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Bishop Walsh School SY 2015-2016 AP Statistics Syllabus Mr. Shane Davis [email protected] mrdavismathbw.weebly.com Course Description: The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. This AP Statistics course is taught as an activitybased course in which students actively construct their own understanding of the concepts and techniques of statistics through the use of small groups, projects, and technology. Course Textbook(s): Bluman, Allan: Elementary Statistics: A Step-by-Step Approach, 7th edition. New York: McGraw-Hill, 2009. ISBN: 978-0-07-353497 Hinders, Duane C.: 5 Steps to a 5: AP Statistics, 2016 New York: McGraw-Hill, 2015. ISBN: 978-0-07-184645-5 Technology: All students need to have access to TI-83, TI-83 Plus, TI-84, TI-89, TI-nspire, or TI-nspire CAS graphing calculators for use in class, at home, on any assignment or assessment, and on the AP Exam. If purchasing a calculator for the first time, then the TI-nspire CAS is strongly recommended for purchase. Students are encouraged to use their calculator throughout the course and become familiar with the keystrokes and underlying operations the calculator is computing. All students will have access periodically to the computer lab to use statistical software (Minitab, Excel) to aid in graphing, problem solving, and simulations. S. Davis 1 Bishop Walsh School SY 2015-2016 Course Outline: Approximate Time Instruction: 2 weeks Test: 1 day Instruction: 2 weeks Test: 1 day S. Davis Topics/Activities Chapter 1: The Nature of Probability and Statistics 1.1 – Descriptive and Inferential Statistics 1.2 – Variables and Types of Data 1.3 – Data Collection and Sampling Techniques Random Sampling Systematic Sampling Stratified Sampling Cluster Sampling Other Sampling Methods 1.4 – Observational and Experimental Studies 1.5 – Uses and Misuses of Statistics Suspect Samples Ambiguous Averages Detached Statistics Implied Connections Misleading Graphs Faulty Survey Questions 1.6 – Computers and Calculators in Statistics Chapter 2: Frequency Distributions and Graphs 2.1 – Organizing Data Categorical frequency distributions Grouped frequency distributions 2.2 – Histograms, Frequency Polygons, and Ogives Histogram Frequency polygon Ogive Relative frequency graphs Distribution shapes 2.3 – Other Types of Graphs Bar graphs Pareto charts Time series graph Pie graph Misleading graphs Stem and leaf plots 2 Bishop Walsh School Instruction: 3 weeks Test: 1 day Instruction: 3 weeks Test: 1 day S. Davis SY 2015-2016 Chapter 3: Data Description 3.1 – Measures of Central Tendency Mean Median Mode Midrange Weighted Mean Distribution shapes 3.2 – 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) Rule 3.3 – Measures of Position Standard scores Percentiles Quartiles and deciles Outliers 3.4 – Exploratory Data Analysis The Five-Number summary and boxplots 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 Probability Multiplication rules Conditional probability Probabilities for “at least” 4.4 – Counting Rules The fundamental counting rule Factorial notation Permutations Combinations 4.5 – Probability and Counting Rules 3 Bishop Walsh School Instruction: 2 weeks Test: 1 day Instruction: 3 weeks Test: 1 day Instruction: 2 weeks Test: 1 day Instruction: 3 weeks Test: 1 day S. Davis SY 2015-2016 Chapter 5: Discrete Probability Distributions 5.1 – Probability Distributions 5.2 – Mean, Variance, Standard Deviation, and Expectation Mean Variance and Standard deviation 5.3 – The Binomial Distribution 5.4 – Other types of Distributions Multinomial, Poisson, and Hypergeometric distributions Chapter 6: The Normal Distribution 6.1 – Normal Distributions Standard normal distribution Finding areas under the standard normal curve Normal distribution curve as a probability 6.2 – Applications of the Normal Distribution Finding data values given specific probabilities Determining normality 6.3 – The Central Limit Theorem Distribution of sample means Finite population correction factor 6.4 – The Normal Approximation to the Binomial Distribution Chapter 7: Confidence Intervals and Sample Size 7.1 – Confidence Intervals for the Mean when σ is Known Confidence intervals Sample size 7.2 – Confidence Intervals for the Mean when σ is Unknown 7.3 – Confidence Intervals and Sample Size for Proportions 7.4 – Confidence Intervals for Variances and Standard Deviations Chapter 8: Hypothesis Testing 8.1 – Steps in Hypothesis Testing 8.2 – z Test for a Mean P-value method for hypothesis testing 8.3 – t Test for a Mean 8.4 – z Test for a Proportion 8.5 – χ2 Test for a Variance or Standard Deviation 8.6 – Additional Topic Regarding Hypothesis Testing Confidence intervals and hypothesis testing Type II error and the power of a test 4 Bishop Walsh School Instruction: 2-3 weeks Test: 1 day Instruction: 2 weeks Test: 1 day Instruction: 1-2 weeks Test: 1 day Instruction: 2 weeks Test: 1 day SY 2015-2016 Chapter 9 : Testing the Difference Between Two Means, Two Proportions, and Two Variances 9.1 – Testing the Difference Between Two Means Using the z test 9.2 – Testing the Difference Between Two Means of Independent Samples Using the t test 9.3 – Testing the Difference Between Two Means Dependent samples 9.4 – Testing the Difference Between Proportions 9.5 – Testing the Difference Between Two Variances Chapter 10: Correlation & Regression 10.1 – Scatter Plots and Correlation 10.2 – Regression Line of best fit Regression line equation 10.3 – 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 interval 10.4 – Multiple Regression Multiple regression equation Testing the significance of R Adjusted R2 Chapter 11: Other Chi-Square Tests 11.1 – Test for Goodness of Fit Test of normality 11.2 – Tests Using Contingency Tables Tests for independence Test for homogeneity of proportions Chapter 14: Sampling and Simulation 14.1 – Common Sampling Techniques 14.2 – Surveys and Questionnaire Design 14.3 – Simulation Techniques and the Monte Carlo Method This 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 on pacing and review. S. Davis 5 Bishop Walsh School SY 2015-2016 AP Statistics Project: Students will complete 2 to 3 projects during the AP Statistics course. Example Project #1 Students will design and conduct an experiment to investigate the effects of response bias in surveys. They may choose the topic for their surveys, but they must design their 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 written report must be typed (singe-spaced, 12-point font) and included graphs should be done on 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 to incorporate direct control, blocking, and randomization. Written Report: The written report should include following sections (clearly labeled): Title Page: in the form of a question Methodology: Describe how the experiment was conducted and justify why the design 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 that conclusions can be easily made. Make sure to label the graphs/tables clearly and consistently. Conclusions: What conclusions can be drawn from the experiment? Be specific. Were any problems encountered during the project? What could be done different if the experiment were to be repeated? What was learned from this project? The original proposal. Poster: The poster should completely summarize the project, yet be simple enough to be understood by any reader. Students should include some pictures of the data collection in progress. Oral Presentation: Both members will participate equally. The poster should be used as a visual aid. Students should be prepared for questions. S. Davis 6