AP Statistics Course Syllabus

Transcription

1 AP Statistics Course Syllabus Textbook and Resource materials The primary textbook for this class is Yates, Moore, and McCabe s Introduction to the Practice of Statistics (TI 83 Graphing Calculator Enhanced) 4 th edition published by WH Freeman, All homework assignments included in this syllabus are from this text. Minitab statistical software is also used in the computer lab for projects. The school owns a perpetual license for 30 computers. The Texas Instruments graphing calculator is used extensively in this course. Students are required to purchase their own TI 84 graphing calculator and must bring it to class everyday. General Time Line and Sequencing of Units Listed in the table below are the approximate number of days that will be spent for each unit for this course. A more detailed breakdown of what is to be covered each day is provided in the syllabus attached. The syllabus is designed to be used on a 90 day block schedule. Unit 1 Description One Variable Statistics Normal Curve Number of class days Two Variable Statistics Sample and Experiment Design Rules of Probability Binomial Distribution Sampling Distribution Central Limit Theorem Confidence Intervals for μ Hypothesis Tests for μ (z test)

2 8 9 Hypothesis Tests for means (t test) Hypothesis Tests for proportions 9 11 Goodness of Fit Test Chi square Distribution Review for AP Statistics Exam Final Exam and Project 8 10 Syllabus for Test One (One Variable Statistics and The Normal Curve) 1. Students will be able to construct appropriate graphical displays using the graphing calculator for single variable data. 2. Students will be able to interpret graphs of single variable data and describe the distribution of the variable. 3. Students will be able to calculate standardized values and use the z table to find percentiles. Day Objectives Assignment Due 1 Administrative items Introduction to dotplots and stemplots 1.5, 1.6 (in class) 2 Histograms vs. Bar Graphs Back to back stemplots Timeplots 3 Boxplots Measures of center and spread 1.29, 1.30 (in class) 4 Standard Deviation Empirical Rule Normal Distributions 2.4, 2.5 (in class) Read p Work problems 1.4, 1.10 Work problems 1.12, 1.17, 1.18 Read p Work problems 1.24, 1.32, 1.34, 1.39 BEGIN TEST ONE (TAKE HOME) Read p Work problems 1.36, 1.47, 2.7, 2.8, 2.12, 2.18

3 (in class, follow up to 2.8) Calculating z values Find percentiles using the z table Tests for normality 2.24, 2.25, 2.27 (in class) Work problems 2.31, 2.32, extra practice problems 6 Test Review Work problems 1.49, 1.50, 1.52, 1.56, 2.26, 2.38, Test One Turn in Take Home Section of Test Syllabus for Test Two (Two Variable Statistics) 1. Students will be able to construct scatterplots and residual plots using the graphing calculator and Minitab for twovariable data. They will correctly interpret each as well as the meanings of the coefficient correlation and the coefficient of determination. 2. Students will be able to determine the best model for any given two variable data set. They will be able to justify their choice using residual plots and linear transformation of the data. Students will use Minitab to complete an assignment for finding the best model for a given set of data. 3. Students will be able to compare marginal and conditional distributions for the comparison of two categorical variables. Day Objectives Assignment Due 1 Create and Interpret Scatterplots Calculate and Interpret Correlation (In class 3.5, 3.7, Ministers vs. Rum) Read p , Calculate LSLR/Interpret Coefficients Interpret R² (In class 3.52) 3 Construct and Interpret Residual Plots Outliers vs. Influential Observations 4 Exponential Models Work 3.23, 3.24, 3.27, 3.30 Read p , Work 3.31, 3.33, 3.36, 3.37 Read p Work 3.42, 3.43, 3.45, 3.47, 3.50 Read p (In class 4.1) Work 4.2, 4.6, 4.7, 4.9

4 5 Power Models and others Read p (In class 4.4) Work 4.12, 4.13, 4.17, Two Variable Activities/Computer Lab Using Minitab software to investigate the relationship between two variables. 7 Interpreting Correlation and Regression Read p (In class 4.22, 4.23, 4.24) 8 Relationships in Categorical Data Simpson s Paradox (In class 4.32, Example 4.12) Work 4.26, 4.27, 4.28, 4.29 Read p Work 4.38, 4.39, 4.40, Unit Two Test Review Work 3.58, 3.59, 4.8, 4.10, 4.52, 4.54, 4.62, Unit Two Test Take Home Test Due Syllabus for Test Three (Experimental Design) 1. Students will be able to design a survey using simple random sampling and a table of random digits. 2. Students will be able to identify bias in sampling and how to remedy it. 3. Students will be able to design an experiment and select the appropriate treatment groups. 4. Students will use simulation techniques using the graphing calculator to find approximate answers to problems involving probability. Day Objectives Assignment Due 1 Identify different sampling methods Recognize bias in sampling Classwork , 5.5, Major Principles of Experimental Design Implementing types of Experimental Design Classwork 5.27, 5.31, 5.33, 5.36, 5.37 Read p Work 5.6, 5.8, 5.10, 5.12, 5.15, 5.22, 5.23 Read p Work 5.32, 5.39, 5.44, 5.46, 5.49, 5.52

5 3 More Experimental Design Inroduction to Simulation 4 Use of simulation to find guessed probabilities of events Simulation by TORD or calculator 5 Group Work Chapter Review Problems 6 Chapter Five (Unit Three) Individual Test Read p Work 5.54, 5.55, 5.56, 5.57 Work 5.59, 5.60, 5.61, 5.62, 5.64, 5.65 Work 5.66, 5.68, 5.70, 5.72, 5.78, 5.80 Syllabus for Test Four (Probability) 1. Students will be able to use basic rules of probability to find the theoretical probabilities for simple random phenomenon. 2. Students will be able to determine the difference between a discrete and continuous random variable and find probabilities of events for each. 3. Students will be able to find the mean and variance for a discrete random variable and solve problems involving sums or differences for more than one variable. 4. Students will be able to use Minitab to conduct a simulation of the Law of Large Numbers to approximate the mean. Day Objectives Assignment Due

6 1 Define the sample space for an event (In class 6.6, 6.8, 6.10) Read p Know the 5 basic rules of probability and apply them Venn Diagrams (In class 6.27, 6.31) 3 Joint Probability Conditional Probability Tree Diagrams In Class (6.38, 6.40, 6.41, 6.53, 6.55) 4 Discrete and Continuous Random Variables Work 6.13, 6.15, 6.16, 6.18, 6.22 Read p Work 6.24, 6.25, 6.26, 6.28, 6.29, 6.32, 6.33, 6.34 Read p Work 6.44, 6.45, 6.47, 6.48, 6.50, 6.54 Read p In Class (7.11, 7.13, 7.14) 5 Expected Value of a discrete r.v. Law of Large Numbers Work 7.1, 7.2, 7.6, 7.7, 7.8, 7.9, 7.15, 7.16 Read p Work 7.17, 7.18, 7.19, 7.21, 7.22, Rules for means and variances for discrete random variables Work 7.25, 7.28, 7.31, 7.32, Test Four Review Work 6.59, 6.60, 6.61, 6.62, 6.63, 6.64, 7.34, 7.35, 7.36, 7.37, 7.38, Unit Four (Probability) TEST Syllabus for Test Five (Binomial Probability and The Central Limit Theorem) 1. Students will be able to distinguish whether or not a variable meets the criteria for the binomial setting. 2. Students will be able to use the calculator or formulas to determine binomial probabilities and construct probability distribution tables and histograms. 3. Students will be able to calculate cumulative distribution functions for binomial random variables and construct histograms.

7 4. Students will be able to calculate means (expected values) and standard deviations for binomial random variables. 5. Students will be given a Minitab assignment that will help them to recognize the fact of sampling variability: a statistic will take different values when you repeat a sample or experiment 6. Students will be able to find the mean and standard deviation of a sample proportion pˆ for an SRS of size n from a population having population proportion p. 7. Students will be able to recognize when you can use the normal approximation to the sampling distribution of pˆ (rules of thumb 1 and 2) and use normal approximation to calculate probabilities that concern pˆ. 8. Students will be able to find the mean and standard deviation of a sample mean x ˉ from an SRS of size n when the mean μ and standard deviation σ of the population are known. 9. Students will understand that x ˉ has approximately a normal distribution when the sample is large (central limit theorem). Use this normal distribution to calculate probabilities that concern x ˉ. Day Objectives Assignment Due 1 Identify the binomial setting Calculate binomial probabilities using formulae and calculator Classwork Finding cumulative probabilities for binomial variables Read p Work 8.5, 8.6, 8.8, 8.9, 8.10, 8.13, 8.14, 8.15, 8.16 Work 8.19, 8.20, 8.21, 8.22, 8.23 Calculating mean and standard deviations for binomials 3 Chapter 8 Review 8.37, 8.38, 8.39, 8.40 Day Objectives Assignment Due

8 4 Identify parameters and statistics Bias and variability of a statistic Classwork , Sampling Distributions (Proportions) Finding mean and standard deviation Rules for using normal approximation 6 Sampling Distributions (Sample Means) Finding mean and standard deviation Central Limit Theorem 7 Use of simulation to verify how the Central Limit Theorem works. Simulate using Minitab software 8 Chapter 9 Review Problems Read p Work 9.8, 9.12, 9.14 Read p Work 9.18, 9.20, 9.22, 9.24 Read p Work 9.30, 9.31, 9.36, 9.38 Computer Lab Work 9.41, 9.42, 9.43, 9.44, Chapter 8 9 (Test Five) Syllabus for Test Six (Confidence Intervals and Hypothesis Testing for means, σ is known) 1. Students will be able to calculate a confidence interval for the mean μ of a normal population with known standard deviation σ using the graphing calculator and interpret its meaning. 2. Students will understand how the margin of error of a confidence interval changes with the sample size and the level of confidence C. 3. Students will be able to 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. 4. Students will be able to state the null and alternative hypotheses in a testing situation when the parameter in question is a population mean μ and explain in non technical language the meaning of the P value. 5. Students will be able to calculate the z statistic and the P value for both one sided and two sided tests about the mean μ of a normal population using the graphing calculator and assess statistical significance at standard levels α, either by comparing P to α or by comparing z to standard normal critical values.

9 6. Students will be able to identify what type I and type II errors are and ways that they can be reduced. They will also know how to calculate the power of a hypothesis test against some particular alternative value of the null hypothesis. Day Objectives Assignment 1 Interpreting confidence intervals Calculate confidence intervals and critical values (z*) 2 Cautions about using confidence intervals Margin of Error influences Sample size required for a desired Margin of Error 3 Stating hypotheses Calculating the z statistic and p values Read p Work 10.1, 10.3, 10.6, 10.8, 10.9, 10.11, Read p Work 10.19, 10.20, 10.21, 10.22, 10.23, Read p Work 10.27, 10.28, 10.33, 10.34, 10.35, In class ( ) 10.36, Z test when σ is known Statistical significance vs. practical significance Work 10.41, 10.43, 10.44, 10.45, 10.46, 10.48, Due 5 Type I and Type II Error Power of a Test 6 Test Six Review Read p Work 10.63, 10.64, 10.65, 10.66, 10.67, Work 10.78, 10.80, 10.81, 10.82, Unit Six TEST Syllabus for Test Seven (Confidence Intervals and Hypothesis Testing for means, σ is not known) 1. Students will be to calculate the t test statistic using the graphing calculator and also learn how to use the t distribution table. 2. Students will be able to calculate a confidence interval with the appropriate t critical value using the graphing

10 calculator. 3. Students will be able to differentiate between a one sample t test and a matched pairs t test. 4. Students will be able to recognize when a test is asking to compare to samples. 5. Students will know the assumptions for comparing two population means. 6. Students will know how to calculate the t test statistic for comparing two samples and confidence intervals using the graphing calculator. 7. Students will know what is meant by pooled t procedures. Day Objectives Assignment Due 1 When to use the t test statistic Calculate degrees of freedom 2 T intervals Matched Pairs t test Robustness of t procedures 3 Comparing two means Confidence Intervals for two means Pooled t procedures Read p Work problems 11.2, 11.3, 11.4, 11.6, 11.8, Read p Work problems 11.12, 11.13, 11.16, 11.18, 11.20, 11.22, 11.23, 11.26, Read p Work problems 11.34, 11.37, 11.38, 11.44, 11.46, 11.48, Chapter 11 Review Problems Work problems 11.58, 11.60, 11.63, 11.64, Unit Seven Test Syllabus for Test Eight (Inference for Proportions) 1. Students will know the assumptions for inference for a proportion.

11 2. Students will be able to calculate confidence intervals and test statistics for a population proportion by hand and by calculator. 3. Students will be able to compute the correct sample size for a desired margin of error when performing a confidence interval for a population proportion. 4. Students will be able to calculate confidence intervals and test statistics for two population proportions by hand and by calculator. Day Objectives Assignment Due 1 Assumptions for inference for a proportion Test statistic and confidence intervals for a single proportion 2 Assumptions for inference for two proportions Test statistic and confidence intervals for two proportions 3 Extra Practice Problems Read p Work problems 12.8, 12.10, 12.13, 12.16, 12.18, Read p Work problems 12.24, 12.26, 12.27, 12.31, 12.32, Chapter 12 Test Review Work problems 12.36, 12.37, 12.38, 12.39, Chapter 12 Test Syllabus for Test Nine (Goodness of Fit and Chi SquareTests) 1. Students will be able to calculate the Chi square test statistic by hand and by using tables and determine the appropriate degrees of freedom for a test for goodness of fit. They will also learn how to calculate Chi Square by using the graphing calculator. 2. Students will be able to use the Chi square table to find p values for the Chi square test statistic.

12 3. Students will be able to state hypotheses for the goodness of fit test and recognize whether or not the assumptions for the goodness of fit test have been met. 4. Students will be able to state hypotheses for the Chi Square Test, determine the appropriate degrees of freedom, and state the assumptions for the test. 5. Students will be able to complete a follow up analysis that examines the differences between the two variables in more detail. Day Objectives Assignment Due 1 Computing Chi Square Reading the Chi Square table Goodness of Fit Test 2 Chi Square Test Follow up Analyses Read p Work problems 13.9, 13.10, 13.11, Read p Work problems 13.15, 13.19, 13.20, 13.23, Extra Practice Problems 4 Chapter 13 Review Work problems 13.28, 13.30, 13.31, 13.32, Unit Nine Test Syllabus for Final Exam (Group Project) AP Statistics Final Exam 1. Determine the hypothesis that you intend to research. You must include a first, second, and third choice. This must by approved by the teacher before you proceed with any research of literature. (Example: Do Chips a hoy cookies really contain 1,000 chips in every bag?) Due by 2. State what you expect the outcome to be before you begin any research or collecting any data. This will become your alternative hypothesis. You must include an abstract outlining what you intend to do. The abstract is very brief (1 2 paragraphs) and is just a general outline of what your research includes and its purpose.

13 3. You must complete a review of the literature on the subject area you select. You must have a minimum of 3 resources for the review. The review should include only research articles previously conducted in your chosen area of study. This section should be a well written essay of about 2 3 pages in length describing what conclusions have been found in previous research about your topic. 4. Methodology Section. This will state the steps that you intend to carry out in your data collection. The steps will include: Subjects Materials Used Variables Measured Procedures Time Schedule Budget 5. Data Collection and Calculations your group must include a well organized table of the data that you gathered as well as any graphs, calculations, or tests that you ran. These should be cut and pasted in to your final document and your Powerpoint. 6. Discussion. This is a short essay ( ½ to 1 page) detailing what methods you selected for making a decision and why they were the appropriate ones for your study. 7. Conclusions. This is the same as parts 4 and 5 of a hypothesis test. 8. References. These should be typed correctly in MLA style. Your group will also be responsible for making a presentation to the class. Your visual aid will be a Powerpoint presentation. It should be 8 10 minutes in length. Powerpoint Slides This is only a guideline. It would satisfy minimum requirements. Slide 1 Should be left blank Slide 2 Title Slide (be sure to include the names of all group members) Slide 3 Methodology I Subjects, Materials Slide 4 Methodology II Procedures, Time and Budget Slide 5 Hypotheses Slide 6 Review of the Literature Slide 7 Results I Slide 8 Results II Slide 9 Results III Slide 10 Conclusion Slide 11 References

14 Your group will make an oral presentation in class the duration of which should not exceed 10 minutes.