AP Statistics Syllabus - Math

Bishop Walsh SchoolSY 2013-2014AP Statistics SyllabusCourse Description:The purpose of this course is to introduce students to the major concepts and tools forcollecting, analyzing, and drawing conclusions from data. Students are exposed to fourbroad conceptual themes: exploring data, sampling and experimentation, anticipatingpatterns, and statistical inference. This AP Statistics course is taught as an activitybased course in which students actively construct their own understanding of theconcepts and techniques of statistics through the use of small groups, projects, andtechnology.Course Textbook:Bluman, Allan: Elementary Statistics: A Step-by-Step Approach, 7th edition.New York: McGraw-Hill, 2009.Technology: All students need to have access to TI-89, TI-nspire, or TI-nspire CAS graphingcalculators for use in class, at home, on any assignment or assessment, and onthe AP Exam. If purchasing a calculator for the first time, then the TI-nspire CASis strongly recommended for purchase. Students are encouraged to use theircalculator throughout the course and become familiar with the keystrokes andunderlying operations the calculator is computing. All students will have access periodically to the computer lab to use statisticalsoftware (Minitab, Excel) to aid in graphing, problem solving, and simulations.S. Davis1

Bishop Walsh SchoolSY 2013-2014Course Outline:ApproximateTimeInstruction:2 weeksTest:1 dayInstruction:2 weeksTest:1 dayS. DavisTopics/ActivitiesChapter 1:The Nature of Probability and Statistics1.1 – Descriptive and Inferential Statistics1.2 – Variables and Types of Data1.3 – Data Collection and Sampling Techniques Random Sampling Systematic Sampling Stratified Sampling Cluster Sampling Other Sampling Methods1.4 – Observational and Experimental Studies1.5 – Uses and Misuses of Statistics Suspect Samples Ambiguous Averages Detached Statistics Implied Connections Misleading Graphs Faulty Survey Questions1.6 – Computers and Calculators in StatisticsChapter 2:Frequency Distributions and Graphs2.1 – Organizing Data Categorical frequency distributions Grouped frequency distributions2.2 – Histograms, Frequency Polygons, and Ogives Histogram Frequency polygon Ogive Relative frequency graphs Distribution shapes2.3 – Other Types of Graphs Bar graphs Pareto charts Time series graph Pie graph Misleading graphs Stem and leaf plots2

Bishop Walsh SchoolInstruction:3 weeksTest:1 dayS. DavisSY 2013-2014Chapter 3:Data Description3.1 – Measures of Central Tendency Mean Median Mode Midrange Weighted Mean Distribution shapes3.2 – Measures of Variation Range Population variance and standard deviation Sample variance and standard deviation Variance and standard deviation for grouped data Coefficient of variation Range rule of thumb Chebyshev’s theorem The Empirical (Normal) Rule3.3 – Measures of Position Standard scores Percentiles Quartiles and deciles Outliers3.4 – Exploratory Data Analysis The Five-Number summary and boxplots3

Bishop Walsh SchoolInstruction:3 weeksTest:1 dayInstruction:2 weeksTest:1 dayS. DavisSY 2013-2014Chapter 4:Probability and Counting Rules4.1 – Sample Spaces and Probability Classical Probability Complementary events Empirical probability Law of large numbers Subjective probability4.2 – The Addition Rules of Probability4.3 – The Multiplication Rules and Conditional Probability Multiplication rules Conditional probability Probabilities for “at least”4.4 – Counting Rules The fundamental counting rule Factorial notation Permutations Combinations4.5 – Probability and Counting RulesChapter 5:Discrete Probability Distributions5.1 – Probability Distributions5.2 – Mean, Variance, Standard Deviation, and Expectation Mean Variance and Standard deviation5.3 – The Binomial Distribution5.4 – Other types of Distributions Multinomial, Poisson, and Hypergeometric distributions4

Bishop Walsh SchoolInstruction:3 weeksTest:1 dayInstruction:2 weeksTest:1 dayInstruction:3 weeksTest:1 dayS. DavisSY 2013-2014Chapter 6:The Normal Distribution6.1 – Normal Distributions Standard normal distribution Finding areas under the standard normal curve Normal distribution curve as a probability6.2 – Applications of the Normal Distribution Finding data values given specific probabilities Determining normality6.3 – The Central Limit Theorem Distribution of sample means Finite population correction factor6.4 – The Normal Approximation to the Binomial DistributionChapter 7:Confidence Intervals and Sample Size7.1 – Confidence Intervals for the Mean when σ is Known Confidence intervals Sample size7.2 – Confidence Intervals for the Mean when σ is Unknown7.3 – Confidence Intervals and Sample Size for Proportions7.4 – Confidence Intervals for Variances and Standard DeviationsChapter 8:Hypothesis Testing8.1 – Steps in Hypothesis Testing8.2 – z Test for a Mean P-value method for hypothesis testing8.3 – t Test for a Mean8.4 – z Test for a Proportion8.5 – χ2 Test for a Variance or Standard Deviation8.6 – Additional Topic Regarding Hypothesis Testing Confidence intervals and hypothesis testing Type II error and the power of a test5

Bishop Walsh SchoolInstruction:2-3 weeksTest:1 dayInstruction:2 weeksTest:1 dayInstruction:1-2 weeksTest:1 dayInstruction1-2 weeksTest:1 dayS. DavisSY 2013-2014Chapter 9 :Testing the Difference Between Two Means, Two Proportions, andTwo Variances9.1 – Testing the Difference Between Two Means Using the z test9.2 – Testing the Difference Between Two Means of Independent Samples Using the t test9.3 – Testing the Difference Between Two Means Dependent samples9.4 – Testing the Difference Between Proportions9.5 – Testing the Difference Between Two VariancesChapter 10:Correlation & Regression10.1 – Scatter Plots and Correlation10.2 – Regression Line of best fit Regression line equation10.3 – Coefficient of Determination and Standard Error of the Estimate Types of variation for the regression model Coefficient of determination Standard error of the estimate Prediction interval10.4 – Multiple Regression Multiple regression equation Testing the significance of R Adjusted R2Chapter 11:Other Chi-Square Tests11.1 – Test for Goodness of Fit Test of normality11.2 – Tests Using Contingency Tables Tests for independence Test for homogeneity of proportionsChapter 12:Analysis of Variance12.1 – One-Way Analysis of Variance12.2 – The Scheffe Test and the Tukey Test12.3 – Two-Way Analysis of Variance6

Bishop Walsh SchoolInstruction:3 weeksTest:1 dayInstruction:2 weeksTest:1 day SY 2013-2014Chapter 13:Nonparametric Statistics13.1 – Advantages and Disadvantages of Nonparametric Methods13.2 – The Sign Test Single-sample sign test Paired-sample sign test13.3 – The Wilcoxon Rank Sum Test13.4 – The Wilcoxon Signed-Rank Test13.5 – The Kruskal-Wallis Test13.6 – The Spearman Rank Correlation Coefficient and the Runs Test Rank correlation coefficient The Runs TestChapter 14:Sampling and Simulation14.1 – Common Sampling Techniques14.2 – Surveys and Questionnaire Design14.3 – Simulation Techniques and the Monte Carlo MethodThis schedule allows for up to three weeks to prepare for the AP Statistics exam.The exam preparation includes at least three model exams with a focus onpacing and review.S. Davis7

Bishop Walsh SchoolSY 2013-2014AP Statistics Project:Students will complete 3 to 5 projects during the AP Statistics course.Example Project #1Students will design and conduct an experiment to investigate the effects of responsebias in surveys. They may choose the topic for their surveys, but they must designtheir experiment so that it can answer at least one of the following questions: Can the wording of a question create response bias?Do the characteristics of the interviewer create response bias?Does anonymity change the responses to sensitive questions?Does manipulating the answer choices change the response?The project will be done in pairs. Students will turn in one project per pair. A writtenreport must be typed (singe-spaced, 12-point font) and included graphs should be doneon the computer using Excel.Proposal: The proposal should Describe the topic and state which type of bias is being investigated.Describe how to obtain subjects (minimum sample size is 50).Describe what the questions will be and how they will be asked, including how toincorporate direct control, blocking, and randomization.Written Report: The written report should include following sections (clearly labeled): Title Page: in the form of a questionMethodology: Describe how the experiment was conducted and justify why thedesign was effective. Note: This section should be very similar to the proposal.Results: Present the data in both tables and graphs in such a way thatconclusions can be easily made. Make sure to label the graphs/tables clearly andconsistently.Conclusions: What conclusions can be drawn from the experiment? Be specific.Were any problems encountered during the project? What could be donedifferent if the experiment were to be repeated? What was learned from thisproject?The original proposal.Poster: The poster should completely summarize the project, yet be simple enough tobe understood by any reader. Students should include some pictures of the datacollection in progress.Oral Presentation: Both members will participate equally. The poster should be used asa visual aid. Students should be prepared for questions.S. Davis8

Chapter 4: Probability and Counting Rules 4.1 – Sample Spaces and Probability Classical Probability Complementary events Empirical probability Law of large numbers Subjective probability 4.2 – The Addition Rules of Probability 4.3 – The Multiplication Rules and Conditional P