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AP Statistics Syllabus Course Overview Advanced Placement Statistics acquaints students with the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will work on projects involving the hands-on gathering and analysis of real world data. Ideas and computations presented in this course have immediate links and connections with actual events. Computers and calculators will allow students to focus on the concepts involved in statistics. This course prepares students for the Advanced Placement examination in Statistics. Texts and Resources: Bock, Velleman, De Veaux. Stats - Modeling the World, 2nd Edition, Pearson Incorporated, 2007. Supplemental Texts Yates, Moore, McCabe. The Practice of Statistics, 2nd edition, W.H. Freeman and Company, 1999 Other Resources Technology TI – 83+ caculator ActivStats software Computer Labs Internet Resources for AP Statistics AP Statistics list serve Interactive Sites Rice Virtual Lab in Statistics http://www.ruf.rice.edu/~lane/stat_sim/index.html Java applets that illustrate: sampling distributions (wow!), mean & median, normal approximation to the binomial, components of r, regression by eye, and repeated measures (independent vs. correlated t-tests). Webster West's Java Applets http://www.stat.sc.edu/~west/javahtml Histogram applet on Old Faithful data; also regression, confidence intervals, Let's Make a Deal, and power of a test. Java Demos for Probability and Statistics http://www.math.csusb.edu/faculty/stanton/m262/probstat.html Virtual Laboratories in Probability and Statistics http://www.math.uah.edu/stat Statistics Home Pages Al Coons at Buckingham, Brown, & Nichols http://www.bbns.org/us/math/ap_stats Daren Starnes' Home Page http://www.webb.org/math/starnes/ap_statistics.htm Sanderson Smith’s Page (Herkimer’s Hideaway) http://www.cate.org/sms99/apst99/stathmp.htm Page 1 of 21 John Burnette’s Page (Kincaid School) http://www.kinkaid.org/~jburne/OldFiles/stats_index.html Assessment Brian Schott's Database of Questions at Ga. State http://www.gsu.edu/~dscbms/ibs/ibsd.html John Burnette's Sample Test Questions http://www.kinkaid.org/~jburne/ Sources for data StatLib http://lib.stat.cmu.edu U.S. Bureau of the Census Home Page http://www.census.gov/ Gallup Poll Home Page http://www.gallup.com/ CUWU Statistics Data Applet http://www.stat.uiuc.edu/~stat100/cuwu/ Exploring Data http://exploringdata.cqu.edu.au/ . Free Software WinStat by Rick Parris, Phillips Exeter http://www.exeter.edu/rparris/default.html This guy is a wizard. His software is free, and will do about anything statistical you can think of. Better yet, he updates it regularly. Professional Organizations American Statistical Association College Board National Council of Teachers of Mathematics http://www.amstat.org/ http://www.collegeboard.org/ http://www.nctm.org/ On-Line Textbooks HyperStat Online http://davidmlane.com/hyperstat/index.html Complete with links to other sites on the web. Other Sites Chi square http://www.mste.uiuc.edu/patel/chisquare/keyprob.html Ken White's Coin Flipping Page http://shazam.econ.ubc.ca/flip/index.html STEPS Statistics glossary http://www.cas.lancs.ac.uk/glossary_v1.1/main.html Page 2 of 21 Course Outline Weeks 1-2 Resources, Assessments, and Strategies Unit of Study, Topics, and Student Objectives Organizing Data: Looking For Patterns and Departures from Patterns Topics: Exploring Data Displaying Distributions with Graphs Describing Distributions with Numbers Objectives: Gather information from a variety of sources; organize, sort, and categorize the information; interpret resulting data; make inferences and draw conclusions from relationships and patterns that emerge; communicate what has been learned.Gaining specific facts, ideas, vocabulary Graphical displays of distributions of univariate data: dot plots, stem-and-leaf plots, histograms (Center and spread, Clusters and gaps, Outliers and other unusual features, Shape and skewness); Summarizing distributions of univariate data (Measuring central tendency -- mean, median, mode, Measuring spread -- range, inter quartile range, standard deviation, Measuring position -- quartiles, percentiles, Box-and-whiskers plots, Changing units and standardizing scores); Comparing distributions of univariate data (dot plots , back-to-back stem-and-leaf plots, parallel box-and-whiskers plots) Page 3 of 21 Resources: Internet Text handouts Assessments: Chapter 1 Test Quizzes (2) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Labs & Other Strategies: Lab – Pulse Rates Have each person describe themselves with 2 words and 2 numbers. Object: Complex objects and phenomenon are frequently described with a few numbers. Find the mean, median, and mode in simulated sets of data with both odd and even numbers of data points. Draw box and whiskers plots both on paper and with TI-83 calculators using simulated data 3-4 The Normal Distributions Resources: Internet Text handouts Topics: Density Curves Normal Distributions Standard Normal Calculations Properties of Normal Distributions Using as a model for measurements Assessing normality Using normal probability tables Assessments: Chapter 2 Test Quiz (2) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Objectives: locate median and mean on a density curve recognize symmetric, left-skew, and right-skew distributions Use the Empirical Rule compute the standardized vale of an observation use the table or the calculator to calculate the proportion of values above (or below) a stated number calculate a point having a stated proportion of all values above it to be able to assess normality Page 4 of 21 Labs & Other Strategies: Lab- Rolling a Normal Distribution Lab- A Fine Grained Distribution Looking at Normal Distributions in test scores, heights, weights. 5-6 Examining Relationships Resources: Internet Text handouts Topics: Scatterplots Correlation Least-Squares Regression Analyzing patterns in scatterplots Correlation and linearity Median-median line Residual plots Least Squares line Outliers and influential points Re-expression of data Fitting models to data Assessments: Chapter 3 Test Quizzes (3) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Labs & Other Strategies: Lab- Making SAT/ACT Comparisons Analyzing Newspaper Scatterplots Objectives: Identify explanatory and response variables Make a scatterplot, and be able to include a categorical variable Describe the form, direction, and strength of the overall pattern of a scatterplot, as well as outliers and potentially influential observations Find and know the basic properties of correlation Explain slope and intercept from a linear regression equation Find the least-squares regression line with a calculator Use a regression line for prediction. Recognize extrapolation and be aware of its dangers Use r^2 to describe how much of the variation in one variable can be accounted for by a straight-line relationship with another variable Calculate and plot residuals and recognize unusual patterns. Page 5 of 21 7-8 More on Two-Variable Data Resources: Internet Text handouts Topics: Modeling Non-Linear Data Interpreting Correlation and Regression Relations in Categorical Data Objectives: recognize that exponential growth (or decay) results when a variable is multiplied by a fixed number greater than 1 (or positive number less than 1) in each time period recognize that a power function is the result of one variable being proportional to a power of a second variable Use semi-log transformations to linearize exponential data use log-log transformations to linearize power relationships Use least-squares regression on the transformed points, and inverse transformations to produce a curvilinear model for the original points Plotting residuals for the transformed data against a fitted line makes it easier to determine deviations from the overall pattern understand that both r and the least-squares regression line can be strongly influenced by a few extreme observations recognize possible lurking variables that may explain the observed association between two variables understand that even a strong correlation does not mean that there is a cause-and-effect relationship between x and y from a two-way table of counts, find the marginal distributions of both variables express any distribution in percents by dividing the category counts by their total describe the relationships between two categorical variables by computing and comparing percents, usually by comparing the conditional distributions of one variable for the different categories of the other variable Page 6 of 21 Assessments: Chapter 4 Test Quizzes (3) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Labs & Other Strategies: Lab- Designing a Game of Chance Lab- Looking at Annual Percentage Rates Lab- Flu Epidemic (Spreading Rumors) 9-10 Producing Data Topics: Designing Samples -Simple random sampling, Methods of data collection, Planning and conducting surveys, Questionnaire design Designing Experiments - Stratifying to reduce variation, Planning and conducting experiments, Randomized comparative experiments, Blocking to reduce variation Simulating Experiments Objectives: identify the population in a sampling situation recognize bias due to voluntary response samples and other inferior sampling methods use a table of random digits or a calculator to select a simple random sample (SRS) from a population. recognize the presence of under-coverage and non-response as sources of error in a sample survey. recognize the effect of the wording of questions on the response. Use random digits to select a stratified random sample from a population when the strata are identified recognize whether a study is an observational study or an experiment. recognize bias due to confounding of explanatory variables with lurking variables in either a study or an experiment. Identify the factors, treatments, response variables, and experimental units or sub jects in an experiment. outline the design of a completely randomized experiment using a diagram to include the size of the groups, the specific treatments, and the response variable. Use a table of random digits to carry out the random assignment of subjects to groups in a completely randomized experiment. recognize the placebo effect. recognize when double-blind techniques should be used. Explain why a randomized comparative experiment can give good evidence for causeand-effect relationships. Recognize that many random phenomena can be investigated by means of a carefully designed simulation. Run a simulation Use a random number table, a calculator, or software to conduct simulations. Page 7 of 21 Resources: Internet Text handouts Assessments: Chapter 5 Test Quizzes (3) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Labs & Other Strategies: Lab- A Class Survey Lab- Modifying A Class Survey Lab- Coke vs Pepsi The Real Challenge Using Die, Coins, Cards to Simulate Project- “Survey Project” (a sample of the student handout is included on page 18. 11-12 Probability: The Study of Randomness Resources: Internet Text handouts Topics: Randomness Probability Models More about Probability Multiplication, addition, and complement principles Probability of events occurring together Conditional probability Independent and mutually exclusive events Assessments: Chapter 6 Test Quizzes (3) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Objectives: Describe the sample space of a random phenomenon. For a finite number of outcomes, use the multiplication principle to determine the number of outcomes, and use counting techniques, Venn diagrams, and tree diagrams to determine simple probabilities For the continuous case, use geometric areas to find probabilities (areas under simple density curves) of events (intervals on the horizontal axis) Know the probability rules and be able to apply them to determine probabilities of defined events. In particular, determine if a given assignment of probabilities is valid. Determine if two events are disjoint, complementary, or independent. Find unions and intersections of two or more events. Know the general addition rule for the union of two events, and define joint probability. Apply these characterizations to solve problems. Define conditional probability and use the definition to find conditional probabilities of events. Use the multiplication rule to find the joint probability of two events. construct tree diagrams to organize the use of the multiplication and addition rules to solve problems with several states. Page 8 of 21 Labs & Other Strategies: Using Cards, Die, Coins and Calculator Lab- The Spinning Wheel 13-14 Random Variables Resources: Internet Text handouts Topics: Discrete and Continuous Random Variables Means and Variances of Random Variables Objectives: Recognize and define a discrete random variable, and construct a probability distribution table and a probability histogram for the random variable Recognize and define a continuous random variable, and determine probabilities of events as areas under density curves Given a normal random variable, use a table or calculator to find probabilities of events as areas under the stand normal distribution curve. Calculate the man and variance of a discrete random variable. Find the expected payout in a raffle or similar game of chance. use simulation methods and the law of large numbers to approximate the mean of a distribution. Use rules for mans and rules for variances to solve problems involving sums and differences of random variables. Page 9 of 21 Assessments: Chapter 7 Test Quizzes (2) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Labs & Other Strategies: Lab- The Game of Craps Project- Write a program to play the game of Craps 15-16 Binomial and Geometric Distributions Topics: Binomial Distributions - Binomial Probabilities, Binomial Formulas, Simulating Binomial Experiments, Mean and Standard Deviation of a Binomial Random Variable Geometric Distributions - Geometric Probabilities, Mean of a Geometric Random Variable Objectives: identify parameters and statistics in a sample or experiment. Recognize the fact of sampling variability: a statistic will take different values when you repeat a sample or experiment. Interpret a sampling distribution as describing the values taken by a statistic in all possible repetitions of a sample or experiment under the same condition. Describe the bias and variability of a statistic in terms of the man and spread of its sampling distribution. Understand that the variability of a statistic is controlled by the size of the sample (larger samples are less variable). Recognize when a problem involves a sample proportion, p-hat. Find the mean and standard deviation of a sample proportion for an SRS of size n from a population having population proportion pi. Know that the standard deviation of the sampling distribution of p-hat gets smaller at the rate of the square root of n, as n gets larger. Recognize when you can use the normal approximation to the sampling distribution of phat. Use the normal approximation to calculate probabilities that concern p-hat. Recognize when a problem involves the mean x-bar of a sample. Find the mean and standard deviation of a sample mean x-bar from an SRS of size n when the mean mu and standard deviation sigma of the population are known. Know that the standard deviation of the sampling distribution of x-bar gets smaller at the rate of the square root of n as the sample size n gets larger. Understand that x-bar has approximately a normal distribution when the sample is large (central limit theorem). Use this normal distribution to calculate probabilities that concern x-bar. Use the law of large numbers to interpret the population mean mu as the average of an indefinitely large number of observations drawn from the population Page 10 of 21 Resources: Internet Text handouts Assessments: Chapter 8 Test Quizzes (2) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Labs & Other Strategies: Lab- A Gaggle of Girls Activity- Simulations of Binomial and Geometric Settings 17-18 Sampling Distributions Topics: Sampling Distributions - Parameter vs. Statistic, Bias and Variability, Sample Proportions – Means and Standard deviation of sample proportions Sample Means – Means and Standard deviation of sample means Sample Means from a Normal Population Central Limit Theorem; Law of Large Numbers Objectives: identify parameters and statistics in a sample or experiment. Recognize the fact of sampling variability: a statistic will take different values when you repeat a sample or experiment. Interpret a sampling distribution as describing the values taken by a statistic in all possible repetitions of a sample or experiment under the same condition. Describe the bias and variability of a statistic in terms of the man and spread of its sampling distribution. Understand that the variability of a statistic is controlled by the size of the sample (larger samples are less variable). Recognize when a problem involves a sample proportion, p-hat. Find the mean and standard deviation of a sample proportion for an SRS of size n from a population having population proportion pi. Know that the standard deviation of the sampling distribution of p-hat gets smaller at the rate of the square root of n, as n gets larger. Recognize when you can use the normal approximation to the sampling distribution of phat. Use the normal approximation to calculate probabilities that concern p-hat. Recognize when a problem involves the mean x-bar of a sample. Find the mean and standard deviation of a sample mean x-bar from an SRS of size n when the mean mu and standard deviation sigma of the population are known. Know that the standard deviation of the sampling distribution of x-bar gets smaller at the rate of the square root of n as the sample size n gets larger. understand that x-bar has approximately a normal distribution when the sample is large (central limit theorem). Use this normal distribution to calculate probabilities that concern x-bar. use the law of large numbers to interpret the population mean mu as the average of an indefinitely large number of observations drawn from the population. Page 11 of 21 Resources: Internet Text handouts Assessments: Chapter 9 Test Quizzes (3) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Labs & Other Strategies: Lab- Sampling Pennies Lab- The Distribution of Height 19-20 Introduction to Inference Topics: Estimating with Confidence - Logic of confidence intervals, Tests of Significance - null and alternative hypotheses, p-values, one and two-sided tests Using Significance Tests Inference as Decision - Type I and Type II errors, power against the alternative Objectives: State in non-technical language what is meant by "95% confidence." Interpret confidence level as well as the interval. Calculate a confidence interval for the mean mu of a normal population with known standard deviation sigma. Recognize when you can safely use the confidence interval formula and when the sample design or a small sample from a skewed population makes it inaccurate. Understand how the margin of error of a confidence interval changes with the sample size and the level of confidence C. Find the sample size required to obtain a confidence interval of specified margin of error m when the confidence level and other information are given. Determine what Type I and Type II errors are in the context of a situation. Recognize that for a significance level alpha, alpha is the probability of a Type I error, and the power against a specific alternative is 1 minutes the probability of a Type II error for that alternative. Recognize that increasing the size of the sample increases the power (reduces the probability of Type II error) when the significance level remains fixed. State the null and alternative hypotheses in a testing situation when the parameter in question is a population mean mu. Explain in non-technical language the meaning of the P-value when you are given th4e numerical value of p for a test. Calculate the z statistic and the P-value for both one-sided and two-sided tests about the mean mu of a normal population. Assess statistical significance at standard levels alpha, either by comparing p to alpha or by comparing z to standard normal critical values. Recognize that significance testing does not measure the size or importance of an effect. Recognize when you can use the z test and when the data collection design or a small sample from a skewed population makes in appropriate. Page 12 of 21 Resources: Internet Text handouts Assessments: Chapter 10 Test Quizzes (4) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Labs & Other Strategies: Lab- Pick a Card Lab- “Thumbtacks” up or down and their proportions 21-23 Inference for Distributions Resources: Internet Text handouts Topics: Inference for the Mean of a Population Comparing Two Means t-distributions; t-confidence intervals and tests; matched pairs t-procedures; choosing sample size comparing two means two-sample t-procedures; robustness; technology for more accurate levels in the t-procedures; pooled two-sample t-procedures; Assessments: Chapter 11 Test Quizzes (2) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Objectives: Recognize when a problem requires inference about a mean or a proportion. Recognize from the design of a study whether one-sample, matched pairs, or a single proportion procedure is needed. use the t-procedures to obtain a confidence interval at a stated level of confidence for the mean mu of a population. Carry out a t-test for the hypothesis that a population mean mu has a specified value against either a one-sided or a two-sided alternative. recognize when the t-procedures are appropriate in practice, in particular that they are quite robust against lack of normality but are influenced by outliers. Also recognize when the design of the study, outliers, or a small sample from a skewed distribution make the t-procedures risky. Recognize matched pairs data and use the t-procedures to obtain confidence intervals and to perform tests of significance for such data. Give a confidence interval for the difference between two means. Use the two-sample t statistic with conservative degrees of freedom or the calculator. Recognize when the two-sample t procedures are appropriate in practice. Page 13 of 21 Labs & Other Strategies: Lab- Paper Airplane Experiment Lab- Dominant & Non-Dominant Hand Activity Lab- Pulse Rates between male and female students 24-25 Inference for Proportions Resources: Internet Text handouts Topics: Inference for a Population Proportion Comparing Two Proportions assumptions for inference about a proportion z procedures; choosing sample size; the sampling distribution of p-hat 1 minus p-hat 2; confidence intervals for pi 1 minus pi 2; significance tests for pi 1 minus pi 2. Assessments: Chapter 12 Test Quizzes (2) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Objectives: Calculate from sample counts the sample proportion that estimates the population proportion. Use the z procedure to give a confidence interval for a population proportion pi. Use the z statistic to carry out a test of significance for the hypothse about a population proportion pi against either a one-sided or a two-sided alternative. Check that you can safely use z procedures in a particular setting. Test the hypothesis that two populations have equal means against either a one-sided or two-sided alternative. use the two-sample t test with conservative degrees of freedom or [preferably] a calculator or software. use the two-sample z procedure to give a confidence interval for the difference pi 1 - pi 2 between proportions in two populations based on independent samples from the population. use a z statistic to test the hypothesis that proportions in two distinct populations are equal. check that you can safely use 2-proportion z procedures in a particular setting. Page 14 of 21 Labs & Other Strategies: Lab- Is One Side of a Coin Heavier? Lab- Testing M&M proportions 26-27 Inference for Two-Way Tables: Chi Square Topics: Inference for Two-Way Tables Test for Goodness of Fit test for goodness of fit; chi-square distributions; expected counts; inference for two-way tables: a single SRS with each individual classified according to both of two categorical variables; an entire population, with each individual classified according to both of two categorical variables Objectives: For goodness of fit, calculate expected counts for each category in a distribution, the chisquared statistic, and the p-value. State null and alternative hypotheses for a difference between two distributions. If the test is significant, use components of the chi-square statistic to identify the most important deviations between observed and expected counts. Arrange data on successes and failures in several groups into a two-way table of counts of successes and failures in all groups. Use percents to describe the relationships between two categorical variables starting from the counts in a two-way table. Locate expected cell counts, the chi-square statistic, and its P-value in output from software or calculator. Explain what null hypothesis the chi-square statistic tests in a specific two-way table. If a test of independence is significant, use percents, comparison of expected and observed counts, and the components of the chi-square statistic to see what deviations from the null hypothesis are most important. In doing the chi-square test, calculate the expected count for any cell from the observed counts in a two-way table. Calculate the component of the chi-square statistic for any cell, as well as the overall stat Give the degrees of freedom of a chi-square statistic. Use the chi-square critical values from a table to approximate the P-value of a chi-square test. Page 15 of 21 Resources: Internet Text handouts Assessments: Chapter 13 Test Quizzes (2) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Labs & Other Strategies: Lab- “I Didn’t Get Enough Blues!” What type of distribution is most useful for evaluating surveys for voting or yes or no questions? Why does the binomial distribution start to look like a normal distribution when the sample size is large? 28-29 Inference for Regression Resources: Internet Text handouts Topics: Inference about the Model Inference about Prediction Checking the Regression Assumptions Objectives: Assumptions for inference: SINR [S: Standard deviation of responses about the true line is the same for each x] [I: Independent observations] [N: Normal distribution of responses about the line [check residuals for normality!] [R: Randomly selected observations] calculate standard error s about the line calculate confidence interval for regression slope test the hypothesis of no linear relationship [test for regression slope] Page 16 of 21 Assessments: Chapter 14 Test Quizzes (3) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Labs & Other Strategies: Labs- The Legacy of Jet Skis Labs- ACT/SAT Scores Activity- “Leaning Tower of Pisa” 30-34 AP Exam Review Resources: Internet Text handouts Topics: Review 1st Semester Review 2nd Semester Objectives: Complete and grade practice exams Learn Grading processes for AP Exam Learn Testing Strategies for Multiple Choice, Short Answer, and Essay Scoring Guidelines for AP Exams Rubric of Scoring Guidelines Labs & Other Strategies: Hints and Reminders about AP Exam Key Phrases to Remember Common Mistakes of Students Review Project – Students split into groups and prepare an oral presentation and a written assessment over assigned topics from throughout the year. Resources: Internet Text handouts Final Project Topics: Review 1st Semester Review 2nd Semester Assessments: Objectives: Assessments: Previous AP Exams Quizzes (Previous AP Questions) Prep for Exam from Golden Binder Homework – odd numbered problems each section as normal assignment Demonstrate ability to combine topics from throughout the course in order to effectively apply statistical procedures to a real-world topic. Page 17 of 21 A copy of both the student handout and a simplified grading rubric from Stats: Modeling the World is provided on pages 19-21. Statistics Group Survey Project Group Members: ________________________ ________________________ ________________________ The Survey must: Have an appropriate Parameter it is attempting to investigate. Include at least 5 questions Have at least 50 respondents. Use an appropriate form of random sampling. The Written Report must include: Copy of your survey Copy of your results. Description and analysis of your sampling method. Discussion of your Population, Parameter, and Sampling Frame Discussion of any potential forms for bias affecting your sample. Discussion of any recommended ways to enhance/improve your survey design. The Oral Report must include: between 2-5 minutes in length Visual Aid o neat o clearly visible for entire class during presentation All topics covered in the written report must be included. Page 18 of 21 Page 19 of 21 Page 20 of 21 Page 21 of 21