Mater Academy Charter High School



Mater Academy Charter High School

AP Statistics

Syllabus

Introduction

The basic function of the Statistics is the compilation and scrutiny of data to formulate conclusions by using the accumulate information. The intention of the AP Statistics course is introduce high school learners to the main concepts and instruments for collecting, analyzing, and drawing conclusions from data through of the study of the following four central themes:

• Exploring Data: Describing patterns and departures from patterns

• Sampling and Experimentation: Planning and conducting a study

• Anticipating Patterns: Exploring random phenomena using probability and simulation

• Statistical Inference: Estimating population parameters and testing hypotheses.

The design of the AP Statistics course covers the information, skills, and assessments consistent with a one- semester, non-calculus-based introductory statistics college course. Consequently, students who effectively complete the course and pass the exam from the College Board may get college credits in accordance with a typical introductory college class in statistics.

Mater Academy High school plans to offer the AP Statistics course as a one-year course for students who have fruitfully concluded two Algebra courses and demonstrated mathematical maturity and quantitative reasoning skills to be able to face the challenge of a rigorous college course which may give them the opportunity to expand their mathematical background.

The Statistics course may represent an incredible experience to build up working- in- team ability since it design combine both, the individual work and the students’ labor on small groups which give learners occasion to interact, share ideas, discus, and formulate conclusion. The course provide a plenty opportunity to think through problems, make decisions, and share questions and conclusions with other students as well as with the teacher, who will act as a consultant.

Additionally the course will allow students to develop interdisciplinary connections with other subjects and the real world as a result of interactive and investigative projects and many other problem-solving activities include as a part of the course.

Technology (C5)

The use of technology represents an essential part of the AP Statistics course. Therefore, student will access to computer and graphing calculators in class, at home, and on the AP Exam.

This AP Statistics course demands the application of appropriate tools, including Statistical software, Microsoft Excel, and TI-83+ and TI-84 family of graphing calculators. Consequently, the statistical functions of the graphing calculator will be used daily and extensively for each unit of the course.

C5—The courses teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploring and analyzing data, assessing models, and performing simulations.

Course Textbook and Supplements

Primary Textbook

• Bock, David; Velleman, Paul; and De Veaux, Richard. “Stats, Modeling the World”. 2nd Edition. Pearson/Addison Wesley, 2007. ISBN 0-13-187621-X

Supplements

• Bock, David; Velleman, Paul; and De Veaux, Richard. “AP* Statistics” Pearson Education. AP*Test Prep Series, 2007. ISBN 0-131-87622-8

• Larson, Ron and Farber, Betsy. “Elementary Statistics, Picturing the World”. Pearson Prentice Hall, 4th Edition, New Jersey, 2009.

• Bock, David and Craine, William. “Printed Test Bank and Resource Guide”. Pearson Addison-Wesley, Boston, 2007. ISBN 0-13-195004-5

• Web resources, for instance:

o Materials posted by other teachers.

o Software-calculators, commercial software, and some web software.

o Statistical software, including Microsoft Excel, and TI-83+ and TI-84 family of graphing calculators.

o Diverse sources of data.

o Statistics Background.

Course Outline

(Organized from the College Board’s Course Description-Statistics and related to the chapter in the primary textbook))

An Introduction to Statistics

Total Time: 1 day (90 minutes per day)

• Activity: “What is (are) Statistics? Statistics in a world”. ( Discursion)

1. Exploring Data: Describing patterns and departures from patterns. (C2b) / (C5)

Total Time: 16 days (90 minutes per day)

A. Constructing and interpreting graphical displays of distribution of univariate data (dot plot, stem plot, histogram, and cumulative frequency plot). (Chapters 4 and 5)

▪ Center and spread (chapters 4-5)

▪ Clusters and gaps (chapter 4)

▪ Outliers and other unusual features (chapters 4-5)

▪ Shape(chapter 4)

B. Summarizing distributions of univariate data.( Chapters 5 and 6)

▪ Measuring center: median, mean (chapter 5)

▪ Measuring spread: range, interquartile range, standard deviation (chapters 5-6)

▪ Measuring position: quartiles, percentiles, standardized scores (z-scores) (chapters 5-6)

▪ Using boxplots (chapter 5)

▪ The effect of changing units on summary measures (chapter 6)

C. Comparing distributions of univariate data

(dotplots, back-to-back stemplots, parallel boxplots). (Chapters 4-5)

▪ Comparing center and spread: within group, between group variation (chapters 4-5)

▪ Comparing clusters and gaps (chapter 4)

▪ Comparing outliers and other unusual features (chapters 4-5)

▪ Comparing shapes (chapter 4)

C2a: The course provides instruction in each of the following four broad conceptual themes outlined in the Course Description with appropriate emphasis on exploring data.

D. Exploring bivariate data (Chapters 7-10)

▪ Analyzing patterns in scatter plots (chapter 7)

▪ Correlation and linearity (chapter 7)

▪ Least-squares regression line (chapter 8)

▪ Residual plots, outliers, and influential points (chapter 9)

▪ Transformations to achieve linearity: logarithmic and power transformations (chapter 10)

E. Exploring categorical data (chapter 3)

▪ Frequency tables and bar charts

▪ Marginal and joint frequencies for two-way tables

▪ Conditional relative frequencies and association

▪ Comparing distributions using bar charts

C2b: The course provides instruction in each of the following four broad conceptual themes outlined in the Course Description with appropriate emphasis on sampling and experimentation.

C5—The courses teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploring and analyzing data, assessing models, and performing simulations.

2. Sampling and Experimentation: Planning and conducting a study

Total Time: 8 days (90 minutes per day)

A. Overview of methods of data collection (Chapter 12 and 13)

▪ Census (chapter 12)

▪ Sample survey (chapter 12)

▪ Experiment (chapter 13)

▪ Observational study (chapter 13)

B. Planning and conducting surveys (chapter 12)

▪ Characteristics of a well-designed and well-conducted survey

▪ Populations, samples, and random selection

▪ Sources of bias in sampling and surveys

▪ Sampling methods, including simple random sampling, stratified random

▪ sampling, and cluster sampling

C. Planning and conducting experiments (chapter 13)

▪ Characteristics of a well-designed and well-conducted experiment

▪ Treatments, control groups, experimental units, random assignments,

▪ and replication

▪ Sources of bias and confounding, including placebo effect and blinding

▪ Completely randomized design

▪ Randomized block design, including matched pairs design

D. Generalizability of results and types of conclusions that can be drawn from observational studies, experiments and surveys. (Chapters 12 and 13)

3. Anticipating Patterns: Exploring random phenomena using probability and simulation.

Total Time: 16 days (90 minutes per day)

A. Probability (chapters 11, 14-17)

▪ Interpreting probability, including long-run relative frequency interpretation

(chapter 14)

▪ “Law of Large Numbers” concept (chapter 14)

▪ Addition rule, multiplication rule, conditional probability, and independence (chapter 14 and 15)

▪ Discrete random variables and their probability distributions, including binomial and geometric (chapter 16 and 17)

▪ Simulation of random behavior and probability distributions (chapter 11)

▪ Mean (expected value) and standard deviation of a random variable, and linear transformation of a random variable (chapter 16)

B. Combining independent random variables (chapter 16)

▪ Notion of independence versus dependence

▪ Mean and standard deviation for sums and differences of independent random variables

C. The normal distribution (chapter 6)

▪ Properties of the normal distribution

▪ Using tables of the normal distribution

▪ The normal distribution as a model for measurements

D. Sampling distributions

▪ Sampling distribution of a sample proportion(chapter 18)

▪ Sampling distribution of a sample mean (chapter 18)

▪ Central Limit Theorem (chapter 18)

▪ Sampling distribution of a difference between two independent sample proportions (chapter 22)

▪ Sampling distribution of a difference between two independent sample means (chapter 24)

▪ Simulation of sampling distributions (chapter 11)

▪ t-distribution (chapter 23)

▪ Chi-square distribution (chapter 26)

C2c: The course provides instruction in each of the following four broad conceptual themes outlined in the Course Description with appropriate emphasis on anticipating patterns.

C2b: The course provides instruction in each of the following four broad conceptual themes outlined in the Course Description with appropriate emphasis on sampling and experimentation.

C5—The courses teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploring and analyzing data, assessing models, and performing simulations.

4. Statistical Inference: Estimating population parameters and testing hypotheses [C2d]

Total Time: 28 days (90 minutes per day)

A. Estimation (point estimators and confidence intervals)

▪ Estimating population parameters and margins of error (chapter 19)

▪ Properties of point estimators, including unbiasedness and variability (chapter 19)

▪ Logic of confidence intervals, meaning of confidence level and confidence intervals, and properties of confidence intervals (chapter 19)

▪ Large sample confidence interval for a proportion (chapter 19)

▪ Large sample confidence interval for a difference between two proportions (chapter 22)

▪ Confidence interval for a mean (chapter 23)

▪ Confidence interval for a difference between two means (unpaired and paired) (chapter 24-25)

▪ Confidence interval for the slope of a least-squares regression line (chapter 27)

A. Tests of significance (chapters 20-27)

▪ Logic of significance testing, null and alternative hypotheses; p-values; one- and two-sided tests; concepts of Type I and Type II errors; concept of power (chapter 20-21)

▪ Large sample test for a proportion (chapter 20)

▪ Large sample test for a difference between two proportions (chapter 22)

▪ Test for a mean (chapter 23)

▪ Test for a difference between two means (unpaired and paired) (chapter 24-25)

▪ Chi-square test for goodness of fit, homogeneity of proportions, and independence (one- and two-way tables) (chapter 26)

▪ Test for the slope of a least-squares regression line (chapter 27)

This schedule leaves about 20 hours (10 days) to teach topics that students find most difficult. The remaining time will be used to review the main topics before the AP Exams.

C2d: The course provides instruction in each of the following four broad conceptual themes outlined in the Course Description with appropriate emphasis on statistical inferences.

5. Review for AP Exam and Final Exam

Total Time: 10 days (90 minutes per day)

• Released AP Exams

• Remaining previous AP questions

• Worksheets from AP Test Prep Book

• Final Exam

• AP Exam

6. Post AP Exam (20 days)

• Second Semester Project (see below)

• Chapter 29: Multiple Regression

• Analysis of Variance

• Activity/Guest speakers: Careers in Statistics

AP Statistics Second Semester Example Project [[C2a, b, c, d]] [[C3]] [[C4]] [[C5]]

Activity: “SAT Performance”

In these task students will investigate about students’ SAT scores at Mater Academy High School. The students will design their experiment so that it can answer the following questions:

1. What is the mean SAT-Math score at this high school?

2. How do these students’ SAT Math scores stack up against the rest of the state?

3. Is there a significant difference between Verbal and Math scores for these students?

4. Nationally males tend to have higher Math scores than females. Is that true at this high school, too?

Students could use a copy of data from the SAT Score Roster sent to the high school by the College Board. It shows gender, Verbal scores, and Math scores for students in a graduating class.

The project will be done in groups (4 students per group). Each group will select the information for a school year to investigate the students’ SAT score behavior, from 2005 to 2008. Students will turn in one project per group. A written report must be typed (single-spaced, 12-point font) and included graphs should be done on the computer using JMP-Intro or Excel.

Written Report: The written report should include a title in the form of a question and the following sections (clearly labeled):

• Introduction:

• Methodology: Describe how the experiment was conducted and justify why the design was effective.

• 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?

Oral Presentation: Members will participate equally. A poster should be used as a visual aid. Students should be prepared for questions.

C2a: The course provides instruction in each of the following four broad conceptual themes outlined in the Course Description with appropriate emphasis on exploring data.

C2b: The course provides instruction in each of the following four broad conceptual themes outlined in the Course Description with appropriate emphasis on sampling and experimentation.

C2c: The course provides instruction in each of the following four broad conceptual themes outlined in the Course Description with appropriate emphasis on anticipating patterns.

C2d: The course provides instruction in each of the following four broad conceptual themes outlined in the Course Description with appropriate emphasis on statistical inferences.

C3: The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions.

C4—The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics.

C5—The courses teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploring and analyzing data, assessing models, and performing simulations.

Major Assessments

• Students will receive sets of questions in AP format for each topic to help them prepare for the AP exam.

• Bock, David; Velleman, Paul; and De Veaux, Richard. “AP* Statistics” Pearson Education. AP*Test Prep Series, 2007. ISBN 0-131-87622-8.

This book will be used as learning and practicing material.

• Students will be required to take a Mid-Term that is in the AP Exam format.

• Students must complete selected questions from the Chapter Review at the end of each chapter.

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