Ms. Story's  Page

 Classical AP Statistics, 2008-2009

• AP STATISTICS Class Overview The classroom is set up traditionally with individual student desks in rows that we may move into groups when we are working in smaller groups.  In the school-year 2006-2007 I had 2 classes with 20 students in them each.  I anticipate the same make up for next year.  The school-year is set up quarterly beginning the Wednesday after Labor Day.  In order to be enrolled in the AP Statistics class, students must have earned at least a B+ average in their Algebra II and have Department Head approval. Students are strongly encouraged to form study groups – location can be provided if necessary.  Students have access to computers at the high school and software (Autograph) is available for the students to upload for their home computer.  During the school-year 2006-7 classes were 46 minutes long and met each day.  There are approximately 45 days per quarter.  Next year the schedule is proposed to be changed to include a rotating schedule with a one period a day long block which is approximately 90 minutes in length (that will make up for a missing day later in the schedule) but the total class time remains unchanged.  The specifics are not yet known.             The school has purchased text books specifically designed for the high school AP Statistics Curriculum and resource materials from David Bock, Pearson/Addison Wesley Publishers.  It is my plan to utilize these materials as much as possible as a way to keep on track and keep student expectations high. By doing this I feel the students will have a good foundation in statistics.  I plan to follow closely the estimated timeline outlined in the textbook.  By using the resource materials provided in the textbook package, I believe that all of the 4 broad conceptual themes described in the College Board AP Statistics Course Description, May 2007, 2008 are covered completely.                During class time I use a variety of teaching techniques to include but not limited to: class lecture, white board use (both by myself and by the students), graph board use, overhead projector with appropriate handouts, graphing calculator w/ overhead hook up,  presentation station link between classroom computer and TV monitor, group investigations, graphing calculator activities, Minitab 14 (software) activities and/or Autograph (software) activities in the schools computer lab and/or at home use, ActivStats, warm up questions at the beginning of class, notebook checks, homework problems, partner work, small group work and of course the traditional chapter quizzes and unit exams.  Also, please note that if we work on a problem (ie. from the homework or from another source) during class time –whether individual or grouped - students are expected to write a formal conclusion of their learning’s of that particular problem in their notebooks that serve as class “notes” for that day.               All students have a TI-83 or TI-83 Plus graphing calculator for use at all times.  Each topic that has a graphing calculator component has an explicit lesson that explains how to use the calculator and these explorations are incorporated in the classroom instruction.             The at–home–work is divided into 3 parts and they are attached at the end of this document along with their curricular requirements:  Homework – Problems from the chapters (usually odd numbered problems) that are checked off either on a due date or during the quarterly notebook check.  These problems are expected to be completed in students’ notebook correctly and completely (I expect their work to correctly communicate the results and interpretations using proper statistical vocabulary.)  The students are given complete solutions to similar problems (usually some of the even numbered exercises) as examples of how to correctly communicate the results and interpretations using proper statistical vocabulary.              C.A.G.’s – Collect and grade.  CAG’s are usually problems from the chapter   evens’ exercises (the ones I did not give out solutions for) and from the chapter        review sections that are collected and graded for correct communication of the   results of the review questions and interpretations using proper    statistical vocabulary.  Students are usually given at least 2 days to prepare a           C.A.G.  C.A.G.’s may be problems from the Unit we are currently working on or    from previous Units as a way to keep past topics fresh.             Investigative Tasks – Some chapters have an Investigative Task that Bock    suggests to be used to assess student learning with a rubric designed to replicate         the AP  Statistics criteria/rubric.  I plan to use 11 of these throughout the school-       year.  Students are given at least 1 week to complete these Investigative Tasks and        often we will work on these investigations during class group time.               Grading is determined as follows:                         Notebook check = 1 test grade                         Homework Average = 1 test grade                         Every 4 C.A.G.’s = 1 test grade                         Each Investigative Task = 1 test grade                         Each quiz = 1 test grade                         Each Unit Exam = 2 test grades                         *2nd and 4th quarters also have mid-term and final projects = 2 test grades                                 each Primary Textbook             Bock, David E., Paul F. Velleman, and Richard D. DeVeaux. Stats: Modeling the World. Boston : Pearson/Addison-Wesley, 2007 Resource Materials             Bock, David E., William B. Craine III. Stats: Modeling the World: Printed Test Bank and Resource Guide.  Boston : Pearson/Addison-Wesley, 2007.              Humphrey, Patricia, David E. Bock, William B. Craine III. Stats: Modeling the World: TI-83/84 Plus and TI-89 Manual.  Boston : Pearson/Addison-Wesley, 2004.             Bohan, James F.  AP Statistics: Preparing for the Advanced Placement Examination.  New York : Amsco School Publications, Inc., 2006 Technology             TI-83 or TI-83 Plus Graphing Calculators; Minitab 14 software; Autograph software; ActivStats software Miscellaneous Materials              Handouts of correctly solved even numbered problems from each chapter from the text; formula sheets from AP Central; Past AP questions from AP Central   AP Statistics Course Outline The 4 conceptual themes are woven throughout the course.  The following Chapters are broken up into quarters.  (Note: There are approximately 45 days per quarter – any “left over days” not accounted for in “Class Days” are for review, assessment purposes, assemblies, snow days etc.)  I have listed most of the skills learned with each Chapter (as quoted from the text book) along with chapter exercises, graphing calculator explorations, quizzes, ActivStats, Investigative tasks, and tests.  I have taught this course for 2 years and both years I failed to spend as much time as needed on the information in the last few chapters – it is my hope that if I follow closely the course outline suggested by Boch, I will far surpass the needed material and hold the students to a high standard of learning, as an AP class should be.   It is because of this that I have set up the course outline according to the text chapters.   Quarter 1: Chapter 1 “Stats Starts Here” (Class Days: 1)   Skills: Describes text set-up   Chapter 2 “Data” (Class Days: 2) Conceptual Theme: Exploring Data: Describing patterns and departures from patterns Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations   Skills: Be able to identify and describe the who, what, when, where, why and how of data, or recognize when some of this information has not been provided Be able to identify the cases and variables in any data set Be able to classify a variable as categorical or quantitative depending on its use. For any quantitative variable be able to identify the units in which the variable has been measured (or note that they have not been provided)   Exercises: See Chapter 2 Exercises to be completed   Chapter 2 Quiz   Technology: Entering data into graphing calculator/computer software; ActivStats lesson1&2:types of data  and context Quarter 1: Chapter 3 “Displaying and Describing Categorical Data” (Class Days: 3) Conceptual Theme: Exploring Data: Describing patterns and departures from patterns Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations   Skills: Be able to recognize when a variable is categorical and choose an appropriate display for it. Understand how to examine the association between categorical variables by comparing conditional and marginal percentages. Be able to summarize the distribution of a categorical variable with a frequency table. Be able to display the distribution of a categorical variable with a bar chart or pie chart. Know how to make and examine a contingency table. Know how to make and examine displays of the conditional distributions of one variable for two or more groups. Be able to describe the distribution of a categorical variable in terms of its possible values and relative frequencies. Know how to describe and discuss any anomalies or extraordinary features revealed by the display of a variable. Be able to describe and discuss patterns found in a contingency table and associated displays of conditional distributions.   Exercises: See Chapter 3 Exercises to be completed   Chapter 3 Quiz   Technology: Using software to display data; ActivStats lesson 3-1: distribution on 1 variable, displays of categorical data   Quarter 1: Chapter 4 “Displaying Quantitative Data” (Class Days: 4) Conceptual Theme: Exploring Data: Describing patterns and departures from patterns Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations   Skills: Be able to identify an appropriate display for any quantitative variable. Be able to guess the shape of the distribution of a variable by knowing something about the data. Know how to display the distribution of a quantitative variable with a stem-and-leaf display, a dot plot, and/or a histogram (by hand, graphing calculator, software) Know how to make and describe a time plot of data that may vary over time. Be able to describe the distribution of a quantitative variable in terms of its shape, center, and spread. Know how to describe any anomalies or extraordinary features revealed by the display of a variable. Know how to compare the distributions of two or more groups by comparing their shapes, centers, and spreads. Be able to discuss any outliers in the data, noting how they deviate from the overall pattern of the data. Exercises: See Chapter 4 Exercises to be completed   Chapter 4 Quiz   Technology: TI-83/software – how to make histograms and dotplots( ActivStats) Investigative Task: Dollars for Students     Quarter 1: Chapter 5 “Displaying Distributions Numerically” (Class Days: 5) Conceptual Theme: Exploring Data: Describing patterns and departures from patterns Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations   Skills: Be able to select a suitable measure of center and a suitable measure of spread for a variable based on information about its distribution. Know the basic properties of the median: The median divides the data into halves. Know the basic properties of the mean: The mean is the point at which the histogram balances. Know that the standard deviation summarizes how spread out all the data are around the mean. Know how to compute the mean, median, standard deviation, 5 number summary, IQR of a set of data. Be able to construct a boxplot (by hand, by calculator, and by software). Understand that the median and IQR resist the effects of outliers, while the mean and standard deviation do not. Understand that in a skewed distribution, the mean is pulled in the direction of the skewness relative to the median. Know how to describe summary measures in a sentence. Be able to describe the distribution of a quantitative variable with a description of the shape of the distribution, a numerical measure of center, and a numerical measure of spread.  Noting any unusual features (outliers).   Exercises: See Chapter 5 Exercises to be completed   Chapter 5 Quiz   Technology: Boxplots, 1 variable statistics on TI83/software; ActivStats: standard deviation   Investigative Task: Auto Safety Quarter 1: Chapter 6 “The Standard Deviation as a Ruler and the Normal Model” (Class Days: 7) Conceptual Theme: Exploring Data: Describing patterns and departures from patterns Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations   Skills: Understand how adding (subtracting) a constant or multiplying (dividing) by a constant changes the center and/or spread of a variable. Recognize when standardization can be used to compare values. Understand that standardizing uses the standard deviation as a ruler. Recognize when a Normal model is appropriate. Know how to calculate the z-score. Know how to compare values of two different variables using their z-scores. Be able to use Normal models and the Empirical Rule to estimate the percentage of observations falling 1, 2 or 3 standardizations of the mean. Know how to find the percentage of observations falling below any value in a Normal model using a Normal table and appropriate technology. Know how to check whether a variable satisfies the Nearly Normal Condition by making a Normal probability plot or histogram. Know what a z-score is and be able to explain how extraordinary (or not) a value may be by using a Normal model. Exercises: See Chapter 6 Exercises to be completed   Chapter 6 Quiz Technology: Using normalpdf; normalcdf; invnorm on TI83; scatterplots on TI83/software; ActivStats lesson 6: Normal model   TEST: UNIT 1 (chapters 1-6) Quarter 1: Chapter 7 “Scatterplots, Association, and Correlation” (Class Days: 3) Conceptual Theme: Exploring Data: Describing patterns and departures from patterns Curricular Requirements:  The course provides instruction with appropriate emphasis on exploring data.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.   Skills: Recognize when interest in the pattern of possible relationship between two quantitative variables suggests making a scattterplot. Know how to identify the roles of the variables and to place the response variable on the y-axis and the explanatory variable on the x-axis. Know the conditions for correlation and how to check them. Know that correlations are between -1 and 1, and that each extreme indicates a perfect linear association. Understand how the magnitude of the correlation reflects the strength of a linear association as view in a scatterplot. Know that correlation has no units. Know that the correlation coefficient is not changed by changing the center or scale of either variable. Understand that causation cannot be determined by a scatterplot or correlation. Know how to make a scatterplot (by hand or appropriate technology). Know how to compute the correlation of two variables. Know how to read a correlation table produced by a statistics program. Be able to describe the direction, form, and strength of a scatterplot. Be able to describe points that deviate from the overall pattern. Be able to use correlation as part of the description of a scatterplot. Be alert to misinterpretations of correlation. Understand that finding a correlation between two variables does not indicate a causal relationship between them.  Beware of the dangers of suggesting causal relationships when describing correlations.   Exercises: See Chapter 7 Exercises to be completed   Chapter 7 Quiz   Technology: Scatterplots, linear regression on TI83/software; ActivStats lesson 7:scatterplots   Quarter 1: Chapter 8 “Linear Regression” (Class Days: 8) Conceptual Theme: Exploring Data: Describing patterns and departures from patterns Curricular Requirements:  The course provides instruction with appropriate emphasis on exploring data.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.     Skills: Be able to identify response (y) and explanatory(x) variables in context. Understand how a linear equation summarizes the relationship between two variables. Recognize when a regression should be used to summarize a linear relationship between two quantitative variables. Be able to judge whether the slope of a regression line makes sense. Know how to examine data for violations of the Straight Enough Condition that would make it inappropriate to compute a regression. Understand that the least squares slope is easily affected by extreme values. Know that residuals are the differences between the data values and the corresponding values predicted by the line and that the least squares criterion finds the line that minimizes the sum of the squared residuals. Know how to use a plot of the residuals against predicted values to check the Straight Enough Condition or look for outliers. Know how to find a regression equation from the summary statistics for each variable and the correlation between the variables. Know how to find the regression equation using statistics software and how to find the slope and intercept values in a regression output table. Know how to use regression to predict a value of y for a given x. Know how to compute the residual for each data value and how to display them. Be able to write a sentence explaining what a linear equation says about the relationship between y and x, basing it on the fact that the slope is given in y-units per x unit. Understand how the correlation coefficient and the regression slope are related.  Be able to describe a prediction made from a regression equation, relating the predicted value to the specified x value. Exercises: See Chapter 8 Exercises to be completed   Chapter 8 Quiz   Technology: residuals on TI83/software; ActivStats lesson 8: Least squares regression   Investigative Task: Smoking   Quarter 1: Chapter 9 “Regression Wisdom” (Class Days:4) Conceptual Theme: Exploring Data: Describing patterns and departures from patterns Curricular Requirements:  The course provides instruction with appropriate emphasis on exploring data.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.     Skills: Understand when to use a linear model. Look for subgroups in data before you find a regression, and analyze them separately. Know the danger of exploiting beyounf the range of the x-values used to find the linear model, especially when the extrapolation tries to predict into the future. Understand the points may be unusual by having a large residual or by having high leverage. Understand that an influential point can change the slope and intercept of a regression line. Look for lurking variables whenever considering the association between two variables.  Know how to display residuals from a linear model by making a scatterplot of the residuals against predicted values or against the x- variable, and know what patterns to look in the picture. Know how to examine a scatterplot. Include diagnostic information such as plots of residuals and leverages as part of your report of a regression. Report any high leverage points.  Analyze data with and without any outliers. Include appropriate cautions about extrapolation when reporting predictions from a linear model. Discuss any lurking variables.   Exercises: See Chapter 9 Exercises to be completed   Chapter 9 Quiz   Technology: regression and residuals on TI83/software; ActivStats lesson 7: correlation tool; lesson 8 and 9: Linear regression   Investigative Task: Olympic Long Jump Quarter 1: Chapter 10 “Re-expressing Data” (Class Days: 8)   Conceptual Theme: Exploring Data: Describing patterns and departures from patterns Curricular Requirements:  The course provides instruction with appropriate emphasis on exploring data.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations. Skills: Recognize when a well-chosen re-expression may be helpful. Understand the value of re-expressing data to improve symmetry, to make the scatter around a line more constant, or to make the scatterplot more linear. Recognize when the pattern of the data indicates that no re-expression can improve the structure of the data. Know how to re-express the data with powers and how to find an effective re-expression for your data using statistics software or a calculator. Be able to reverse any of the common re-expressions to put a predicted value or residual back into the original data units. Be able to describe a summary or display of a re-expressed variable making clear how it was re-expressed and giving its re-expressed units. Be able to describe a regression model fit to re-expressed data in terms of the re-expressed variables.   Exercises: See Chapter 10 Exercises to be completed   Chapter 10 Quiz   Technology: re-expressing data on TI83/software; ActivStats lesson 10: re-expressing data      TEST: UNIT 2 (chapters 7-10)   Quarter 2 Chapter 11 “Understanding Randomness” (Class Days: 4) Conceptual Theme: Sampling and Experimentation: Planning and conducting a study Curricular Requirements: The course provides instruction with appropriate emphasis on sampling and experimentation. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations   Skills: Be able to recognize random outcomes in a real-world situation. Be able to recognize when a simulation might usefully model random behavior in the real world. Know how to perform a simulation either by generating random numbers on a computer, calculator, or by using some other source of random variables such as dice, a spinner, or a table of random numbers. Be able to describe a simulation so that others could repeat it. Be able to discuss the results of a simulation study and draw conclusions about the question being investigated. Exercises: See Chapter 11 Exercises to be completed   Chapter 11 Quiz   Technology: Random number generator on the TI-83/software; ActivStats lesson 11: randomness Investigative Task: ESP Quarter 2 Chapter 12 “Sample Surveys” (Class Days: 5) Conceptual Theme: Sampling and Experimentation: Planning and conducting a study Curricular Requirements: The course provides instruction with appropriate emphasis on sampling and experimentation. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations   Skills: Know the basic concepts of sampling. Recognize population parameters in descriptions of populations and samples. Understand the value of randomization as a defense against bias. Understand the value of sampling to estimate population parameters from statistics calculated on representative samples drawn from the population. Understand that eh size of the sample determines the precision of estimates. Know how to draw a SRS from a master list of a population, using a computer or a table of random numbers. Know what to report about a sample as part of your account of a statistical analysis. Be able to report possible sources of bias in sampling methods. Recognize voluntary response and non-response as sources of bias in a sample survey.   Exercises: See Chapter 12 Exercises to be completed   Chapter `12 Quiz Technology: ActivStats lesson 12: sample surveys  Quarter 2 Chapter 13 “Experiments and Observational Studies” (Class Days: 6) Conceptual Theme: Sampling and Experimentation: Planning and conducting a study Curricular Requirements: The course provides instruction with appropriate emphasis on sampling and experimentation. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations Skills: Recognize when an observational study is appropriate. Be able to identify observational studies as retrospective or prospective, and understand the strengths and weaknesses of each method. Know the four basic principles of sound experiment design: control, randomization, replication, and block, and be able to explain each. Be able to recognize the factors, the treatments, and the response variable in a description of a designed experiment. Understand the essential importance of randomization in assigning treatments to experimental units. Understand the importance of replication to move from anecdotes to general conclusions. Understanding the value of blocking so that variability due to differences in attributes of the subjects can be removed. Understand the importance of the control group and the need for a placebo treatment in some studies. Understand the importance of blinding and double blinding in studies on human subjects, and be able to identify blinding and the need for blinding in experiments. Understand the value of the placebo in experiments with human participants. Be able to design a completely randomized experiment to test the effect of a single factor. Be able to design an experiment in which blocking is used to reduce variation. Know how to use graphical displays to compare responses for different treatment groups. Know how to report the results of an observational study.  Identify the subjects, how the data were gathered, and any potential biases or flaws you may be aware of.  Identify the factors known and those that might have been revealed by the study. Know how to compare the responses in different treatment groups to assess whether the differences are larger than they could be reasonably expected from ordinary sampling variability. Know how to report the results of an experiment. Be able to report on the statistical significance of the result in terms of whether the observed group to group differences are larger than could be expected from ordinary sampling variation. Exercises: See Chapter 13 Exercises to be completed   Chapter 13 Quiz Technology: ActivStats lesson 13: designed experiments Investigative Task: Backhoe& Forklifts TEST:UNIT III Quarter 2 Chapter 14 “From Randomness to Probability” (Class Days: 3) Conceptual Theme: Anticipating Patterns: Exploring random phenomena using probability and simulation Curricular Requirements:  The course provides instruction with appropriate emphasis on anticipating patterns.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.     Skills: Understand that random phenomena are unpredictable in the short term but show long-run predictability. Be able to recognize random outcomes in a real-world situation. Know that the relative frequency of an outcome of a random phenomenon settles down as we gather more random outcomes. Be able to state the Law of Large Numbers. Know the basic definitions and rules of probability. Recognize when events are disjoint and when events are independent.  Understand the difference, and that disjoint events cannot be independent. Be able to use the facts abut probability to determine whether an assignment of probabilities is legitimate.  Each probability must be between 0 and 1 and the sum of the probabilities assigned to all possible outcomes must be 1. Know how and when to apply the addition rule.  Know that events must be disjoint for the addition rule to apply. Know how and when to apply the multiplication rule.  Know that events must be independent for the multiplication (combinations). Complement rule ( at least). Be able to use statements about probability in describing random phenomenon. Know and correctly use vocabulary with respect to probability.     Exercises: See Chapter 14 Exercises to be completed   Chapter 14 Quiz    Investigative Task: Dollars for Students Technology: use the TI-83/software for arithmetic; ActivStats lesson 14:LLN  Quarter 2 Chapter 15 “Probability Rules” (Class Days: 4) Conceptual Theme: Anticipating Patterns: Exploring random phenomena using probability and simulation Curricular Requirements:  The course provides instruction with appropriate emphasis on anticipating patterns.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.   Skills: Understand that the probability of an event is the proportion of times it occurs in many repetitions of a random phenomenon. Understand Conditional probability. Understand the concept of Independence. Know how and when to apply the General Addition/Multiplication Rules. Know how to find probabilities for compound events using a 2 way table. Know how to make and use a tree diagram. Be able to make a clear statement about a conditional probability that makes clear how the condition affects the probability. Avoid making statements that assume independence when there is none.   Exercises: See Chapter 15 Exercises to be completed   Chapter 15 Quiz   Technology: use the TI-83/software for arithmetic; ActivStats lesson 15: conditional probability and independence   Quarter 2 Chapter 16 “Random Variables” (Class Days: 4) Conceptual Theme: Anticipating Patterns: Exploring random phenomena using probability and simulation Curricular Requirements:  The course provides instruction with appropriate emphasis on anticipating patterns.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.     Skills: Be able recognize random variables. Understand that random variables must be independent in order to determine the variability of their sum or difference by adding variances. Be able to find the probability model for a discrete random variable. Know how to find the expected mean and variance of a random variable. (and adding and multiplying constants; adding or subtracting 2 independent random variables.) Stress proper notation. Be able to interpret the meaning of the expected value and standard deviation of a random variable in the proper context.   Exercises: See Chapter 16 Exercises to be completed   Chapter 16 Quiz   Technology:  Finding the expected mean and standard deviations using lists and 1- variable stats on the TI-83/software.  ActivStats lesson 16 randomness and CLT   Quarter 2 Chapter 17 “Probability Models” (Class Days: 6) Conceptual Theme: Anticipating Patterns: Exploring random phenomena using probability and simulation Curricular Requirements:  The course provides instruction with appropriate emphasis on anticipating patterns.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.   Skills: Know how to tell if a situation involves Bernoulli trials. Be able to choose whether to use a Geometric or a Binomial model for a random variable involving Bernoulli trials. Know and state the appropriate conditions for using a Geometric, Binomial, or Normal model. Know how to find the expected value of a Geometric model. Be able to calculate Geometric and Binomial probabilities. Know how to find the mean and standard deviation of a Binomial model. Be able to estimate with a Normal model. Be able to interpret means, standard deviations, and probabilities in the Bernoulli trial context.     Exercises: See Chapter 17 Exercises to be completed   Chapter 17 Quiz   Technology: finding Geometric and Binomial Probabilities on the TI-83/software ActivStats lesson 17: probability models   TEST:UNIT IV   Mid-term Project (Class Days:5)   Quarter 3: Chapter 18 “Sampling Distribution Models” (Class Days:4) Conceptual Theme: Statistical Inference: Estimating population parameters and testing hypotheses Curricular Requirements:  The course provides instruction with appropriate emphasis on statistical inference.  The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.       Skills: Understand that the variability of a statistic depends on the size of the sample. Understand the Central Limit Theorem. Be able to demonstrate a sampling distribution by simulation. Be able to use a sampling distribution model to make simple statements about the distribution of a proportion or mean under repeated sampling. Be able to interpret a sampling distribution model as describing the values taken by a statistic in all possible realizations of a sample or randomized experiment under the sample conditions.     Exercises: See Chapter 18 Exercises to be completed   Chapter 18 Quiz   Technology:  use the TI-83/software to help compute standard error; ActivStats lesson 18 CLT    Investigative Task: Simulated Coins Quarter 3: Chapter 19 “Confidence Intervals for Proportions” (Class Days: 4) Conceptual Theme: Statistical Inference: Estimating population parameters and testing hypotheses Curricular Requirements:  The course provides instruction with appropriate emphasis on statistical inference.  The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.     Skills: Understand confidence intervals as a balance between the precision and the certainty of a statement about a model parameter. Understand the margin of error of a confidence interval for a proportion changes with the sample size and the level of confidence. Know hoe to examine your data for violations of conditions that would make inference about a population proportion unwise or invalid. Be able to construct a one-proportion z-interval. Be able to interpret a one-proportion z-interval in a simple sentence or two.     Exercises: See Chapter 19 Exercises to be completed   Chapter 19 Quiz   Technology: creating a one-proportion z-interval on the TI-83/software; ActivStats lesson  19: inference for proportions Quarter 3: Chapter 20 “Testing Hypotheses about Proportions” (Class Days: 2) Conceptual Theme: Statistical Inference: Estimating population parameters and testing hypotheses Curricular Requirements:  The course provides instruction with appropriate emphasis on statistical inference.  The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.     Skills: Be able to state the null and alternative hypotheses for a one-proportion z-test. Know the conditions that must be true for a one-proportion z-test to be appropriate and know how to examine your data for violations of those conditions. Be able to identify and use the alternative hypothesis when testing hypotheses.  Understand how to choose between a one-sided and a two-sided alternative hypothesis and be able to explain your choice. Be able to perform a one-proportion z-test. Be able to write a sentence interpreting the results of a one-proportion z-test. Know how to interpret a P-value both in general and in the context of a problem.   Exercises: See Chapter 20 Exercises to be completed   Chapter 20 Quiz   Technology: Do a one-proportion z-test on the TI-83/software; ActivStats lesson 20:testing hypotheses Quarter 3: Chapter 21 “More about Tests” (Class Days: 3) Conceptual Theme: Statistical Inference: Estimating population parameters is and testing hypotheses Curricular Requirements:  The course provides instruction with appropriate emphasis on statistical inference.  The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions.  The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.  The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.     Skills: Understand the close relationship between hypothesis tests and confidence intervals. Be able to identify and use the alternative hypothesis when testing hypotheses.