AP Statistics
Instructor: Mr. Josh Urich / Contact Info:Room 216 / Phone: 970-686-8100 ext. 3673
Email:
Course Description*
AP Statistics uses an activity and discussion-based approach in which students construct their understanding of the following conceptual themes:
· Exploring Data: Describing patterns and departures from patterns (20-30%)
· Sampling and Experimentation: Planning and conducting a study (10-15%)
· Anticipating Patterns: Exploring random phenomena using probability and simulation (20-30%)
· Statistical Inference: Estimating population parameters and testing hypotheses (30-40%)
The course is conducive to student engagement in activities and discussions investigating statistical concepts, exploring and analyzing data, assessing models, and performing simulations using appropriate technology such as TI-83+/TI-84 graphing calculators and Microsoft Excel. Cooperative group problem solving and student writing are learning approaches that are utilized. The teacher serves as a facilitator/consultant. All aspects of the course including assignments, exams, activities, and projects are conceptually oriented, and as a result, the teaching will support this focus.
*Note: as per the College Board course description
Expectations
Be in class on time, prepared, and ready to begin when the bell rings. Participate in classroom activities. Be respectful of others and avoid being a disturbance in class. Try your hardest, always giving your best. Communicate.
Materials
· Textbook
o Yates, D. S., Moore, D. S., & Starnes, D. S. (2008).
The practice of statistics (3rd ed.). New York: W.H. Freeman.
ISBN: 978-0-7167-7309-2
· TI 83/84 Plus Graphing Calculator
· 3 ring binder
AP Exam
The AP exam grade is a weighted combination of the score on the multiple-choice section and on the free-response section. Students who earn AP exam grades of 3 or above are generally considered to be qualified to receive college credit and/or placement into advanced courses; however, each college or university determines the awarding of credit and placement. It is your responsibility to check with individual institutions regarding their individual policies. The cost to take the test is typically $87.00.
The district expects that students will take the culminating exams that are a part of the course of study for any of the weighted courses.
Grading
A weighted grading scale will be implemented for this course.
Class Work: 15% / A 90% - 100% / A 5 Quality PointsAssessments: / B 80% - 89% / B 4 Quality Points
Quizzes: 25% / C 70% - 79% / C 3 Quality Points
Exams: 50% / D 60% - 69% / D 1 Quality Points
Final Exam: 10% / F 59% - below / F 0 Quality Points
Assessments
Quizzes will be administered for each section of a chapter and may be given online. Exams will cover an entire chapter and will be structured similar to the AP Exam. Each test will include both multiple choice and free response questions to help prepare you for the AP Exam. Additionally, the exams will be cumulative. Class work or/and practice problems will be assigned daily, but not every assignment will be graded.
Course Outline
Content Objectives/Skills / Chapter/Timeframe / ActivitiesProducing Data: Designing Samples, Designing Experiments
· Distinguish between and discuss observational studies and experiments.
· Identify and give examples of different types of sampling methods
· Identify and give examples of sources of bias in sample surveys.
· Identify and explain the basic principles of experimental design.
· Explain what is meant by completely randomized design.
· Distinguish between the purposes of randomization and blocking in an experimental design.
· Use random numbers from a table or technology to select a random sample. / Chapter 5
· Section 5.1
· Section 5.2
Timeframe: Approximately 6 blocks / Bottled or Tap
· Student collect data by taste-testing various samples of water and try to determine if the samples are from bottled water or tap water.
Eenie Meanie
· Students learn what is meant by a simple random sample and recognize the variability in subjective and random sampling techniques by investigating the helper vs. hinderer study. Additionally, students use both a graphing calculator and excel to perform a simulation to aid in the investigation.
Jelly Blubbers pt. 1
· Students use various sampling techniques including convenience, simple, stratified, clustered, and systematic then compare and contrast the advantages/disadvantages of each.
Exploring Data: Displaying Data with Graphs, Describing Distributions with Numbers
· Display data distributions including bar graphs, pie charts, stemplots, histograms, ogives, time plots, and boxplots.
· Interpret graphical displays in terms of shape, center, and spread of the distribution, as well as gaps and outliers.
· Describe distributions of data using mean, median, five-number summary, standard deviation, range, and variance.
· Interpret numerical measures in context.
· Identify outliers in a data set.
· Explore the effects of a linear transformation of a data set. / Chapter 1
· Section 1.1
· Section 1.2
Timeframe: Approximately 6 blocks / Departing on Time
· The departure times for flights leaving from O’Hare Airport and scheduled to arrive in Mexico City are listed. Students must rank the five airlines in terms of most likely to be on time to least likely to be on time. Statistical procedures are used and described in a letter to the Spanish Club who is interested in the information.
Describing Location in a Distribution: Measures of Relative Standing and Density Curves, Normal Distributions
· Be able to compute measures of relative standing for individual values in a distribution including z-scores and percentile ranks.
· Demonstrate an understanding of a density curve, including its mean and median.
· Demonstrate an understanding of the Normal distribution and the 68-95-99.7 Rule.
· Use tables and technology to find the proportion of values on an interval of the Normal distribution.
· Use a variety of techniques including constructing a normal probability plot to assess the Normality of a distribution. / Chapter 2
· Section 2.1
· Section 2.2
Timeframe: Approximately 5 blocks / McDonald’s Case Analysis
· Students take the side of prosecution or defense and provide statistical reasoning (percentiles, z-scores, etc.) to support their stance regarding a particular case. Students must communicate their ideas through a 1-page closing argument addressing the jury.
Building Boats
· Students build aluminum foil boats and fill them until they sink. Students must collect and record data and assess the normality of their data.
Examining Relationships: Scatterplots and Correlation, Least-Squares Regression, Correlation and Regression Wisdom
· Construct and interpret a scatterplot for a set of bivariate data.
· Compute and interpret the correlation r between two variables.
· Demonstrate an understanding of the basic properties of the correlation r.
· Explain the meaning of a least squares regression line.
· Construct and interpret a regression line given bivariate data.
· Demonstrate understanding of how to determine the quality of a regression line as a model for bivariate data. / Chapter 3
· Section 3.1
· Section 3.2
· Section 3.3
Timeframe: Approximately 6 blocks / Barbie Bungee Jumping
· Students collect data based on the number of rubber bands vs. the bungee distance of Barbie. Students then complete a scatter plot, construct a regression line and equation of the line, interpret the equation and line in context, and determine the correlation coefficient. Students then apply the information to make predictions about the number of rubber bands needed for bungee distances and vice versa.
Further Exploration of Relationships: Transforming to Achieve Linearity, Relationships between Categorical Variables, Establishing Causation
· Identify settings in which a transformation might be necessary in order to achieve linearity.
· Use transformations involving powers and logarithms to linearize curved relationships.
· Explain and describe the parts of a two-way table.
· Explain what gives the best evidence for causation.
· Explain the criteria for establishing causation when experimentation is not feasible. / Chapter 4
· Section 4.1
· Section 4.2
· Section 4.3
Timeframe: Approximately 4 blocks / Shake It, But Don’t Break It
· Linear transformation activity in which students collect data then examine various residual plots to determine the “best” fit for the data. Students must communicate clearly why they chose the plot they did.
Probability: Simulation, Probability Models, General Probability Rules
· Perform simulations using random number tables and technology (TI-83/83+/84)
· Explore sample space using various methods including lists, tables, and tree diagrams and use them to answer probability questions
· Describe what is meant by the intersection and union of two event
· Use rules of probability including additional rules multiplication rules to solve probability problems
Solve problems involving conditional probability / Chapter 6
· Section 6.1
· Section 6.2
· Section 6.3
Timeframe: Approximately 7 blocks / Lucky Ducks
· Students complete various simulations using a 5-step process in which they must communicate the problem, assumptions, method, simulation, and conclusions.
Random Variables: Discrete and Continuous Random Variables, Means and Variances of Random Variables
· Define what is meant by a random variable.
· Define a discrete random variable.
· Define a continuous random variable.
· Explain what is meant by the probability distribution for a random variable.
· Explain what is meant by the law of large numbers.
· Calculate the mean and variance of a discrete random variable.
· Calculate the mean and variance of distributions formed by combining two random variables. / Chapter 7
· Section 7.1
· Section 7.2
Timeframe: Approximately 6 blocks / Casino Lab
· Students explore the rules of probability in a real-world setting through the simulation of various casino games including craps, blackjack, and roulette.
The Binomial and Geometric Distributions: Binomial Distributions, Geometric Distributions
· Explain what is meant by a binomials setting and binomial distribution.
· Use technology to solve probability questions in a binomial setting.
· Calculate the mean and variance of a binomial random variable.
· Solve a binomial probability problem using a Normal approximation.
· Explain what is meant by a geometric setting.
· Calculate the mean and variance of a geometric random variable. / Chapter 8
· Section 8.1
· Section 8.2
Timeframe: Approximately 5 blocks / Plinko
· Students explore the game of Plinko through simulation using the TI-83/84 and answer various questions including those related to the binomial distribution.
Sampling Distributions: Sampling Distributions, Sample Proportions, Sample Means
· Define a sampling distribution.
· Contrast bias and variability.
· Describe the sampling distribution of a sample proportion (shape, center, and spread).
· Use a Normal approximation to solve probability problems involving the sampling distribution of a sample proportion.
· Describe the sampling distribution of a sample mean.
· State the central limit theorem.
· Solve probability problems involving the sampling distribution of a sample mean. / Chapter 9
· Section 9.1
· Section 9.2
· Section 9.3
Timeframe: Approximately 6 blocks / Jelly Blubbers pt. 2
· Students extend upon random sampling methods, examine a sampling distribution, and communicate the results of the sampling distribution.
Estimating with Confidence: Confidence Intervals, Estimating a Population Mean, Estimating a Population Proportion
· Describe statistical inference.
· Describe the basic form of all confidence intervals.
· Construct and interpret a confidence interval for a population mean and for a population proportion.
· Describe a margin of error and ways to control the size of the margin of error.
· Determine the sample size necessary to construct a confidence interval for a fixed margin of error.
· Compare and contrast the t-distribution and the Normal distribution.
· List the conditions that must be present to construct confidence intervals for population means and population proportions.
· Explain what is meant by the standard error.
· Determine the standard error of and. / Chapter 10
· Section 10.1
· Section 10.2
· Section 10.3
Timeframe: Approximately 6 blocks / Paper Airplanes pt. 1
· Students use confidence intervals to compare flight distances of different paper airplane models.
Testing a Claim: Significance Tests, Carrying Out Significance Tests, Use and Abuse of Tests, Using Inference to Make Decisions
· Explain the logic of significance testing.
· List and explain the differences between a null hypothesis and an alternative hypothesis.
· Discuss the meaning of statistical significance.
· Use the Inference Toolbox to conduct a large sample test for a population mean.
· Compare two-sided significance tests and confidence intervals when doing inference.
· Differentiate between statistical and practical “significance.”
· Explain and distinguish between Type I and Type II errors in hypothesis testing.
· Define and discuss the power of a test. / Chapter 11
· Section 11.1
· Section 11.2
· Section 11.3
· Section 11.4
Timeframe: Approximately 7 blocks / TBA
Significance Tests in Practice: Tests about a Population Mean, Tests about a Population Proportion
· Conduct one-sample and paired data t-tests.
· Explain the difference between the one-sample confidence interval for a population proportion and the one-sample significance test for a population proportion.
· Conduct a significance test for a population proportion. / Chapter 12
· Section 12.1
· Section 12.2
Timeframe: Approximately 4 blocks / TBA
Comparing Two Population Parameters: Comparing Two Means, Comparing Two Proportions
· Identify the conditions that need to be satisfied in order to do inference for comparing two population means.
· Construct a confidence interval for the difference between two population means.
· Perform a significance test for the difference between two population means.
· Identify the conditions that need to be satisfied in order to do inference for comparing two population proportions.
· Construct a confidence interval for the difference between two population proportions.
· Perform a significance test for the difference between two population proportions. / Chapter 13
· Section 13.1
· Section 13.2
Timeframe: Approximately 4 blocks / Double Stuf Oreos
· Student collect data to determine whether or not double stuffed oreos are really double stuffed.
Paper Airplanes pt. 2
· Students use significance tests to compare flight distances of different paper airplane models.
Inference for Distribution of Categorical Variables: Chi-Square Procedures: Test for Goodness of Fit, Inference for Two-Way Tables
· Explain what is meant by a chi-square goodness of fit test.
· Conduct a chi-square goodness of fit test.
· Given a two-way table, compute conditional distributions.
· Conduct a chi-square test for homogeneity of populations.
· Conduct a chi-square test for association/independence.
· Use technology to conduct a chi-square significance test. / Chapter 14
· Section 14.1
· Section 14.2
Timeframe: Approximately 4 blocks / Plain and Peanut
· Students perform a Chi-Square analysis for both plain and peanut M & Ms to verify or refute the company’s claim. Students must provide a written conclusion of their results.
Inference for Regression
· Identify the conditions necessary to do inference for regression.
· Given a set of data, check that the conditions for doing inference for regression are present.
· Explain what is meant by the standard error about the least-squares line.
· Compute a confidence interval for the slope of the regression line.
· Conduct a test of the hypothesis that the slope of the regression line is zero (no correlation) in the population. / Chapter 15
Timeframe: Approximately 2 blocks / Short or Tall
· Students collect a sample of data regarding height and shoe size then determine if the slope is significant using a hypothesis test. Students must communicate their conclusion in a written format.
Review for Exam
· 2002/2007 Released Multiple Choice
· Released Free Response items
· Cumulative Final Exam / Timeframe: Approximately 3 blocks
After Exam
· Group Research Projects/Presentations / Time Permitting / Research Project
· Students must demonstrate and communicate various aspects of a statistical study.
· Students must provide a written report as well as a brief oral presentation of their findings.
References