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K12MATH014: Advanced Statistics

Course Syllabus for "K12MATH014: Advanced Statistics"

Welcome to the amazing world of statistics! You might be thinking that the topic is just about a bunch of charts, graphs, and odd-looking formulas, but in fact, it is a fascinating and challenging field of study. In this course, we will indeed study those charts and graphs, and yes, that array of complex formulas. But beyond those tools, we will find an entire new way of thinking, a new way of approaching and understanding the world around us. We will learn why taking aspirin helps lower the risk and severity of a heart attack; how researchers have determined that the more friends you have on a social networking site, the more likely you are to have fewer friends in real life; and how political pollsters almost always know the outcome of an election even before the polls open. The course is divided into 10 units of study. The first two units are devoted to simple statistical calculations and graphical representations of data. Most of this material will be familiar to you from previous math or science courses. Unit 3 is devoted to a foundational concept of statistics, which is the study of probability. Unit 4 will introduce you to random variables and a very important distribution called the binomial distribution. Unit 5 will focus entirely on one topic: the bell curve. You may have studied the bell curve, also called the normal distribution, in other courses, but this unit will make sure that you are confident and competent in knowing its properties, its uses, and its central importance to all of the material in the rest of the course and in the entire field of statistics. The first five units build the foundation of concepts, vocabulary, knowledge, and skills for success in the remainder of the course. In the final five units, we will take the plunge into the domain of inferential statistics, where we make statistical decisions based on the data that we have collected. In Unit 6, we will learn how to design statistically sound experiments and studies, in order to collect valid, reliable data. In Unit 7 and Unit 8, we will learn how to analyze the data, using confidence intervals and hypothesis tests, to make statistically sound decisions and inferences about our results. The final two units will be devoted to two topics frequently used in statistical research: linear regression and chi-square analysis. These exotic-sounding topics will act as springboards for your further study of the discipline in your college undergraduate or graduate programs. We will use a variety of resources in addition to the text. An online course needs to be multidimensional so that you won't be lulled into a daily grind of textbook reading and doing homework problems. In light of this, you will supplement your course text with video lessons, interactive applets, and research into some of statistics’ most interesting, controversial, and fascinating experiments and studies. By the end of the course, you will have mastered the foundational concepts of a field of endeavor that will assist you in studying and understanding the world around you as never before.

Learning Outcomes

Upon successful completion of this course, you will be able to:

  • Create and interpret graphs and charts as a means of summarizing and communicating data meaningfully.
  • Summarize and interpret the relationship between two quantitative or two qualitative variables.
  • Use and assess the appropriateness of the measures of center and measures of spread in comparing distributions.
  • Construct sample spaces and calculate probabilities for simple and compound events.
  • Formulate a statistically valid experimental or study design for a given research hypothesis.
  • Identify and name four sampling methodologies.
  • Use the appropriate rules for independent or mutually exclusive events, and calculate accurate probabilities and interpret them, in a variety of settings: normal distribution, binomial distribution, t-distribution, or chi-square distribution.
  • Calculate and interpret a confidence interval and know how it is used in the physical and social sciences.
  • Select and perform an appropriate hypothesis test for a given set of data and interpret the significance of the results from the study or experiment.
  • Discuss the ethical and practical uses of statistical data and statistical analysis in our world today.

Course Requirements

In order to take this course, you must:

√    Have access to a computer.

√    Have continuous broadband Internet access.

√    Have the ability/permission to install plug-ins or software (e.g., Adobe Reader or Flash).

√    Have the ability to download and save files and documents to a computer.

√    Have the ability to open Microsoft files and documents (.doc, .ppt, .xls, etc.).

√    Have competency in the English language.

√    Have read the Saylor Student Handbook.

√    Have successfully completed the equivalent of a second-year high school algebra course.

√    Have access to a graphing calculator, such as the TI-83 or TI-84, in which you can enter data into lists, graph the data, and perform statistical tests and calculate confidence intervals. You will be provided detailed instructions on the use of the calculator as you progress through the course.

      OR

√    Have access to a spreadsheet type of software, such as Microsoft Excel (with Data Analysis add-on), Minitab, or SPSS, which can provide for display and analysis of data sets.

Course Information

Welcome to Advanced Statistics. General information on this course and its requirements can be found below.
 
Course Designer: Jill Schmidlkofer
 
Primary Resources: This course is composed of a range of different free, online materials. However, the course makes primary use of the following:

  • An online textbook, specifically designed for the objectives of this course.
  • Video lessons that enhance the text material and support the course and unit objectives.
  • Interactive applets that allow you to practice new skills and to more deeply comprehend the concepts introduced in the text and videos. 

Requirements for Completion: You will be using an online textbook that has been created just for this course; its coverage satisfies Common Core State Standards, and it reflects most topics tested on the Advanced Placement Statistics exam. You will also make extensive use of Khan Academy and SOPHIA videos to supplement your learning.
 
Nearly all subunits include at least one video lecture or an interactive exercise that will enhance your learning.
 
At the end of each subunit, a problem set is assigned. Each set is a short homework assignment. Answer keys and detailed solutions are provided.
 
At the end of each of the 10 major units, you are given an assessment covering material from the entire unit. The assessment includes some AP-type questions.
 
Time Commitment: Completing this course should take you a total of approximately 96 hours and 50 minutes. Each unit includes a “Time Advisory” that lists the amount of time you are expected to spend on each Subunit. It may be useful to take a look at these time advisories and determine how much time you have over the next few weeks to complete each unit and then set goals for yourself. For example, Unit 1 should take approximately 6 hours and 20 minutes to complete. Perhaps you can sit down with your calendar and decide to complete Subunit 1.1 (a total of 50 minutes) on Monday and Tuesday nights, Subunit 1.2 (a total of 30 minutes) on Wednesday, and so forth.
 
Tips/Suggestions: A statistics course can get overwhelming at times. There are so many formulas! The good news is that you will be provided a formula sheet, and you will always be allowed to use the formula sheet and your calculator for assessments in this course. If you plan to take the AP exam, make sure that you become very familiar with both the AP formula sheet and with the graphing calculator and its capabilities.
 
To obtain your own copy of the AP formula sheet for use with this course, please click on the AP Statistics Course Home Page Statistics Course Home Page and select "AP Statistics Course Description.” The downloadable and printable PDF file contains the entire formula sheet and necessary statistical tables on pages 12 - 18.
 
The AP Statistics Exam* consists of multiple-choice questions and five free-response questions, which may take 10 - 15 minutes each and will require you to show all work. For information about the exam, go to AP Statistics Course Home Page. You can find registration information, sample exams from previous years, and other useful information.


*“AP is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product.”