Course Outline

AP Exam Format:

Section 1:  40 Multiple Choice Questions

Section 2:  6 Free Responses (5 short answer and 1 investigation)

Primary Textbook:

Yates, Moore, and Darren Starnes. The Practice of Statistics

Calculator Enhanced, 5th edition. New York, NY: W.H. Freeman and Company,2015.

Technology:

 The TI-83/84 Plus calculators are an essential component of this course.  Students will use the calculator to master and analyze numerous statistical concepts.  Many of these concepts are cumbersome to calculate by hand and the use of the calculator allows the students to focus on the meaning and significance of the concept without being weighted down with lengthy computations.  The calculator is not a substitute for learning the manual calculations required in many statistical procedures.  It is used only when the process has been learned by hand and it helps the students to explore deeper into these complex concept. 

Course Description:

Advanced Placement Statistics will be most high school students’ first introduction to the complex and real-life applicable subject of statistics.  Students’ will be introduced to major statistical concepts and tools that explore the areas of Data Analysis, Data Collection, Probability, and Statistical Inference.  Students will collect, analyze, describe, and compare univariate and bivariate distributions of data.  The use of the TI-84 Plus graphing calculator and computer output help students visualize and better understand the distributions of data.  Students will recognize patterns in data and apply linear regression techniques that will enable the student to develop a model for the data and use it for predicting. They will examine and critique different methods of data collection, and apply their findings in actual sample surveys and experiments performed within our school community and beyond.  Newspaper, television, and the Internet will be used to emphasize the importance of proper sampling and experimentation in the outside world.  Students will be able to recognize unique characteristics of different types of statistical distributions, and understand how and why these distributions behave in this manner.  Simulations of probability models and data distributions will be carried out so that students can analyze and examine long-run behaviors.  Several different statistical inference tests will be introduced and examined.  Students will learn the proper procedures for carrying out the tests, and how to draw conclusions based on the results.  An emphasis is placed on the importance and relevance of these significance tests to occupations dealing with research and design, medicine, and quality control and production.  Released AP Exam questions are frequently used throughout the course to give the students more practice with these concepts. Students use the rubrics created by the College Board to assess their understanding of the question and the accuracy of their response. These questions are valuable tools that help the student become comfortable with the format and content of the AP Exam.

 
Course Outline:
Unit 1:  Exploring Data (20%)

“Describing patterns and departures from patterns.”

 

  1. Introduction to Data (Chapter 1)
    1. Constructing statistical graphs for both categorical and quantitative data.  (dot plots, stem and leaf plots, modified box plots, bar graphs, pie charts, time plots, histograms, and cumulative relative frequency graphs)
    2. Describing important characteristics of statistical graphs using four main components.  (Center, Shape, Spread, and outliers or other unusual characteristics)
    3. Using the TI-84 Plus calculator to store, organize and graph data, and then analyze the distribution.
    4. Use formulas and methods to determine numerical values for measuring the center of distributions; mean and median.
    5. Use formulas and methods to determine numerical values for measuring the spread of distributions; standard deviation, overall range, and interquartile range.
    6. The effects of skewness and extreme values on resistant and non-resistant measures of center and spread.
    7. The effects of linear transformations on summary statistics such as mean, median, quartiles, standard deviation, and interquartile range.
    8. Analyzing distributions of univariate data by using back-to-back stem plots and side-by-side box plots to compare their shapes, centers, and spreads.

       

  2. The Normal Distribution (Chapter 2)
    1. Discuss properties of density curves and how to find areas under the curves.
    2. Make connections to the mean and median of density curves.
    3. Label and find values on a Normal Distribution curve using the 68-95-99.7 Rule.
    4. Explore the Standard Normal Distribution and use it to calculate exact proportions under the curve and percentiles.
    5. Standardize values (z-scores) in order to use Tables containing Standard Normal probabilities.
    6. Assess normality of data sets using the 68-95-99.7 Rule, and constructing normal probability plots using the graphing calculator.

       

  3. Examining Relationships, Bivariate Data (Chapter 3)
    1. Construct scatter plots to determine if explanatory/response relationships exist between two variables.
    2. Describe scatter plots by addressing form, strength, direction, and presence of outliers.
    3. Find a numerical value to represent the strength of a scatter plot, correlation, by formula and the use of the calculator.
    4. Examine facts regarding correlation and how extreme values, outliers and influential values, affect it.
    5. Discuss cautions about correlation and regression, extrapolation, lurking variables, causation, common response, and confounding.
    6. Develop linear models using least-squares regression procedures.
    7. Make predictions using these linear models.
    8. Understand and interpret the coefficient of determination (r2).
    9. Use residual and residual plots to determine if scatter plots truly reveal linear patterns.
    10. Transform logarithmic and power functions in order to achieve linearity and develop an accurate model to fit the data.


Unit 2: Sampling and Experimentation  (15%)

“Planning and conducting a study”

 

  1. Producing Data (Chapter 4)
    1. Differences between observational survey and experiment.
    2. Sampling methods; census, convenience sampling, voluntary response, simple random samples, multi-stage sampling, and stratified sampling.
    3. Sources of bias in sampling methods.
    4. Characteristics of well-designed and well-conducted observational surveys.
    5. Sources of bias in experiments; the Placebo effect, the Hawthorne effect, and blinding.
    6. Different types of experimental designs; block design, and matched pairs.
    7. Characteristics of well designed and well conducted experiments; Control, Randomize, and Replicate.
    8. Generalizability of findings and results of experiments, and observational studies.
    9. Simulate random assignment of subjects and treatments in to different experimental designs.


Unit 3: Anticipating Patterns (25%)

“Exploring random phenomena using probability and simulation”

 

  1. Probability (Chapter 5)
    1. Understanding probability as it relates to long-run situations
    2. Use, interpret, and simulate probability models and distributions.
    3. Addition Rule, Multiplication Rule, Conditional Probability, and Independence of random events.

       

  2. Random Variables (Chapter 6)
    1. Discrete and Continuous random variables and their probability distributions.
    2. Mean and standard deviation of a probability distribution involving discrete random variables.
    3. Law of Large Numbers.
    4. Linear transformation and combination of independent random variables.
    5. Properties and characteristics of Binomial and Geometric distributions.
    6. Understand calculations and graph construction of probability distribution functions and cumulative distribution functions for binomial and geometric settings.
    7. Mean and standard deviation of Binomial and Geometric distributions.
    8. Normal approximations to binomial distributions.

       

  3. Sampling Distributions (Chapter 7)
    1. Explore properties of sampling distributions of sample proportions and sample means.
    2. Bias and variability of a statistic.
    3. Central Limit Theorem.
    4. Simulation of sampling distributions.


Unit 4: Statistical Inference (40%)

“Estimating population parameters and testing hypotheses”

 

  1. Estimating with Confidence (Chapter 8)
    1. Confidence intervals for a population mean when data is an SRS from the population of interest and the sampling distribution is approximately normal.
    2. Behavior of confidence intervals and how to interpret and draw conclusions from them in context to problem.
    3. One and two sided significance test for population means using, null and alternative hypotheses, z-test statistics, p-values, and critical values.
    4. Drawing logical conclusions based on the results of these significance tests.
    5. Concepts of Type I and Type II errors, and their significance and impact on real-life situations, as well as the importance of power against an alternative mean.

       

  2. Testing a Claim (Chapter 9)
    1. Confidence intervals for a mean using t-procedures.
    2. Confidence intervals for a difference of two means both paired and unpaired.
    3. Significance test for a mean using t-procedures.
    4. Significance test for a difference of means, both paired and unpaired, using t-procedures.
    5. Robustness of t-procedures.

       

  3. Comparing Two Groups or Populations (Chapter 10)
    1. Confidence intervals for a proportion coming from a large sample.
    2. Confidence intervals for a difference of two proportions coming from a large sample.
    3. Significance test for a proportion coming from a large sample.
    4. Significance test for a difference of proportions coming from a large sample.

       

  4. Inference for Distributions of Categorical Data (Chapter 11)
    1. Chi-Square test for goodness of fit.
    2. Chi-Square test for homogeneity of proportions.
    3. Chi-Square test for independence. (two-way table)

       

  5. Inference for Linear Regression (Chapter 12)
    1. Confidence interval for the slope of a least square regression line.
    2. Significance test for the slope of a least square regression line.