COURSE OF STUDY
AP STATISTICS Revised by: Francine Florio 2007
INTRODUCTION
Advanced Placement Statistics is a college course designed for the above average student who has Successfully completed Algebra II and possesses sufficient mathematical maturity and quantitative reasoning ability. The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. The four broad topics that are covered are exploring data, sampling and experimentation, anticipating patterns, and statistical inference. This course will provide the student with a statistics background to better prepare him/her for college.
DISTRICT GOALS
The following Goals are addressed in Advanced Placement Statistics: 1. To acquire the background knowledge in mathematics that enables problem solving and communication in everyday life. 2. To acquire entry level job skills and to acquire the knowledge necessary for further education. 3. To learn to enjoy the process of learning and to acquire the skills necessary for adaptation to change. 4. To know one’s own abilities, potentials, worth, and limitation in order to make effective decisions. 5. To become an effective and responsible contributor to the political decision making processes. 6. To acquire the knowledge, skills, and understanding to be a responsible consumer. 7. To acquire ethical principals and values needed for life. 8. To acquire the ability to form responsible relationships with a diverse population.
COURSE GOALS
1. The student will appreciate the usefulness of obtaining and analyzing data for making decisions and advancing knowledge. 2. Students will understand the importance of data collection and be able to critique the quality of studies based upon issues of data collection. 3. Students will be able to apply basic data analytical techniques to uncover patterns and truths within data sets, and will understand the primary importance of graphing the data. 4. The student will be able to apply the basic techniques of statistical inference to data, to interpret the results of a statistical analysis using the concepts of confidence interval or tests of significance, and to assess when particular inferential procedures are appropriate. 5. Students will be able to communicate the results of statistical analyses or quantitative findings in writing. 6. The student who successfully completes the course and examination may receive credit and/or advanced placement for a one- semester introductory college statistics course.
COURSE OUTLINE
The following list of content/skill areas and topics outline the objectives in this course:
I. Exploring Data a. Displaying Distributions with Graphs b. Describing Distributions with Numbers II. The Normal Distributions a. Density Curves and the Normal Distributions b. Standard Normal Calculations III. Examining Relationships a. Scatterplots b. Correlation c. Least-Squares Regression IV. More on Two-Variable Data a. Modeling Nonlinear Relationships b. Interpreting Correlation and Regression c. Relations in Categorical Data V. Producing Data a. Designing Samples b. Designing and Simulating Experiments VI. Probability: The Study of Randomness a. Randomness b. Probability Models c. More About Probability VII. Chapter 7: Random Variables a. Discrete and Continuous Random Variables b. b. Means and Variances of Random Variables VIII. Chapter 8: The Binomial and Geometric Distributions a. The Binomial Distributions b. The Geometric Distributions IX.
Sampling Distributions a. Sampling Distributions b. Sample Proportions c. Sample Means
COURSE OUTLINE
X.
Introduction to Inference a. Estimating with Confidence b. Tests of Significance c. Using Significance Tests d. Inference as a Decision
XI.
Inference for Distributions a. Inference for the Mean of a Population b. Comparing Two Means
XII.
Inference for Proportions a. Inference for a Population Proportion b. Comparing Two Proportions
XIII.
Inference for Tables: Chi-Square Procedures a. Test for Goodness of Fit b. Inference for two-way Tables
XIV.
Inference for Regression a. Inference About the Model and Prediction b. Checking the Regression Assumptions
XV.
Analysis of Variance a. Inference for Population Spread b. One-Way Analysis of Variance
PROFICIENCY REQUIREMENTS for AP Statistics At the conclusion of this course the student will be able to: 1. Identify the individuals and variables in a set of data as categorical or quantitative. 2. Make a dot plot that records dots for individual observations. 3. Make a histogram of the distribution of a quantitative variable when you are given counts for classes of equal width and when they are chosen 4. Make a stem plot of the distribution of a small set of observations and interpret it. 5. Assess from a dot plot, stem plot, or histogram whether the shape of a distribution is roughly symmetric, distinctly skewed, or neither. 6. Decide which measures of center and spreads are more appropriate: the mean and standard deviation or the fivenumber summary. 7. Recognize outliers. 8. Make and analyze a time plot of data. 9. Calculate the mean and standard deviation of a set of observations using a calculator and determine the median. 10. Calculate the quartiles and the IQR for a set of observations. 11. Know that areas under a density curve represent proportions of all observations and that the total area under a density curve is 12. Approximately locate the mean and median on a density curve. 13. State what percent of the observations from a normal distribution fall between two points. 14. Plot a histogram, stem plot, and/or box plot to determine if a distribution is bell-shaped. 15. Construct and interpret normal probability plots. 16. Identify the explanatory and response variables in situations where one variable explains or influences another. 17. Make a scatter plot for two quantitative variables, add a categorical variable and interpret the scatter plot 18. Explain y = b + mx and draw the graph of the line. 19. Calculate and find the slope and intercepts of the least squares regression line. 20. Calculate and analyze the residuals and plot them against the explanatory variable x or against other variables. 21. Analyze two-variable data that show a linear pattern and construct models for data that fit an exponential function or power function. 22. Identify the population in a sampling situation and recognize bias. 23. Plan and conduct surveys, experiments, simulations and observational studies and generalize the results. 24. Know and apply the sample space of a random phenomenon and the probability rules. 25. Recognize and define a discrete, continuous and random variable. 26. Identify a random variable as binomial or geometric, determine binomial and geometric probabilities and calculate means and standard deviations of binomial random variables. 27. Identify and recognize sampling distribution, sample proportions and sample means. 28. Define, calculate and interpret a confidence interval for the mean of a normal population.
29. State the null and alternative hypotheses in a testing situation when the parameter in question is a population mean. 30. Explain the meaning of the P-value when you are given the numerical value of P for a test. 31. Calculate the z statistic and the P-value for both one-sided and two-sided tests about the mean of a normal population. 32. Recognize from a design of a study whether one-sample, matched pairs, or two-sample procedures are needed. 33. Obtain confidence interval using one- and two-sample t procedures. 34. Use the one- and two- sample z procedure to give confidence intervals for a population proportion. 35. To determine if a population distribution has changed by using a goodness of fit test. 36. Locate expected cell counts, the chi-square statistic, and its P-value in output from a calculator. 37. Make and inspect a scatter plot, find the correlation and the least squares regression line on a calculator. 38. Draw connections between all aspects of the statistical process, including design, analysis, and conclusions. 39. Communicate methods, results, and interpretations using the vocabulary of statistics. 40. Use graphing calculators and demonstrates the use of computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models and simulations.
STUDENT ASSESSMENT AP Statistics The student assessment for each marking period is as follows: Tests/Quizzes………………………90% Homework/Projects……..……..10%
It is expected that all homework will be done in a timely manner. Projects will be given during the school year. They will be done individually or in pairs depending on the project. Each project will describe a situation and state one or more questions to investigate. A general format for the reports must include: Introduction- where the situation that is being investigated will be described and why it was chosen Methodology – where describes the survey/experiment design Analysis- where the data is examined both numberically and graphically, using a computer utility Conclusions- a summary of the investigation findings, including any pitfalls and extensions Presentation- A way to communicate methods, results, and interpretations using the vocabulary of statistics. Present your findings and explain the material that was mastered.
Suggested Activity/ TIMELINES
CONTENT/OBJECTIVE
Textbook: The Practice of Statistics: Yates, Moore, Mc Cabe. Workbook: Workshop Statistic: Discovery with Data and The Graphing Calculator: Second Edition by Allen Rossman
I. Organizing Data: Looking for Patterns and Departures from Patterns
Chapter 1: Exploring Data
8 days
Appropriate Materials-Equipment
1. Identify the individuals and variables in a set as categorical or quantitative. 2. Make a dotplot that records dots for individual observations. 3. Make a histogram of the distribution of a quantitative variable when you are given counts for classes of equal width and when they are chosen. 4. Make a stemplot of the distribution of a small set of observations and interpret it. 5. Assess from a dotplot, stemplot, or histogram whether the shape of a distributions roughly symmetric, distinctly skewed, or neither. 6. Decide which measures of center and spreads are more appropriate: the mean and the standard deviation or the five-number theory. 7. Recognize outliers. 8. Make and analyze a time plot of data. 9. Calculate the mean and standard deviation of a set of observations using a calculator and determine the median. 10. Calculate the quartiles and the IQR for a set of observations.
ALL ASSIGNMENTS ARE FROM THE THE PRACTICE OF STATISTICS, UNLESS NOTED.
FOR EVERY SECTION, THE STUDENTS WILL COMPLETE AN OUTLINE WORKSHEET THAT WILL INCLUDE KEY VOCABULARY TERMS, CALCULATOR SKILLS, AND ANSWERING QUESTIONS PERTAINING TO OBJECTIVES IN THE SECTION TO HELP COMMUNICATE STATISTICS.
Pg. 8-9 1.1, 1.2, 1.3
Pg. 15-18 1.4- 1.8
Evaluati on / N Projects/Reports: The Golden Resourse Binder: Yates, Moore, Starnes. Students will be assigned special problems/activities from the resource binder for certain chapters. They are all to be completed in report form with displays throughout the report. Students are to use their TI83/minitab to complete each special problem.
Technology: Students will use the graphing calculator extensively throughout the year. I use the TI-83 overhead to demonstrate the necessary calculator methods. On some assignments and activities, students, in addition to the TI-83, use Minitab to analyze and interpret data. Java Applets are demonstrated in class for confidence intervals, visualizing correlation in scatterplots, and linear regression decomposition.
Pg. 20-21 1.9 –1.1
Pgs.22-23 1.12, 1.13 Pg. 34 1.24, 1.25 Pg. 42-43 1.31- 1.34 Project: M & M activity Workshop Statistics
NJCCCS: 4.1, 4.2, 4.7,
Chapter 2: The Normal Distributions
7 days
11. Know that areas under a density curve represent proportions of all observations and that the total area under a density curve is 1. 12. Approximately locate the mean and median on a density curve. 13. Determine the proportion of observation within one, two and three standard deviations of the mean, and compare with the 68-9599.7 rule. 14. State what percent of the observations from a normal distribution is bell- shaped. 15. Plot a histogram, stemplot, and/or boxplot to determine if a distribution is bell-shaped. 16. Construct and interpret normal probability plots.
Pg. 71 – 72 2.1-2.5
NJCCCS: 4.1, 4.2, 4.4, 4.5, 4.6, 4.9, 4.12
Pg. 77-78 2.6 – 2.10
Pg. 96-97 2.26 – 2.36 even
Chapter 3: Examining Relationships
8 days
17. Identify the explanatory and response variables in situations where one variable explains or influences another. 18. Make a scatterplot for two quantitative variables, add a categorical variable and interpret the scatterplot. 19. Define and interpret correlation and explain y = b + mx and draw the line. 20. Calculate and find the slope and intercepts of the least-squares regression line. against other variables
Pg. 111 3.1-3.4
Pg. 113 3.5-3.8
Chapter 2 Test
Special Problem 3A: Are SAT scores linked? Students will write a Report to describe Their investigation. Minitab/TI84 will be used To complete data Analysis and the Appropriate plots to be Inserted throughout the Report where necessary Show the statistical process Of conclusion.
Suggested Activity/ TIMELINES
Chapter 4: More on TwoVariable Data
CONTENT/OBJECTIVE
Appropriate Materials-Equipment
NJCCCS: 4.1, 4.2, 4.5, 4.9, 4.11,4.12
21. Calculate and analyze the. residuals and plot them against the explanatory variable x or 22. Analyze two- variable data that show a linear pattern and construct models for data that fit an exponential function or power function.
Pg. 130 3.18 – 3.24
23. Understand extrapolation. 24. State marginal distributions and describe the relationship between them.
Pg. 188 4.1 – 4. 12. 4.20-24, 30-39
9 days
Evaluation / NJCCCS Reference
Pg. 142 3.31-3.38 Chapter 3 Test Pg. 159 3.39-3.41
Special Problem 4E: Paradox
NJCCCS: 4.1, 4.2, 4.4, 4.7, 4.9, 4.10, 4.12
Simpson’s Chapter 4 Test
Part II: Producing Data: Samples and Experiments Chapter 5: Producing Data
9 days
25. Identify the population in a sampling situation and recognize bias. 26. Plan and conduct surveys, experiments, simulations and observational studies and generalize the results.
Part III: Probability: Foundations of Inference Chapter 6: Probability: The Study of Randomness
7 days
27. Know and apply the sample space of a random phenomenon and the probability rules. 28. Recognize, define and find the mean and variance of a discrete, continuous and random variable.
Pg. 261 5.14 –5.25, 45-57 odd Special Problem 5D: Airline overvbooking – Students will set up a simulation using TI84, choose a model, define a trial, perform repetitions of trails, and analyze the results. Students’ must report their findings in report form.
NJCCCS: 4.1, 4.4, 4.5, 4.9, 4.10, 4.11, 4.12
Chapter 5 Test
NJCCCS: 4.1, 4.2, 4.3, 4.4, 4.5, 4.7, 4.9, 4.12 Pg. 316 6.1 – 6.25 odd Pg. 345 6.37-6.43 odd ACTIVITY: Do husbands help out at home? Use Java applet to simulate choosing many women independently. Over the long run, what proportion agree?
Chapter 6 Test
Suggested Activity/ TIMELINES Chapter 7: Random Variables 7 days
Chapter 8: The Binomial and Geometric Distributions
CONTENT/OBJECTIVE
29. Identify a random variable as binomial or geometric, determine binomial and geometric probabilities and calculate means and standard deviations of binomial random variables.
30. Identify and analyze sampling distribution, sample proportions and sample means.
7 days
Chapter 9: Sampling Distributions
10 days
31. Define, calculate and interpret a confidence interval for the mean of a normal population. 32. State the null and alternative hypotheses in a testing situation when the parameter in question is a population mean. 33. Explain the meaning of the P-value when you are given the numerical value of P for a test.
13 days
Pg. 373 7.1 –7.5, 7.17 – 7.27 odd ACTIVITY: The Casino Lab Students will simulate events using the TI84 to compare experimental and theoretical probability, expected values of random variables, distinguish between discrete and continuous random variables, and develop rules that will be needed for inference.
Pg. 433 8.19 – 8.23 Pg. 444 8.30 – 8.36
Evaluation / NJCCCS Refe NJCCCS: 4.1, 4.2, 4.3, 4.4, 4.5, 4.9, 4.10, 4.12
Chapter 7 Test
NJCCCS: 4.1, 4.2, 4.4, 4.5, 4.9, 4.10, 4.12
Chapter 8 Test
NJCCCS: 4.1, 4.2, 4.4, 4.5, 4.10, 4.11, 4.12
Chapter 9 Test Pg. 469 9.11 – 9.14 Pg. 479 9.22 – 9.25 Pg. 494 9.36 – 9.40 ACTIVITY: EXAMINING TYPE II ERROR THROUGH SIMULATION
Part IV: Inference: Conclusions with Confidence Chapter 10: Introduction to Inference
Appropriate Materials-Equipment
34. Calculate the z statistic and the Pvalue for both one-sided and two0sided tests about the mean of a normal population. 35. Recognize from a design of a study whether one-sample, matched pairs, or two-sample procedures are needed. 36. Obtain confidence intervals using one- and two- sample t procedures.
NJCCCS: 4.1, 4.2, 4.4, 4.9, 4.10, 4.11, 4.12 SPECIAL PROBLEM 10A: A STUDY IN PSYCHOLOGY- A MINITAB EXPLORATION IN WHICH STUDENTS PERFORM INFERENCE ABOUT A POPULATION WITH KNOWN STANDARD DEVIATION.
Chapter 10 Test
Chapter 11: Inference for Distributions 8 days
Chapter 12: Inference for Proportions 8 days
Chapter 13: Inference for Tables: Chi-Square Procedures
8 days
37. Use the one- and two-sample z procedures to give confidence intervals for a population proportion.
38. To determine if a population distribution has changed by using a goodness of fit test.
39. Locate expected cell counts, the chi-square statistic, and its P-value in output from a calculator.
Pg. 613 11.21 – 11.30 Pg. 640 11.45 – 11.55
NJCCCS: 4.1, 4.2, 4.3, 4.4, 4.5, 4.8, 4.9, 4.11, 4.12
SPECIAL PROBLEM 11A: A MULTIPART QUESTIONS THAT REQUIRES STUDENTS TO COMBINE DATA PRODUCTION IDEAS FROM CH.5 WITH INFERENCE TECHNIQUES. THE PROBLEM SHOULD BE COMPLETED IN REPORT FORM .
Chapter 11 Test
NJCCCS: 4.1, 4.2, 4.4, 4.5, 4.9, 4.11, 4.12 Chapter 12 Test
NJCCCS: 4.1, 4.2, 4.3, 4.4, 4.5, 4.10, 4.11 Pg. 675 12.12 – 12.20 Pg. 690 12.25 – 12.30
Chapter 13 test
Chapter 14: Inference for Regression
11 days
40. Make and inspect a scatterplot, find the correlation and the least-squares regression line on a calculator.
NJCCCS: 4.4, 4.5, 4.9, 4.10, 4.11, 4.12 Pg. 742 13.28 – 13.38
Chapter 14 Test
41. Use and interpret ANOVA to compare means. 14.15 – 14.24
Chapter 15 TEST 4.1, 4.2,4.4, 4.5, 4.8, 4.9, 4.10
Suggested Activity/ TIMELINES
CONTENT/OBJECTIVE
Appropriate MaterialsEquipment
Evaluation / NJCCCS Reference
REVIEW FOR AP EXAM 1. COMPARE AND CONTRAST ALL RELEASED OPEN ENDED QUESTIONS TO HELP STUDENTS COMMUNICATE METHODS, RESULTS, AND INTERPRETATIONS USING THE VOCABULARY OF STATISTICS.
DURING REVIEW, THE STUDENTS WILL BE ABLE TO MAKE CONNECTIONS BETWEEN DESIGN, ANALYSIS, AND CONCLUSION. 2. STUDENTS WILL GRADE EACH OTHERS FREE RESPONSE QUESTIONS TO ENSURE UNDERSTANDING OF WHAT IS EXPECTED TO RECEIVE FULL/PARTIAL/NO CREDIT.
End of Year Project: Each student is to pick a topic, develop a question, research that topic, use statistical analysis to determine an answer, write a report of their findings, and present their findings to the class. In order to draw connections between all aspects of the statistical process, the students must include the following in their report: 1. Introduction- where the situation that is being investigated will be described and why it was chosen 2. Methodology – where describes the survey/experiment design 3. Analysis- where the data is examined both numberically and graphically, using a computer utility 4. Conclusions- a summary of the investigation findings, including any pitfalls and extensions 5.Presentation- a way to communicate your findings and explain the material that was mastered. Each student must use a graphing utility, minitab, or a computer program to complete all computations and graphs to enhance the development of statistical understanding.
