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AP Statistics is a year-long every other day (A-day/B-day) class. Each period is 90 minutes. Students enrolled in the course passed an Honors level Algebra II course, a Pre-Calculus course, or both. The majority of the students are 11th and 12th graders, some taking Pre-Calculus or AP Calculus concurrently. Select 10th grade students are also permitted to take the course but are rare, 1 or 2 a year. For many students this is the first and sometimes only AP course they take. Students must take the AP Statistics Exam in May.
COURSE CONTENT
The Course is based on the objectives listed in the topic outline for AP Statistics from the College Board. The TI-83 plus graphing calculators are used on a daily by the students and used by the instructor to model their used in this course. TI-89 calculators are used by some students. Explanation of this calculators uses for statistical calculations is explained in detail in the textbook used. Student used built-in statistical functions of the TI-83 plus, such a 1-varstats, normcdf, etc. Additionally, the TI-83 plus calculator applications, including catalog help and the probability simulator, are also used. Students are asked to discover the connection between calculator graphical displays, tabular displays and results from calculator functions and the concept of the day. Examples of topics where this approach is used are: finding an outlier, determining symmetry or skewness from boxplots, etc. The instructor models the use of each of the calculator processes on an overhead calculator display.
Computer resources are also used by the instructor to promote the understanding and interpretation of computer printouts which is essential to success on the AP Exam. Students are introduced to Minitab through the course and encouraged to use Excel when preparing and writing the statistical project that is required in this course.
The project is due at the end of March. From experience this has proven to provide enlightenment for how everything works together for students who have not yet seen the connections. The project shows students how planning and conducting a study, describing patterns and departures from those patterns, using concepts involving random phenomena to understand the integration of collected data and the pattern seen and making inferences based on the entire process and an appropriate statistical test all fits together.
Students are assigned approximately 60 minutes of homework per class. Tests are administered about every two weeks as units are completed. Supplementary materials and laboratory activities are used in each unit to supplement the text. A four week review for the AP Exam is built into the pacing guide. Students regularly work in group settings when conducting laboratory activities and solving problems in class.
Each unit test is made up using Free Response questions from prior exams, these are also used during the review. In the process of solving Free Response questions students practice writing explanations. These explanations are based on the appropriate interpretations/processes used to draw conclusions from the calculated values. Students are expected to learn the mechanics of writing statistical interpretations and are instructed from the beginning of the course to use writing techniques.
Students will take a full length practice exam prior to the May test date. A released Exam will be used for this purpose.
COURSE OUTLINE & PACING GUIDE
TOPIC 1: EXPLORING DATA
(6 days- Goals 1 through 3, however this material is reviewed and applied repeatedly throughout the course.)
Goal 1: The leaner will construct and interpret graphical displays of univariate data.]
Objectives: Construct plots from the data, including dotplot, stemplot, histogram, cumulative frequency plot with and without the TI-83 plus (including the used the Stat Editor and StatPlot functions). Find center and spread, clusters, gaps, probable outliers, and shape from graph. Determine best graph to used based on shape of distribution.
Goal 2: The learner will apply numerical measurements to summarize distributions.
Objectives: Calculate center (median and mean), spread (range, interquartile range and standard deviation), and position (quartiles, percentiles, standardized scores) with and without the TI-83 plus (including 1-var stat function and boxplot.)
Collect biased data by convenience sampling to apply summary concepts and make conjectures.
Examine the effect of changing units of measure on summary measures.
Determine best measures to be used based on shape of distribution.
Write analysis of summary statistics using shape, center and spread, and deviations.
Goal 3: The leaner will compare distributions of univariate data pictured graphically.
Objectives: Write comparative statements about sets of data from both within the set and between multiple sets using information garnered from Goal 2, (shape, center and spread, and deviations).
Determine best measures to use for distributions based on shaped and spread of distributions, especially the middle 50% of the data.
(8 days- Goal 4)
Goal 4: The learner will explore bivariate data.
Objectives: Analyze graphical displays of bivariate data, discussing form, direction, strength and deviations.
Analyze data numerically for determination of form, direction, strength and deviations (correlation.)
Calculate the equation of the linear sets of data.
Determine linearity using graphical displays and numerical calculations (residual plots, residual values, correlation, outliers and influential points.).
Use linear concepts to transform logarithmic and power functions and to verify the type of graph formed.
Collect biased data from convenience samples to practice interpretation of bivariate data, examine computerized graphical displays and outputs and write descriptions of data using appropriate vocabulary, calculations and analysis. Use the TI-83 plus to calculate descriptive numerical calculations for bivariate data and to create graphs of this data.
(2 days- Goal 5, however this material will be used throughout the course and will be applied accordingly.)
Goal 5: The learner will explore categorical data.
Objectives: Construct frequency tables and bar graphs.
Construct two-way tables and segmented bar graphs.
Calculate marginal and joint frequencies from this
Data using the information garnered to interpret
meaning of statistical data in contextual situations.
Compare distributions using both bar charts and
Segmented bar graphs and write an appropriate
analysis of the information.
TOPIC 2: SAMPLING AND EXPERIMENTATION
(7 days- Goals 6 through 9)
Goal 6: The learner will examine methods of data collection.
Objectives: Determine the typed of collection method used to gather data; census, variety of types of sampling, variety of types experiments and observational studies.
Goal 7: The learner will study concepts needed to plan and conduct survey.
Objectives: Learn the characteristics of a well-designed and well- conducted survey, including but no limited to the wording of questions and the appearance interviewer.
Determine the population to be studied, the method to be used to randomly select a sample, and possible sources of bias.
Identify the type of sampling method to be used for best results in a survey: simple random sampling, stratified random sampling, and cluster sampling.
Randomly select a sample from a defined population (this is part of the project to be conducted at the end of the year).
Write a description of the process followed to correctly design a survey, including but not limited to the process used to acquire a random sample.
Goal 8: The learner will study concepts needed to plan and conduct experiments.
Objectives: Learn the characteristics of a well-designed and well- conducted experiment, including treatments, control groups, experimental units, random assignment and replication.
Conduct a group experiment where all aspects of a well- designed experiment are discussed and incorporated into the activity and then carried out.
Determine sources of bias and/or confounding that may cause results of the experiment to be unreliable, including used of placebos and blind and double-blind methods.
Design experiments using the methods of complete randomization, randomized block design and matched pairs designs.
Write a description of the complete process used in designing an experiment.
Goal 9: The learner will apply generalize the results and types of conclusions that can be drawn from observational studies, experiments, and surveys and be able to explain this generalization in written form.
TOPIC 3: ANTICIPATING PATTERNS
(35 days-Goals 10 through 13)
Goal 10: The learner will explore random phenomena using probability.
Objectives: Interpret probability, including long-run relative frequency interpretation.
Analyze expected outcomes using the Law of Large Numbers.
Perform probability calculations using addition and multiplication rules, conditional probability and rules for independence.
Calculate probabilities for discrete random variables and their probability distributions, including binomial and geometric distributions.
Stimulate data based on random behavior and probability distributions, including the use of the TI-83 plus application ProbSim.
Calculating expected value and standard deviation of a random variable, including by TI-83, plus functions, and transforming random variables linearly.
Goal 11: The learner will calculate probabilities for independent random variables.
Objectives: Determine the independence of a random variable distribution.
Calculate mean and standard deviation for sums and differences of independent random variables.
Goal 12: The learner will apply the probability of the normal distribution.
Objectives: Learn the properties of the normal distribution.
Use tables and TI-83 plus calculator functions, normcdf and invnorm, to find probability values for normal distributions.
Use the normal distribution as a measure to describe data.
Goal 13: The learner will apply the probability of sampling distributions.
Objectives: Apply the concept of sampling distributions to calculate probabilities involving a sample proportion, the difference between two independent sample proportions, a sample mean and the difference between two sample means.
Apply the Central Limit Theorem.
Use simulation techniques and the TI-83 plus calculator to simulate sampling distributions.
Apply probability calculations to both distributions and Chi-square distributions.
TOPIC 4: STATISTICAL INFERENCE
(28 days- Goals 14 &15)
Goal 14: The learner will use statistical inference to estimate confidence intervals.
Objectives: Estimate population parameters and margins of error.
Use properties of point estimators, including bias and variability.
Analyze confidence intervals explaining the meaning of the confidence level and interval.
Calculate large sample confidence intervals for a proportion and the difference between two proportions, both with and without the TI-83 plus confidence interval functions.
Calculate confidence intervals for a mean and the difference between two means, both with and without the TI-83 plus confidence interval functions.
Calculate confidence intervals for the slope of a least-squared regression line, both with and without the TI-83 plus confidence interval functions.
Analyze the results of a confidence interval and put the analysis in written form.
Goal 15: The learner will use statistical inference with tests of hypothesis.
Objectives: Apply the logic of significance tests with regard to hypotheses, p- values, and one- and two- sided tests.
Determine the Type I and Type II errors involved in specific application problems.
Determine the accuracy of results based on the concept of power.
Calculate the results of significance testing for large sample proportions and the difference between two proportions, for a mean and the difference between two means, Chi-square goodness of fit, homogeneity of proportions, and independence for one- and two-way tables, and the slope of a least-squares regression line, both with and without the TI-83 plus calculator functions.
Analyze the results of significance tests and put the analysis in written form.
(20 days)
Goal 16: The learner will review all materials taught in this course in preparation for the AP Exam.
(15 days)
Goal 17: The learner will present results of statistical to project to members of the AP class and will explore the use of statistics in careers.
The balance of the days will be used for Formal Mid-term and Term Examinations.
References and Materials
Primary Textbook:
Yates, Daniel S., Moore, David S., and Starnes, Daren S. The Practice of Statistics.
2nd ed. New York: W.H. Freeman and Company, 2003. ISBN: 0-7167-4773-1.
References:
Yates, Daniel S., and Starnes, Daren S. Golden Resource Binder. New York: W.H. Freeman and Company, 2002. ISBN: 0-7167-8345-2.
Statistics: Decisions Through Data. COMAP, Lexington, MA 1-800-772-6627.
HYPERLINK "http://www.comap.com" www.comap.com
Scheaffer, Richard, et al., Activity Based Statistics: Instructor Resources. New York: Springer- Verlag, 1996. ISBN 0-387-94597-0.
Technology:
TI-83 plus and TI-89 graphing calculators
Minitab statistical software.
Microsoft Excel software.
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