Instructional Unit Anticipating Patterns: Producing models using probability theory and simulation Anticipating Patterns: The students will be -Understand the concept of -data collection 2.7.11.A, Producing models using able to understand the law of large numbers -classroom 2.7.11.C, probability theory and and apply the laws -Utilize Venn diagrams to experiments 2.7.11.D, simulation of probability. show pictorial relationships -problem solving 2.7.11.E -Law of large numbers among events -applications to real concept -Determine if events are life data -Addition rule, multiplication disjoint, complementary, or -AP Statistics exam rule, conditional probability, and independent independence -Utilize the rules for -Discrete random variables probability to determine the and their probability probability of complex s, including binomial events -Understand and find -Simulation of probability conditional probabilities s, including binomial -Construct tree diagrams to and geometric organize information in -Mean and standard deviation solving problems of several of a random variable, and stages linear transformation of a random variable -Notion of independence versus dependence -Mean and standard deviation for sums and differences of independent random variables -Properties of the normal -Using tables of the normal Monday, August 18, 2003 Page 1 of 18
Instructional Unit Anticipating Patterns: Producing models using probability theory and simulation -The normal as a model for measurements sample proportion sample mean -Central Limit Theorem difference between two independent sample proportions practice questions difference between two independent sample means -Simulation of sampling Monday, August 18, 2003 Page 2 of 18
Instructional Unit Anticipating Patterns: Producing models using probability theory and simulation Anticipating Patterns: The students will be -Recognize and define both -data collection 2.6.11.D, Producing models using able to evaluate discrete and continuous -classroom 2.6.11.H, probability theory and random variables, random variables experiments 2.7.11.D simulation as well as binomial -Using tables or technology -problem solving -Law of large numbers and geometric find the areas under the -applications to real concept s. standard normal life data -Addition rule, multiplication curve given a normal -AP Statistics exam rule, conditional probability, and random variable independence -Calculate the mean and -Discrete random variables variance of a discrete and their probability random variable. s, including binomial -Using simulation and the law of large numbers, -Simulation of probability approximate the mean of a s, including binomial and geometric -Solve problems involving -Mean and standard deviation sums, differences, and of a random variable, and linear combinations of linear transformation of a random variables using random variable rules for means and -Notion of independence variances versus dependence -Mean and standard deviation for sums and differences of independent random variables -Properties of the normal -Using tables of the normal -The normal as a model for measurements sample proportion Monday, August 18, 2003 Page 3 of 18
Instructional Unit Anticipating Patterns: Producing models using probability theory and simulation sample mean -Central Limit Theorem difference between two independent sample proportions practice questions difference between two independent sample means -Simulation of sampling Monday, August 18, 2003 Page 4 of 18
Instructional Unit Anticipating Patterns: Producing models using probability theory and simulation Anticipating Patterns: The students will be -Standardize an observation -data collection 2.6.11.I Producing models using able to model data using a z-score -classroom probability theory and using a normal -Apply the empirical rule experiments simulation. -Recognize the shape of a -problem solving -Law of large numbers normal curve and estimate -applications to real concept the mean and standard life data -Addition rule, multiplication deviation -AP Statistics exam rule, conditional probability, and -Calculate the proportion of independence values above, below or -Discrete random variables between stated values on a and their probability normal curve using both s, including binomial tables and technology -Simulation of probability s, including binomial and geometric -Mean and standard deviation of a random variable, and linear transformation of a random variable -Notion of independence versus dependence -Mean and standard deviation for sums and differences of independent random variables -Properties of the normal -Using tables of the normal -The normal as a model for measurements sample proportion Monday, August 18, 2003 Page 5 of 18
Instructional Unit Anticipating Patterns: Producing models using probability theory and simulation sample mean -Central Limit Theorem difference between two independent sample proportions practice questions difference between two independent sample means -Simulation of sampling Monday, August 18, 2003 Page 6 of 18
Instructional Unit Anticipating Patterns: Producing models using probability theory and simulation Anticipating Patterns: The students will be -Recognize sampling -data collection 2.6.11.H, Producing models using able to analyze variability in a repetitive -classroom 2.6.11.I probability theory and sampling experiment experiments simulation s and -Interpret a sampling -problem solving -Law of large numbers correlate this -applications to real concept understanding to the -Describe the bias and life data -Addition rule, multiplication introduction to variability of a statistic in -AP Statistics exam rule, conditional probability, and terms of the mean and independence spread of its sampling -Discrete random variables and their probability -Calculate the mean and s, including binomial standard deviation of a sampling of a -Simulation of probability sample proportion and a s, including binomial sample mean and geometric -Interpret the relationship -Mean and standard deviation between sample size and of a random variable, and standard deviation linear transformation of a -Understand and apply the random variable Central Limit Theorem -Notion of independence - versus dependence -Mean and standard deviation for sums and differences of independent random variables -Properties of the normal -Using tables of the normal -The normal as a model for measurements sample proportion Monday, August 18, 2003 Page 7 of 18
Instructional Unit Anticipating Patterns: Producing models using probability theory and simulation statistical inference. practice questions sample mean -Central Limit Theorem difference between two independent sample proportions difference between two independent sample means -Simulation of sampling Monday, August 18, 2003 Page 8 of 18
Instructional Unit Exploring Data: Observing patterns and departures from patterns Exploring Data: Observing The students will be -Construct dotplots, -data collection 2.6.11.A, patterns and departures from able to interpret stemplots, histograms, -classroom 2.6.11.B, patterns graphical displays of cumulative frequency plots experiments -Center and spread s of -problem solving -Clusters and gaps univariate data. -Identify variables as -applications to real -Outliers and other unusual categorical or quantitative life data features -Describe the overall pattern -AP Statistics exam -Shape of a (center, -Measuring center: median, spread, shape) mean -Describe the overall shape -Measuring spread: range, of a (symmetric, interquartile range, standard skewed, outliers) deviation -Construct a time plot -Measuring position: -Analyze a time plot for quartiles, percentiles, trends and seasonal standardized scores -Boxplots -Comparing center and spread; within and between group variation -Comparing clusters and gaps -Comparing outliers and other unusual features -Comparing shapes -Analyzing patterns in scatterplots -Correlation and linearity -Least-squares regression line -Residual plots, outliers, and influential points -Transformations to achieve Monday, August 18, 2003 Page 9 of 18
Instructional Unit Exploring Data: Observing patterns and departures from patterns linearity; logarithmic and power variations practice questions transformations -Marginal and joint frequencies for two-way tables -Conditional relative Monday, August 18, 2003 Page 10 of 18
Instructional Unit Exploring Data: Observing patterns and departures from patterns Exploring Data: Observing The student will be -Determine measures of -data collection 2.6.11.A, patterns and departures from able to summarize center -classroom 2.6.11.B patterns s of -Determine measures of experiments -Center and spread univariate data. spread -problem solving -Clusters and gaps -Determine measures of -applications to real -Outliers and other unusual position life data features -Compare s of -AP Statistics exam -Shape univariate data using -Measuring center: median, dotplots, back-to-back mean stemplots, parallel boxplots -Measuring spread: range, interquartile range, standard deviation -Measuring position: quartiles, percentiles, standardized scores -Boxplots -Comparing center and spread; within and between group variation -Comparing clusters and gaps -Comparing outliers and other unusual features -Comparing shapes -Analyzing patterns in scatterplots -Correlation and linearity -Least-squares regression line -Residual plots, outliers, and influential points -Transformations to achieve Monday, August 18, 2003 Page 11 of 18
Instructional Unit Exploring Data: Observing patterns and departures from patterns linearity; logarithmic and power transformations -Marginal and joint frequencies for two-way tables practice questions -Conditional relative Monday, August 18, 2003 Page 12 of 18
Instructional Unit Exploring Data: Observing patterns and departures from patterns Exploring Data: Observing The students will be -Identify explanatory and -data collection patterns and departures from able to explore response variables -classroom patterns bivariate data. -Construct scatterplots of experiments -Center and spread bivariate data -problem solving -Clusters and gaps -Interpret the meaning of r, -applications to real -Outliers and other unusual the correlation coefficient life data features -Determine the -AP Statistics exam -Shape least-squares regression line -Measuring center: median, mean -Determine and interpret the -Measuring spread: range, slope and intercept of a interquartile range, standard regression line deviation -Examine the fit of a -Measuring position: regression line; numerically, quartiles, percentiles, visually, and with a residual standardized scores plot -Boxplots -Transform nonlinear data to -Comparing center and achieve linearity spread; within and between -Evaluate points as group variation -Comparing clusters and gaps -Comparing outliers and other unusual features -Comparing shapes -Analyzing patterns in scatterplots -Correlation and linearity -Least-squares regression line -Residual plots, outliers, and influential points -Transformations to achieve Monday, August 18, 2003 Page 13 of 18
Instructional Unit Exploring Data: Observing patterns and departures from patterns linearity; logarithmic and power influential practice questions transformations -Marginal and joint frequencies for two-way tables -Conditional relative Monday, August 18, 2003 Page 14 of 18
Instructional Unit Planning a Study: Deciding what and how to measure Planning a Study: Deciding The students will be -Understand that successful -data collection 2.6.11.A, what and how to measure able to understand statistical inference -classroom 2.6.11.E, -Census and apply methods requires production of data experiments 2.6.11.G, -Sample survey of data collection. -Differentiate between -problem solving 2.6.11.H -Experiment samples versus populations -applications to real -Observational study and experiments versus life data -Characteristics of a observational studies -AP Statistics exam well-designed and -Generate a simple random well-conducted survey sample using several -Populations, samples, and techniques of randomization random samples -Sources of bias in surveys -Understand and apply varying techniques of -Simple random sampling sampling, e.g. stratification -Stratified random sampling and blocking -Characteristics of a well-designed and well-conducted experiment -Treatments, control groups, experimental units, random assignments, and replication -Sources of bias and confounding, including placebo effect and blinding -Completely randomized design -Randomized block design, Monday, August 18, 2003 Page 15 of 18
Instructional Unit Planning a Study: Deciding what and how to measure Planning a Study: Deciding The students will be -Understand the -data collection 2.6.11.A, what and how to measure able to plan and characteristics of a well -classroom 2.6.11.E, -Census conduct surveys designed survey and experiments 2.6.11.G, -Sample survey and experiments. experiment -problem solving 2.6.11.H -Experiment -Identify and utilize the four -applications to real -Observational study basic principals of life data -Characteristics of a experimental design -AP Statistics exam well-designed and -Incorporate the use of well-conducted survey blindness and double -Populations, samples, and blindness into experimental random samples design -Sources of bias in surveys -Design studies that reduce the effect of bias -Simple random sampling -Explain how bias can be -Stratified random sampling reduced through the use of -Characteristics of a blocking and stratification well-designed and well-conducted experiment -Treatments, control groups, experimental units, random assignments, and replication -Sources of bias and confounding, including placebo effect and blinding -Completely randomized design -Randomized block design, Monday, August 18, 2003 Page 16 of 18
Instructional Unit Statistical Inference: Confirming models Statistical Inference: The students will be -State the meaning of a -data collection 2.6.11.H Confirming models able to compute and confidence interval -classroom -The meaning of a interpret a -Calculate a confidence experiments confidence interval confidence interval. interval for both a mean and -problem solving -Large sample confidence proportion -applications to real interval for a proportion -Determine the validity of a life data -Large sample confidence confidence interval based -AP Statistics exam interval for a mean on the sample data -Large sample confidence -Investigate the interval for a difference interrelationship among between two proportions margin of error, sample -Large sample confidence size, and level of interval for a difference confidence between two means (unpaired -Calculate and interpret a and paired) confidence interval for the -Logic of significance difference in both means testing, null and alternative and proportions hypotheses; p-values; oneand two-sided tests; concepts of Type I and Type II errors; concept of power -Large sample test for a proportion -Large sample test for a mean -Large sample test for a difference between two proportions -Large sample test for a difference between two means (unpaired and paired) -Chi-square test for goodness of fit, homogeneity Monday, August 18, 2003 Page 17 of 18
Instructional Unit Statistical Inference: Confirming models of proportions, and independence (one- and two-way tables) -t-s -Single sample t procedures -Two sample (independent and matched pairs) t procedures practice questions Monday, August 18, 2003 Page 18 of 18