatory and response variables. • I can make and analyze scatter plots to assess a relationship between two variables. • I can find and interpret the correlation r between two quantitative variables. • I can find and analyze regression lines. • I can use regression lines to predict values and assess the validity of these predictions. • I can calculate residuals and use their plots to recognize unusual patterns. • I can recognize limitations in both r and least-squares regression lines due to extreme values. • I can recognize lurking variables. • I can explain the difference between correlation and causality. Learning Targets (“I Can” Statements) • I can identify populations in sampling situations. • I can identify different methods of sampling, strengths and Correlation Correlation Coefficient Explanatory Variable Response Variable Lurking Variable LSRL Residual Slope Intercept R-squared Extrapolation Leverage Influential Point Vocabulary Random Simulation Sample survey Bias Sample Size Census 3 4.Observational study B.Planning and conducting surveys 1.Characteristics of a well-designed and wellconducted survey 2.Populations, samples and random selection 3.Sources of bias in sampling and surveys 4.Sampling methods, including simple random sampling, stratified random sampling and cluster sampling C.Planning and conducting experiments 1.Characteristics of a well-designed and wellconducted experiment 2.Treatments, control groups, experimental units, random assignmentsand replication 3.Sources of bias and confounding, including placebo effect and blinding 4.Completely randomized design 5.Randomized block design, including matched pairs design D.Generalizability of results and types of conclusions that can be drawn from observational studies, experiments and surveys Days Unit/Topic 66-90 Unit 4: Probability Common Core Standards III.Anticipating Patterns: Exploring random phenomena using probability and simulation A.Probability 1.Interpreting probability, including long-run relative frequency interpretation 2.“Law of Large Numbers” concept 3.Addition rule, multiplication rule, conditional probability and independence 4.Discrete random variables and their probability distributions, including binomial and geometric 5.Simulation of random behavior and probability distributions Activities AP Multiple Choice Bellringers FRQ Practice Data Collection Common assessment weaknesses of each, and possible bias that might result from sampling issues. • I can recognize the difference between an observational study and an experiment. • I can design randomized experiments. • I can recognize confounding of variables and the placebo effect, explaining when double-blind and block design would be appropriate. • I can explain how to design an experiment to support cause-andeffect relationships. Simple Random Sample (SRS) Sampling Frame Stratified Random Sample Cluster Sample Systematic Sample Voluntary Response Bias Response Bias Nonresponse Bias Convenience Sample Undercoverage Observational Study Experiment Factor Level Treatment Control Group Blocking Replication Control Randomization Blinding Placebo Confounding Learning Targets (“I Can” Statements) • I can describe and generate sample spaces for random events. • I can apply the basic rules of probability. • I can use multiplication and addition rules of probability appropriately. • I can identify disjointed, Vocabulary Trial Outcome Event Sample Space Law of Large Numbers Independence Probability Complement Mutually Exclusive (Disjoint) Conditional 4 6.Mean (expected value) and standard deviation of a random variable, and linear transformation of a random variable B.Combining independent random variables 1.Notion of independence versus dependence 2.Mean and standard deviation for sums and differences of independent random variables C.The normal distribution 1.Properties of the normal distribution 2.Using tables of the normal distribution 3.The normal distribution as a model for measurements complementary, and independent events. • I can use tree diagrams, Venn diagrams, and counting techniques in solving probability problems. • I can recognize and define discrete and continuous variables. • I can find probabilities related to normal random variables. • I can calculate mean and variance of discrete random variable. • I can use simulation methods using the graphing calculator and the law of large numbers to approximate the mean of a distribution. • I can use rules for means and rules for variances to solve problems involving sums, differences, and linear combinations of random variables. • I can verify four conditions of a binomial distribution: two outcomes, fixed number of trials, independent trials, and the same probability of success for each trial. • I can calculate cumulative distribution functions, cumulative Probability Random Variable Probability Model Expected Value Bernoulii Trials Geometric Distribution Binomial Distribution 5 Days Unit/Topic 91-110 Unit 5: Inference for Proportions Common Core Standards III.Anticipating Patterns: Exploring random phenomena using probability and simulation D.Sampling distributions 1.Sampling distribution of a sample proportion 2.Sampling distribution of a sample mean 3.Central Limit Theorem 4.Sampling distribution of a difference between two independent sample proportions 5.Sampling distribution of a difference between two independent sample means 6.Simulation of sampling distributions Activities AP Multiple Choice Bellringers FRQ Practice Data Collection Common assessment distribution tables and histograms, means and standard deviations of binomial random variables. • I can use a normal approximation to the binomial distribution to compute probabilities. • I can verify four conditions of a geometric distribution: two outcomes, the same probability of success for each trial, independent trials, and the count of interest is the number of trials required to get the first success. • I can calculate cumulative distribution functions, cumulative distribution tables and histograms, means and standard deviations of geometric random variables. Learning Targets (“I Can” Statements) • I can identify parameters and statistics in a sample. • I can interpret a sampling distribution, including bias and variability and how to influence each. • I can recognize when a problem involves a sample proportion. Vocabulary Sampling Distribution Central Limit Theorem Standard Error Confidence Interval Margin of Error Critical Value Hypothesis Test Null Hypothesis Alternative Hypothesis 6 IV.Statistical Inference: Estimating population parameters and testing hypotheses A.Estimation (point estimators and confidence intervals) 1.Estimating population parameters and margins of error 2.Properties of point estimators, including unbiasedness and variability 3.Logic of confidence intervals, meaning of confidence level and confidence intervals, and properties of confidence intervals 4.Large sample confidence interval for a proportion 5.Large sample confidence interval for a difference between two proportions B.Tests of significance 1.Logic of significance testing, null and alternative hypotheses; p-values; one- and two-sided tests; concepts of Type I and Type II errors; concept of power 2.Large sample test for a proportion 3.Large sample test for a difference between two proportions Days Unit/Topic 111-130 Unit 6: Inference for Means Common Core Standards IV.Statistical Inference: Estimating population parameters and testing hypotheses A.Estimation (point estimators and confidence intervals) 1.Estimating population parameters and margins of error 2.Properties of point estimators, including Activities AP Multiple Choice Bellringers FRQ Practice Data Collection Common assessment • I can analyze problems involving sample proportions, including using the normal approximation to calculate probabilities. • I can describe confidence intervals and use them to determine sample size. • I can assess statistical significance by comparing values. • I can analyze the results of significance tests. • I can explain Type I error, Type II error, and power in significance testing. • I can use the z procedure to test significance of a hypothesis about a population proportion. • I can use the twosample z procedure to test the hypothesis regarding equality of proportions in two distinct populations. Learning Targets (“I Can” Statements) • I can recognize when a problem involves sample means. • I can analyze problems involving sample means and understand how to use P-value Statistically Significant Alpha Level Confidence Level Type 1 Error Type 2 Error Power Pooling Vocabulary Student’s t Disribution Matched Pairs 7 unbiasedness and variability 3.Logic of confidence intervals, meaning of confidence level and confidence intervals, and properties of confidence intervals 6.Confidence interval for a mean 7.Confidence interval for a difference between two means (unpaired and paired) B.Tests of significance 1.Logic of significance testing, null and alternative hypotheses; p-values; one- and two-sided tests; concepts of Type I and Type II errors; concept of power 4.Test for a mean 5.Test for a difference between two means (unpaired and paired) Days Unit/Topic 131-145 Unit 7: Common Core Standards III.Anticipating Patterns: Exploring random Activities AP Multiple Choice the central limit theorem to approximate a normal distribution. • I can state null and alternative hypotheses in a testing situation involving a population mean. • I can calculate the one-sample t statistics and P-value for both one-sided and twosided tests about the mean μ using the graphing calculator. • I can recognize whether one-sample, matched pairs, or twosample procedures are needed. • I can recognize when inference about a mean or comparison of two means is necessary. • I can perform and analyze a one-sample t test to hypothesize a population mean and discuss the possible problems inherent in the test. • I can perform and analyze a two-sample t test to compare the difference between two means and discuss the possible problems inherent in the test. Learning Targets (“I Can” Statements) • I can choose the Vocabulary Chi-Squared 8 Inference for Counts and Slopes Days Unit/Topic 146-175 Unit 8: AP Exam Review phenomena using probability and simulation D.Sampling distributions 8.Chi-square distribution IV.Statistical Inference: Estimating population parameters and testing hypotheses A.Estimation (point estimators and confidence intervals) 1.Estimating population parameters and margins of error 2.Properties of point estimators, including unbiasedness and variability 3.Logic of confidence intervals, meaning of confidence level and confidence intervals, and properties of confidence intervals 8.Confidence interval for the slope of a leastsquares regression line B.Tests of significance 1.Logic of significance testing, null and alternative hypotheses; p-values; one- and two-sided tests; concepts of Type I and Type II errors; concept of power 6.Chi-square test for goodness of fit, homogeneity of proportions, and independence (one- and two-way tables) 7.Test for the slope of a least-squares regression line I. Exploring Data: Describing patterns and departures from patterns D.Exploring bivariate data 5.Transformations to achieve linearity: logarithmic andpower transformations Common Core Standards All of above Bellringers FRQ Practice Data Collection Common assessment Activities Mock Exam AP Multiple Choice Bellringers FRQ Practice Data Collection appropriate chi-square procedure for a given situation. • I can perform chisquare tests and calculate the various relevant components. • I can interpret chisquare test results obtained from computer output. • I can recognize when linear regression inference is appropriate for a set of data. • I can interpret the meaning of a regression for a given set of data. • I can interpret the results of computer output for regression. • I can recognize exponential growth and decay. • I can use logarithmic transformations to model a linear pattern, linear regression to find a prediction equation for the linear data, and transform back to a nonlinear model of the original data. Learning Targets (“I Can” Statements) All of above Distribution Goodness-of-Fit Homogenity Independence Component Residual Standard Deviation Re-expression Vocabulary All of above 9 10