Business Statistics
Purpose of Course showclose
This course will introduce you to business statistics, or the application of statistics in the workplace. Statistics is a course in the methods for gathering, analyzing, and interpreting data. If you have taken a statistics course in the past, you may find some of the topics in this course familiar. You can apply statistics to any number of fields – from anthropology to hedge fund management – because many of us best interpret data when it is presented in an organized fashion (as it is with statistics). You can analyze data in any number of forms. Summary statistics, for example, provide an overview of a data set, such as the average score on an exam. However, the average does not always tell the entire story; for example, if the average score is 80, it may be because half of the students received 100s and the other half received 60s. This would present a much different story than if everyone in the class had received an 80, which demonstrates consistency. Statistics provides more than simple averages. In this course, you will learn how to apply statistical tools to analyze data, draw conclusions, and make predictions of the future. The course will begin with data distributions, followed by probability analysis, sampling, hypothesis testing, inferential statistics, and, finally, regression. This course is mathematically intensive, and much of what you learn here will deal with things you encounter every day. This course also makes use of spreadsheets, an important tool for working with and making sense of numerical data.
This course provides students the opportunity to earn actual college credit. It has been reviewed and recommended for 3 credit hours by The National College Credit Recommendation Service (NCCRS). While credit is not guaranteed at all schools, we have partnered with a number of schools who have expressed their willingness to accept transfer of credits earned through Saylor. You can read more about our NCCRS program here.
Course Information showclose
Course Designer: David T. Bourgeois, PhD; Bharatendra K. Rai, PhD
Primary Resources: This course makes primary use of the following materials:
 University of California, Berkeley: Dr. Phillip Stark’s Statistical Toolbox for Internet and Classroom Instruction with a Graphical User Interface (SticiGui)
 University of California, Berkeley: Dr. Philip Stark’s Fall 2009 Statistics 21 Lectures (on YouTube and iTunes U)
 College of MicronesiaFSM: Dana Lee Ling’s Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 5^{th} edition (PDF) Click here to access this textbook from the original source (HTML)
YouTube  iTunes U  SticiGui Chapters Covered 
Lecture 1  Lecture 1  Intro to class, Chapter 1 (0:00 to 57:28) 
Lecture 2  Lecture 2  Chapter 3 (1:03:00 to 1:16:08) 
Lecture 3  Lecture 3 
Chapter 3 (0:00 to 54:00), Chapter 4 (54:00 to 1:14:23) 
Lecture 4  Lecture 4 
Chapter 4 (0:00 to 50:00), Chapter 5 (50:00 to 1:16:12) 
Lecture 5  Lecture 5 
Chapter 5 (0:00 to 38:00), Chapter 7 (41:00 to 1:18:57) 
Lecture 6  Lecture 6 
Chapter 9 (3:50 to 57:50), Chapter 11 (57:50 to 1:11:48) 
Lecture 7  Lecture 7  Chapter 11 (0:00 to 47:00), 
Lecture 8  Lecture 8  Chapter 12 (0:00 to 1:16:41) 
Lecture 9  Lecture 10  Chapter 13 (0:00 to 1:15:02) 
Lecture 11  Lecture 14  Chapter 14 (0:00 to 1:20:52) 
Lecture 12  Lecture 15  Chapter 17 (0:00 to 1:20:59) 
Lecture 13  Lecture 16  Chapter 17 (0:00 to 1:23:41) 
Lecture 14  Lecture 17 
Chapter 17 (0:00 to 56:00), Chapter 18 (56:00 to 1:25:13) 
Lecture 15  Lecture 18  Chapter 19 (0:00 to 1:21:08) 
Lecture 16  Lecture 19  Chapter 20 (0:00 to 1:25:21) 
Lecture 17  Lecture 20  Chapter 21 (0:00 to 1:24:52) 
Lecture 18  Lecture 21  Chapter 22 (0:00 to 1:20:42) 
Lecture 19  Lecture 22 
Chapter 23 (0:00 to 1:19:00), Chapter 24 (1:19:00 to 1:23:45) 
Lecture 20  Lecture 23  Chapter 24 (0:00 to 1:19:31) 
Lecture 21  Lecture 24 
Chapter 25 (0:00 to 1:05:00), Chapter 26 (1:05:00 to 1:18:42) 
Lecture 22  Lecture 25 
Chapter 26 (0:00 to 1:12:00), Chapter 27 (1:12:00 to 1:20:03) 
Lecture 23  Lecture 26  Chapter 27 (0:00 to 1:20:57) 
Lecture 25  Lecture 29  Review of semester 
Note: There are no lectures for chapters 15, 16, 29, and 30. 
Special Instructions on SticiGui exercises and Java applets: Every chapter in the online textbook has exercises to check your understanding; you should carefully work through each exercise. The author of the text has provided instructions on how to work with the exercises here: SticiGui: “How to Use These Materials.”*
Embedded throughout the text are the SticiGui Java applets. Think of these applets as little software programs that you can use to explore the different aspects of statistics you are learning. Each Java applet has instructions posted next to it in the text. You can find a listing of all the SticiGui Java applets here;* follow the links to each applet for further description and instructions on how to use each one. These applets should be compatible will all major browsers; Java needs to be enabled in order for them to work.
The minimum system requirements for using these tools are detailed here.*
Requirements for Completion: In order to complete this course, you will need to work through each unit and all of its assigned materials. A key point to remember is that to get the most out of this course, you will need to complete each assignment and be sure you understand it! Many of the units build on each other, so you will want to complete the course in order.
Note that not all of the listed readings and lectures are required for this course. Those that are not required are listed as optional. If you would like to experience the full course as it was presented at University of California, Berkeley, then you will want to go through these optional sections as well. Note that anything considered optional will not be on the Final Exam.
Besides reviewing these materials, you will also need to complete:
 The interactive examples included in the online textbook (SticiGui Exercises and Java applets)
 The assessments at the end of each unit
 The spreadsheet activities at the end of Units 1, 3, and 6
 The Final Exam
In order to pass this course, you will need to earn a 70% or higher on the final exam. Your score on the exam will be tabulated as soon as you complete it. If you do not pass the exam, you may take it again.
Time Commitment: Completing this course should take you a total of 122.25 hours. Note that there are some resources that are indicated as optional. These resources total an additional 24.25 hours. Each unit includes a time advisory that lists the amount of time you are expected to spend on each subunit. These should help you plan your time accordingly. It may be useful to take a look at these time advisories, to determine how much time you have over the next few weeks to complete each unit, and then to set goals for yourself. For example, Unit 1 should take you 13.75 hours. Perhaps you can sit down with your calendar and decide to complete subunits 1.1 and subunit 1.2 (total of 4.75 hours) on Monday and Tuesday nights; subunit 1.3 (about 4.5 hours) on Wednesday and Thursday nights; etc.
Tips/Suggestions: This course uses a complete online textbook, developed by Dr. Philip Stark at the University of California, Berkeley. This textbook is used in Dr. Stark’s Business Statistics course. This textbook includes several interactive examples that you can use to enhance your learning. Do not skip these examples! Learn how they work and try to understand them. Many times, Dr. Stark will use these examples in the online video lectures, so be sure to watch for them and work the examples as he works them in class. You can read what the author of the materials has to say about the best way to use these materials by reviewing the material in the Preface.*
Make sure to also take notes as you navigate through the resources in this course. These notes will be useful to study from as you prepare to take your final exam.
Use of a calculator is also permitted throughout the course and on the final exam. The following online calculator in particular has been authorized for use for proctored exams:
 Online Calculator (HTML).
*Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
This course features a number of Khan Academy™ videos. Khan Academy™ has a library of over 3,000 videos covering a range of topics (math, physics, chemistry, finance, history and more), plus over 300 practice exercises. All Khan Academy™ materials are available for free at www.khanacademy.org.

A version of this course is also available in iTunes U.
Preview the course in your browser or view all our iTunes U courses. 
Learning Outcomes showclose
 explain the importance of statistics to business;
 explain the differences between quantitative and qualitative data, and identify examples of each type of data;
 define and apply the following terms: data sets, mean, median, mode, standard deviation, and variance;
 summarize and interpret data in a tabular format using frequency distributions and visually with histograms;
 define and apply the concept of a probability distribution, and explain the properties of different distributions;
 differentiate between discrete and continuous probability distributions;
 define and apply the concept of a random variable, and differentiate the population from a sample;
 relate the central limit theorem to sample size and normal distribution;
 describe and identify the different sampling methods, including systematic, stratified random, cluster, convenience, panel, and quota sampling, and identify examples of each;
 use a point estimator from a sample to estimate the entire population;
 estimate intervals over which the population parameter could exist using sample data;
 apply hypothesis testing for testing population parameters using one or two samples;
 identify the dependent and independent variables in the linear regression model;
 plot a regression line, and explain how the regression coefficient shapes that line; and
 work with statistical data in a spreadsheet environment.
Course Requirements showclose
√ have access to a computer;
√ have continuous broadband Internet access;
√ have the ability/permission to install plugins or software (e.g. Adobe Reader or Flash);
√ make sure your browser meets the minimum requirements laid out for the online textbook;*
√ have the ability to download and save files and documents to a computer;
√ be competent in the English language.
√ have access to a calculator that includes the ability to do square roots. (A statistical calculator is available as part of the online textbook we are using here.* You may also use the calculator that comes with your operating system, which should have square root capability if you set it to the proper mode.);
√ have read the Saylor Student Handbook; and
√ have completed either MA001, MA003, MA005, or equivalent.
It is suggested, but not mandatory, that you have completed all courses listed in the “The Core Program” section of the Business Administration discipline: BUS103, BUS105, BUS200/ECON101, BUS201/ECON102, BUS202, and BUS203.
*Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
Unit Outline show close

Unit 1: Introduction to Statistical Analysis
Statistics may appear to be a difficult, even scary, subject. You will find, however, that you are already familiar with the fundamentals of statistics from your life experience. For instance, from your experience, you know that the majority of adult males have the same shoe size, which is very close to the average size, and that there are a few adult males on both sides of the average (small and large size). In statistics, this phenomenon shown from the data pattern is said to be a variable that follows a normal distribution.
Unit 1 Time Advisory show close
This unit will provide an introduction to statistical analysis and how it relates to business. For example, you may be interested in learning about the average price of a 50inch digital TV by gathering the price for it from 30 different stores. You take your 30 prices and compute the average price. Given the fact that there are thousands of stores that are selling that particular product, the next question in statistics is: Are you confident enough to say that your computed average is reflective of the real average that would be computing from all the existing prices for that TV sold at all stores?
You are probably familiar with the average of a data set. In this course, we will refer to what most people call the average as the arithmetic mean. The average is actually any single value used to describe the middle of a data set. The most common averages used in statistics are the arithmetic mean, the median, and the mode. Each describes the middle of a dataset in different ways. For example, the median is the numeric value that separates the upper and lower half of a data set. The mean is the sum of all values divided by the number of values. The mode is the most common value within the dataset.
In many instances, the median and the mean are similar, but this introductory unit will also identify many examples where it is not. The distinction between summary statistics is important in business statistics. This unit will define various terms that you may not be familiar with, such as variance and outliers. Understanding this vocabulary will be vital to the successful completion of this course.
Unit 1 Learning Outcomes show close

1.1 Why Do We Need to Study Statistical Analysis as Part of a Business Program?
 Reading: The Saylor Foundation’s “Why Do We Need to Study Statistical Analysis as Part of a Business Program?”
Link: The Saylor Foundation’s “Why Do We Need to Study Statistical Analysis as Part of a Business Program?” (PDF)
Instructions: Read this brief essay for an overview of the different ways that statistics are used in business and why it is essential that decisionmakers have the tools to analyze data as part of their skill set.
Reading this essay should take approximately 15 minutes.
Terms of Use: The resource above is released under a Creative Commons Attribution License. It is attributed to the Saylor Foundation.
 Reading: The Saylor Foundation’s “Why Do We Need to Study Statistical Analysis as Part of a Business Program?”

1.2 Measuring Data
 Reading: University of California, Berkeley: Philip Stark’s SticiGui: “Chapter 3: Statistics”
Link: University of California, Berkeley: Philip Stark’s SticiGui: “Chapter 3: Statistics” (PDF)
Instructions: Read this chapter for an introduction on how to present a summary of data through graphs, tables, and numerical measures such as the average. This will be helpful in terms of analyzing business data in a simple way with the help of the widelyused methods in statistical analysis. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section, and check out the author’s instructions in SticiGui: “How to Use These Materials”. This resource covers the topics outlined in subunits 1.2.1 to 1.2.7.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark’s Statistics 21: “Lecture 2” and “Lecture 3”
Link: YouTube: University of California, Berkeley: Philip Stark’s Statistics 21: “Lecture 2” (YouTube) and “Lecture 3” (YouTube)
Also available in:
iTunes U (Lectures 2 and 3)
Instructions: Watch “Lecture 2” from 1:03:00 to the end, and then watch “Lecture 3” from the beginning until 54:00. These videos are companion lectures to Chapter 3, with the author of the text working through the materials. This resource covers the topics outlined in subunits 1.2.1 to 1.2.7.
Watching these lectures and pausing to take notes should take approximately 1 hour and 30 minutes.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialNo Derivative License. They are attributed to Philip Stark and the University of California, Berkeley. The original versions can be found here and here.
 Reading: University of California, Berkeley: Philip Stark’s SticiGui: “Chapter 3: Statistics”

1.2.1 Types of Variables: Quantitative vs. Qualitative
Note: The material beneath subunit 1.2 covers this topic. For the reading material, focus on the text below the heading “Variable.” Carefully review the box labeled “Examples of Quantitative, Qualitative, and Categorical Variables.” Make sure that you understand the differences between quantitative data, which deals with numeric information, and qualitative data, which measures categories or characteristics.

1.2.2 Sample Data Sets
Note: The material beneath subunit 1.2 covers this topic. Note that a sample is a portion of a population under interest. For example, suppose that you are interested in computing the average age of a manufacturing plant in the United States. Knowing that there are thousands of manufacturing plants, you are more likely to choose for your analysis just a sample, of say 200 manufacturing plants, from the entire population. In the text below the heading “Sample Data Sets,” pay special attention to the data set given in Table 33. This dataset will be used throughout the rest of that chapter.

1.2.3 Frequency Tables
Note: The material beneath subunit 1.2 covers this topic. Review the dataset in Table 33 in the text and the frequency table that follows the table as these tables show you how to put numerical data into a frequency table with the use of class intervals from the data.

1.2.4 Histograms
Note: The material beneath subunit 1.2 covers this topic. Be aware that a histogram is a graph that uses the information from a frequency table.

1.2.5 Skewness and Modes
Note: The material beneath subunit 1.2 covers this topic. As explained in the text below the heading “Skewness and Modes,” a histogram of incomes of individuals or home prices tends to be skewed to the right. Skewness is a measure that shows whether the distribution of a variable is symmetric.

1.2.6 Percentiles and Quartiles
Note: The material beneath subunit 1.2 covers this topic. Note that percentiles are about cutting the histogram into 100 equal pieces. Quartiles are about cutting the histogram into 4 equal parts.

1.2.7 Estimating Percentiles from Histograms
Note: The material beneath subunit 1.2 covers this topic. You should first consider how the 50^{th} percentile is created by just cutting the histogram into two equal parts. Be sure to do the online exercises as shown below the heading “Estimating Percentiles from Histograms.”

1.3 Measures of Spread and Data
 Reading: University of California, Berkeley: Philip Stark’s SticiGui: “Chapter 4: Measures of Location and Spread”
Link: University of California, Berkeley: Philip Stark’s SticiGui: “Chapter 4: Measures of Location and Spread” (PDF)
Instructions: Read this chapter, which will show you all the necessary formulas for computing descriptive statistics for analyzing data from a sample such as the mean, median, mode, variance, range, and standard deviation. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java applets” in the course information section. This resource covers the topics outlined in subunits 1.3.1 to 1.3.7.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark’s Statistics 21: “Lecture 3” and “Lecture 4”
Link: YouTube: University of California, Berkeley: Philip Stark’s Statistics 21: “Lecture 3” (YouTube) and “Lecture 4” (YouTube)
Also available in:
iTunes U (Lectures 3 and 4)
Instructions: Watch “Lecture 3” from 54:00 to the end. Then, watch “Lecture 4” from the beginning until 50:00. These videos are the companion lectures to Chapter 4 with the author of the text working through the materials. This resource covers the topics outlined in subunits 1.3.1 to 1.3.7.
Watching these lectures and pausing to take notes should take approximately 1 hour and 30 minutes.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialNo Derivative License. They are attributed to Philip Stark and the University of California, Berkeley. The original versions can be found here and here.  Web Media: YouTube: Khan Academy’s Statistics: “Variance of a Population,” “Sample Variance,” and “Standard Deviation”
Link: YouTube: Khan Academy’s Statistics: “Variance of a Population” (YouTube), “Sample Variance” (YouTube), and “Standard Deviation” (YouTube)
Instructions: Watch these lectures on variance and standard deviation. The first lecture, “Variance of a Population,” shows the difference between the variance of a population and that of a sample. Secondly, the “Sample Variance” lecture explains how to estimate the variance of a population using the variance of a sample. Finally, the “Standard Deviation” lecture provides a review for what you have learned so far as well as an introduction to standard deviation. These lectures also cover the topics outlined in subunits 1.3.1 through 1.3.4.
Watching these lectures and pausing to take notes should take approximately 1 hour.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialShare Alike License. They are attributed to the Khan Academy.
 Reading: University of California, Berkeley: Philip Stark’s SticiGui: “Chapter 4: Measures of Location and Spread”

1.3.1 Mean
Note: The material beneath subunit 1.3 covers this topic. As explained in Chapter 4, the mean applies to numerical data and not to a categorical variable, which does not have numbers.

1.3.2 Median
Note: The material beneath subunit 1.3 covers this topic. As explained in Chapter 4, the median applies to numerical data and not to a categorical variable, which does not have numbers.

1.3.3 Mode
Note: The material beneath subunit 1.3 covers this topic. As explained in Chapter 4, the mode applies to both numerical and categorical variables as it corresponds to the most frequent value.

1.3.4 Spread and Variability
Note: The material beneath subunit 1.3 covers this topic. Make sure to watch the videos from the Khan Academy to learn how to compute the variance and the standard deviation in detail.

1.3.5 Affine Transformations
Note: The material beneath subunit 1.3 covers this topic. Of concern is the definition of an affine transformation: those variables that are created from other variables through a direct relationship. An example is converting the temperature from Centigrade to Fahrenheit degrees.

1.3.6 Markov’s Inequality
Note: The material beneath subunit 1.3 covers this topic. The best way to learn about this topic is to follow Example 44 in order to see the practicality of this concept.

1.3.7 Chebyshev’s Inequality for Lists
Note: The material beneath subunit 1.3 covers this topic. Be sure to read Examples 45 and 46 as they show you, through examples, how Markov’s inequality and Chebyshev’s inequality differ from each other.
 1.4 Spreadsheet Exercises for Unit 1

1.4.1 Measures of Middle and Spread
 Activity: College of MicronesiaFSM: Dana Lee Ling’s Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4^{th} edition: “Measures of Middle and Spread” and The Saylor Foundation’s “Spreadsheet Activity”
Link: College of MicronesiaFSM: Dana Lee Ling’s Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4^{th} edition: “Measures of Middle and Spread” (PDF) and the Saylor Foundation’s “Spreadsheet Activity” (Open Office) or “Spreadsheet Activity” (Excel)
Instructions: Read Sections 3.1 and 3.2 of the text. The supporting spreadsheet files (in both Excel and Open Office formats) include a tab titled “Starter File,” which contains everything you need to get started on the activity. Once you have worked through the activity, you can click on the “Solution File” tab to see how your finished spreadsheet should look.
Reading and completing this activity should take approximately 45 minutes.
Terms of Use: This work is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Dana Lee Ling, and the original version can be found here.
 Activity: College of MicronesiaFSM: Dana Lee Ling’s Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4^{th} edition: “Measures of Middle and Spread” and The Saylor Foundation’s “Spreadsheet Activity”

1.4.2 Histograms and Frequency Tables
 Activity: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4^{th} edition: “Visualizing Data” and The Saylor Foundation’s “Spreadsheet Activity”
Links: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4^{th} edition: “Visualizing Data” (PDF) and The Saylor Foundation’s “Spreadsheet Activity” (Open Office) or “Spreadsheet Activity” (Excel)
Instructions: Read Chapter 2, then go to the endnote on creating histograms, and walk through the instructions given. Note that the instructions given in the text are for version 2.x of OpenOffice. If you have 3.x, some steps are slightly different; you may need to consult the help documents. The supporting spreadsheet files (links above to both Excel and Open Office versions) include a tab entitled “Starter File,” which contains everything you need to get started on the activity. Once you have worked through the activity, you can click on the “Solution File” tab to see how your finished spreadsheet should look.
Reading and completing this activity should take approximately 45 minutes.
Terms of Use: This work is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Dana Lee Ling and the original version can be found here. Please respect the copyright and terms of use.
 Activity: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4^{th} edition: “Visualizing Data” and The Saylor Foundation’s “Spreadsheet Activity”

1.5 Assessments for Unit 1
 Assessment: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Descriptive Statistics: Homework”
Link: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Descriptive Statistics: Homework” (PDF)
Instructions: For this assessment, please do the following problems: 3, 5, 17, 24–30. When you are finished, you may check your work against the “Descriptive Statistics: Homework Answer Key” (PDF).
Completing this assessment should take approximately 3 hours.
Terms of Use: This work is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Susan Dean and Barbara Illowsky, and the original version can be found here.  Assessment: The Saylor Foundation’s “BUS204 Unit 1 Quiz”
Link: The Saylor Foundation’s “BUS204 Unit 1 Quiz” (HTML)
Instructions: Complete this assessment to gauge your understanding of the topics covered in this unit. The correct answers will be displayed when you click the “Submit” button.
Completing the quiz, and reviewing if necessary, should take approximately 1 hour.
 Assessment: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Descriptive Statistics: Homework”

Unit 2: Counting, Probability, and Probability Distributions
What is the likelihood that an event will occur? What are the chances that a given student will receive a 6069 score? By studying distributions of data, you can determine the probability that a certain event will occur. By looking at the distribution of grades in a class, you can identify the probability that a student will receive between a 60 and 69. The applications of probability in business are infinite; from predicting profits to determining the chances that a business model will affect regulation, businesses use probability to make decisions frequently.
Unit 2 Time Advisory show close
Before you can focus on probability, you must first learn how to count. What's that you say? You already know how to count? Maybe – but in this unit you will learn techniques for counting the different ways that multiple events can occur together. These are called “Combinations” and “Permutations,” and they are a fundamental concept needed to fully understand probability.
Unit 2 Learning Outcomes show close

2.1 Counting
 Reading: University of California, Berkeley: Philip Stark’s SticiGui: “Chapter 12: Counting”
Link: University of California, Berkeley: Philip Stark’s SticiGui: “Chapter 12: Counting” (HTML)
Instructions: Read Chapter 12 to study several of the most common formulas in probability. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above. This resource covers the topics outlined in Subunit 2.1.1 to Subunit 2.1.4.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 8”
Link: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 8” (YouTube)
Also available in:
iTunes U (Lecture 8)
Instructions: Watch “Lecture 8,” which is the companion to Chapter 12 with the author of the text working through the materials. This resource covers topics outlined in subunits 2.1.1 to 2.1.4.
Viewing this lecture and pausing to take notes should take approximately 2 hours.
Terms of Use: This video is licensed under a Creative Commons AttributionNoncommercialNo Derivative License. It is attributed to Philip Stark and the University of California. The original version can be found here.
 Reading: University of California, Berkeley: Philip Stark’s SticiGui: “Chapter 12: Counting”

2.1.1 The Fundamental Rule of Counting
Note: The reading and lecture assigned below subunit 2.1 cover this topic. The tossing of a coin is one of the classical examples taught in a probability course. Make sure you understand the example given in the text under the section titled “The Fundamental Rule of Counting.”

2.1.2 Permutations
Note: The reading and lecture assigned below subunit 2.1 cover this topic. Make sure you read Example 122 as it explains how to use the factorial sign (!) such as 4! = 4x3x2x1 = 24.

2.1.3 Combinations
Note: The reading and lecture assigned below subunit 2.1 cover this topic. Know the difference between a permutation, when the order of possible choices matters, and a combination, when the order does not matter. Of importance is the formula for computing combinations, make sure you know how to use it as explained in the text under the section titled “Combinations (Unordered Choices).”

2.1.4 Card Hands
Note: The reading and lecture assigned below subunit 2.1 cover this topic. Make sure to read Examples 124 through 126 and the table above Example 124 in order to understand the different combinations of cards from a set of 52 typical cards.

2.2 Theories of Probability
 Reading: University of California, Berkeley: Philip Stark’s SticiGui: “Chapter 13: The Meaning of Probability: Theories of Probability”
Link: University of California, Berkeley: Philip Stark’s SticiGui: “Chapter 13: The Meaning of Probability: Theories of Probability” (HTML)
Instructions: Read Chapter 13 for an explanation of the most common theories and formulas in probability. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above. This resource covers the topics outlined in subunits 2.2.1 to 2.2.4.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley, Philip Stark's Statistics 21: “Lecture 9”
Link: YouTube: University of California, Berkeley, Philip Stark's Statistics 21: “Lecture 9” (YouTube)
Also available in:
iTunes U (Lecture 10)
Instructions: Watch “Lecture 9,” which is the companion to Chapter 13 with the author of the text working through the materials. Please note that this is labeled as “Lecture 10” on iTunesU. This resource covers the topics outlined in subunits 2.2.1 to 2.2.4.
Viewing this lecture and pausing to take notes should take approximately 2 hours.
Terms of Use: This video is licensed under a Creative Commons AttributionNoncommercialNo Derivative License. It is attributed to Philip Stark and the University of California. The original version can be found here.  Reading: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4th edition: “05 Probability”
Links: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4th edition: “05 Probability” (PDF)
Also Available in:
HTML
Instructions: Read Section 05 to learn about the intuition behind ways to compute probabilities.
Reading this section should take approximately 15 minutes.
Terms of Use: The resource above is released under a Creative Commons Attribution License. It is attributed to Dana Lee Ling, and the original version can be found here.
 Reading: University of California, Berkeley: Philip Stark’s SticiGui: “Chapter 13: The Meaning of Probability: Theories of Probability”

2.2.1 Random Events
Note: The reading and lecture assigned below subunit 2.2 cover this topic. This concept will appear throughout the course; make sure you understand that a random event is something that happens by chance alone.

2.2.2 Equally Likely Outcomes
Note: The reading and lecture assigned below subunit 2.2 cover this topic. Make sure you know how to apply the concept by using the formula 100%/n, or 1/n, to compute the expected probability of an outcome with n possible outcomes.

2.2.3 Frequency Theory
Note: The reading and lecture assigned below subunit 2.2 cover this topic. Make sure to know the difference between frequency and subjective theory in probability.

2.2.4 Subjective Theory
Note: The reading and lecture assigned below subunit 2.2 cover this topic. Make sure to know the difference between frequency and subjective theory in probability.

2.3 Set Theory
 Web Media: YouTube: Khan Academy’s Statistics: “Probability with Playing Cards and Venn Diagrams” and “Addition Rule for Probability”
YouTube: Khan Academy’s Statistics: “Probability with Playing Cards and Venn Diagrams” (YouTube) and “Addition Rule for Probability” (YouTube)
Instructions: Please view these lectures, which provide demonstrations on how to use Venn Diagrams to understand probability. These videos provide a complementary explanation to the content found in Philip Stark’s “Lecture 11.”
Watching these lectures and pausing to take notes should take approximately 45 minutes.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialShare Alike License. They are attributed to the Khan Academy.  Lecture: YouTube: University of California, Berkeley: Philip Stark's “Lecture 11”
Links: YouTube: University of California, Berkeley: Philip Stark's “Lecture 11” (YouTube)
Instructions: Watch “Lecture 11.”
Viewing this lecture and pausing to take notes should take approximately 2 hours.
Terms of Use: The video above is licensed under a Creative Commons AttributionNoncommercialNo Derivative License. It is attributed to Philip Stark and the University of California.  Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 14: Set Theory: The Language of Probability”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 14: Set Theory: The Language of Probability” (HTML or Java)
Instructions: Read Chapter 14 to study the symbols used in set theory such as for denoting the union of two sets A and B to be A∩B. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 11”
Links: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 11” (YouTube)
Also available in:
iTunes U (Lecture 11)
Instructions: Watch “Lecture 11,” which is the companion to Chapter 14 with the author of the text working through the materials. Please note that this video is labeled as “Lecture 14” on iTunesU.
Viewing this lecture and pausing to take notes should take approximately 2 hours.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialNo Derivative License. They are attributed to Philip Stark and the University of California. The original versions can be found here.  Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 15: Categorical Logic”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 15: Categorical Logic” (HTML)
Instructions: Chapter 15 is an optional reading as it shows you advanced rules when dealing with sets. Read through this chapter if you would like to experience the entire course as it was presented at University of California, Berkeley. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 16: Propositional Logic”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 16: Propositional Logic” (HTML)
Instructions: Chapter 16 is an optional reading as it shows you advanced rules when dealing with sets. Read through this chapter if you would like to experience the entire course as it was presented at University of California, Berkeley. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Web Media: YouTube: Khan Academy’s Statistics: “Probability with Playing Cards and Venn Diagrams” and “Addition Rule for Probability”

2.4 Probability Fundamentals
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 17: Probability, Axioms and Fundaments”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 17: Probability, Axioms and Fundaments” (HTML or Java)
Instructions: Read Chapter 17 to learn the basic rules in probability such as how to find the probability of two dependent events. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above. This resource covers the topics outlined in subunits 2.4.1 to 2.4.5.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 12,” “Lecture 13,” and “Lecture 14”
Links: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 12” (YouTube), “Lecture 13” (YouTube), and “Lecture 14” (YouTube)
Also available in:
iTunes U (Lectures 15, 16, and 17)
Instructions: Watch “Lecture 12” and “Lecture 13” in their entirety, and “Lecture 14” up to 56:00. These video lectures complement Chapter 17 with the author of the text working through the materials. Please note that these are labeled as “Lecture 15,” “Lecture 16,” and “Lecture 17” in iTunesU. These resources cover the topics outlined in subunits 2.4.1 to 2.4.5.
Watching these lectures and pausing to take notes should take approximately 4 hours and 30 minutes.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialNo Derivative License. They are attributed to Philip Stark and the University of California, Berkeley. The original versions can be found here, here, and here.
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 17: Probability, Axioms and Fundaments”

2.4.1 The Axioms of Probability
Note: The reading and lecture assigned below subunit 2.4 cover this topic. In probability, the symbol ∩ is used to denote “and” as in Probability of A and B = P(A ∩ B). The inverted symbol is explained in the text under the section labeled “The Axioms of Probability.”

2.4.2 Conditioning
Note: The reading and lecture assigned below subunit 2.4 cover this topic. Make sure you know how to use the formula for computing the conditional probability of an outcome as explained in the text under the section labeled “Conditioning.”

2.4.3 The Multiplication Rule
Note: The reading and lecture assigned below subunit 2.4 cover this topic. You can follow an example of the multiplication rule in Example 178.

2.4.4 Bayes' Rule
Note: The reading and lecture assigned below subunit 2.4 cover this topic. You can follow an example of the Bayes’ Rule formula in Example 179.

2.4.5 Independence
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 18: The Let's Make a Deal (Monty Hall) Problem”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 18: The Let's Make a Deal (Monty Hall) Problem” (HTML)
Instructions: Chapter 18 is an optional reading as it gives you an example of applying probability theory. Read through this chapter if you would like to experience the entire course as it was presented at University of California, Berkeley. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley, Philip Stark's Statistics 21: “Lecture 14”
Link: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 14” (YouTube)
Also available in:
iTunes U (Lecture 17)
Instructions: This is an optional video. Watch “Lecture 14” from 56:00 to 1:25:13. This video is the companion to Chapter 18, with the author of the text working through the materials. Please note that this is labeled “Lecture 17” on iTunesU.
Viewing this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNoncommercialNo Derivative License. It is attributed to Philip Stark and the University of California. The original version can be found here.
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 18: The Let's Make a Deal (Monty Hall) Problem”

2.5 Probability Distributions and the Binomial Distribution
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 19: Probability Meets Data”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 19: Probability Meets Data” (HTML and Java)
Instructions: Read Chapter 19, which unites probability with samples and explains the nature of a probability distribution. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above.
Reading this chapter should take approximately 3 hours and 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 15”
Link: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 15” (YouTube)
Also available in:
iTunes U (Lecture 18)
Instructions: Watch “Lecture 15,” which is the companion to Chapter 19, with the author of the text working through the materials. Please note that this video is labeled “Lecture 18” on iTunesU.
Viewing this lecture and pausing to take notes should take approximately 2 hours.
Terms of Use: This video is licensed under a Creative Commons AttributionNoncommercialNo Derivative License. It is attributed to Philip Stark and the University of California. The original version can be found here.  Web Media: YouTube: Khan Academy's Statistics “Introduction to Random Variables” and “Probability Density Functions”
Links: YouTube: Khan Academy's Statistics “Introduction to Random Variables” (YouTube) and “Probability Density Functions” (YouTube)
Instructions: View “Introduction to Random Variables,” which introduces you to random variables and probability distribution functions. Also, view “Probability Density Functions” to get an idea about probability distributions.
Watching these lectures and pausing to take notes should take approximately 45 minutes.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialShare Alike License. They are attributed to the Khan Academy.  Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 20: Random Variables and Discrete Distributions”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 20: Random Variables and Discrete Distributions” (HTML or Java)
Instructions: This is an optional reading. Chapter 20 will provide information on random variables and discrete distributions. Read through this chapter if you would like to experience the entire course as it was presented at University of California, Berkeley. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 16”
Link: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 16” (YouTube)
Also available in:
iTunes U (Lecture 19)
Instructions: This is an optional video. Watch “Lecture 16,” which is the companion to Chapter 20, with the author of the text working through the materials. Please note that this video is labeled “Lecture 19” on iTunesU.
Viewing this lecture and pausing to take notes should take approximately 2 hours.
Terms of Use: This video is licensed under a Creative Commons AttributionNoncommercialNo Derivative License. It is attributed to Philip Stark and the University of California. The original version can be found here.
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 19: Probability Meets Data”

2.6 The Long Run and Expected Value
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 21: The Long Run and Expected Value”
Link: University of California, Berkeley: Philip Stark's <em>SticiGui</em>: “Chapter 21: The Long Run and Expected Value” (HTML or Java)
Instructions: Read Chapter 21, which will give you several theorems when dealing with sample data such as the Law of Large Numbers. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above. This resource covers the topics outlined in subunits 2.6.1 to 2.6.7.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 17”
Link: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 17” (YouTube)
Also available in:
iTunes U (Lecture 20)
Instructions: Watch “Lecture 17,” which is the companion to Chapter 21, with the author of the text working through the materials. Please note that this video is labeled “Lecture 20” on iTunesU. This resource covers the topics outlined in subunits 2.6.1 to 2.6.7.
Viewing this lecture and pausing to take notes should take approximately 2 hours.
Terms of Use: This video is licensed under a Creative Commons AttributionNoncommercialNo Derivative License. It is attributed to Philip Stark and the University of California. The original version can be found here.
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 21: The Long Run and Expected Value”

2.6.1 The Law of Large Numbers
Note: The reading and lecture assigned below subunit 2.6 cover this topic. The Law of Large Numbers implies repeated sampling with replacement, meaning that the events considered are assumed to be independent from each other.

2.6.2 Expected Value of a Random Variable
Note: The reading and lecture assigned below subunit 2.6 cover this topic. The expected value is another name for the “mean” (or average) when outcomes have probabilities attached to them. Make sure you know how to compute the expected value as shown for the data from Table 211.

2.6.3 Expected Value of a Sample Sum
Note: The reading and lecture assigned below subunit 2.6 cover this topic. Make sure you know how to apply the formula as given in the text under the section titled “Expected Value of a Sample Sum.”

2.6.4 Properties of the Expected Value
Note: The reading and lecture assigned below subunit 2.6 cover this topic. Make sure you know how to apply the formulas as given in the text under the section titled “Properties of the Expected Value.”

2.6.5 Expected Value of the Sample Mean and Sample Percentage
Note: The reading and lecture assigned below subunit 2.6 cover this topic. Make sure you know how to apply the formulas as given in the text under the section titled “Expected Value of the Sample Mean and Sample Percentage.”

2.6.6 Gambling and Fair Bets
Note: The reading and lecture assigned below subunit 2.6 cover this topic. Make sure to read Example 213.

2.6.7 Expected Values of Some Common Distributions
Note: The reading and lecture assigned below subunit 2.6 cover this topic. Note that the p used in the formulas stands for the probability of a successful outcome. For example, suppose that you are analyzing whether or not customers will buy your product and have these two possible outcomes: yes = successful outcome = the customer will buy and no = not successful = the customer will not buy. If the probability that someone will buy is 0.45; therefore, p = 0.45, and (1p) = 0.55, which is the probability that someone will not buy.
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 22: Standard Error”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 22: Standard Error” (HTML or Java)
Instructions: This is an optional reading. Read Chapter 22 to learn about standard error. Read through this chapter if you would like to experience the entire course as it was presented at University of California, Berkeley. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 18”
Link: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 18” (YouTube)
Also available in:
iTunes U (Lecture 21)
Instructions: This is an optional video. Watch “Lecture 18,” which is the companion to Chapter 22 with the author of the text working through the materials. Please note that this is labeled “Lecture 21” on iTunesU.
Viewing this lecture and pausing to take notes should take approximately 2 hours.
Terms of Use: This video is licensed under a Creative Commons AttributionNoncommercialNo Derivative License. It is attributed to Philip Stark and the University of California. The original version can be found here.
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 22: Standard Error”

2.7 Assessments for Unit 2
 Assessment: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Probability Topics: Homework”
Link: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Probability Topics: Homework” (PDF)
Also Available in:
HTML
Instructions: For this assessment, please select ten of the problems from this set and solve them. Note that not all problems have solutions attached, so please limit your choices to those that have solutions. To see a problem solution, go to the HTML version and click on the “Show Solution” link below the problem. You may download this homework as a DOC by clicking the links to the right in the HTML version.
Completing this assessment should take approximately 2 hours and 30 minutes.
Terms of Use: This work is licensed under a Creative Commons Attribution 2.0 Generic License. It is attributed to Susan Dean and Barbara Illowsky. The original version can be found here. Please respect the copyright and terms of use.  Assessment: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Discrete Random Variables: Homework”
Link: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Discrete Random Variables: Homework” (PDF)
Also Available in:
HTML
Instructions: For this assessment, please do problems 1, 3, 5, 7, 11, 15, 17, and 23. To see a problem solution, go to the HTML version and click on the “Show Solution” link below the problem. You may download this homework as a DOC by clicking the links to the right in the HTML version.
Completing this assessment should take approximately 1 hour and 30 minutes.
Terms of Use: This work is licensed under a Creative Commons Attribution 2.0 Generic License. It is attributed to Susan Dean and Barbara Illowsky. The original version can be found here. Please respect the copyright and terms of use.  Assessment: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Practice 2: Binomial Distribution”
Link: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Practice 2: Binomial Distribution” (PDF)
Also Available in:
HTML
Instructions: Complete all nine problems for this assessment. Each problem has a solution that you can check your work against by going to the HTML version and clicking “Show Solution.” You may also download this homework as a DOC by clicking on the links to the right in the HTML version.
Completing this assessment should take approximately 1 hour.
Terms of Use: This work is licensed under a Creative Commons Attribution 2.0 Generic License. It is attributed to Susan Dean and Barbara Illowsky. The original version can be found here. Please respect the copyright and terms of use.  Assessment: The Saylor Foundation’s “BUS204 Unit 2 Quiz”
Link: The Saylor Foundation’s “BUS204 Unit 2 Quiz” (HTML)
Instructions: Complete this assessment to gauge your understanding of the topics covered in this unit. The correct answers will be displayed when you click the “Submit” button.
Completing the quiz, and reviewing if necessary, should take approximately 2 hours.
 Assessment: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Probability Topics: Homework”

Unit 3: The Normal Distribution
A distribution is a line graph representation of the probability that an event will occur. It is similar to a histogram, but in a distribution, the user does not determine the grouping; instead, data is grouped according to the likelihood that it will occur within the dataset. Distributions also allow for analysis of a specific event, whereas a histogram requires events be grouped.
Unit 3 Time Advisory show close
An important type of this distribution is the “normal” distribution. The normal distributionis used to approximate realworld occurrences. If you can make certain assumptions about the occurrence of an event, then you can use the normal distribution to find out the probabilities of that event occurring. Many of the events that are important to business can be approximated using the normal distribution.
Unit 3 Learning Outcomes show close

3.1 The Normal Distribution
 Web Media: YouTube: Khan Academy’s Statistics “Normal Distribution Problems: Qualitative Sense of Normal Distributions”
Link: YouTube: Khan Academy’s Statistics “Normal Distribution Problems: Qualitative Sense of Normal Distributions” (YouTube)
Instructions: View the video lecture, which gives an intuitive explanation of variables in real life that follow a normal distribution.
Viewing this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNoncommercialShare Alike License. It is attributed to the Khan Academy.  Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 23: The Normal Curve, the Central Limit Theorem, and Markov's and Chebyshev's Inequalities for Random Variables”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 23: The Normal Curve, the Central Limit Theorem, and Markov's and Chebyshev's Inequalities for Random Variables” (HTML or Java)
Instructions: Read Chapter 23 for an explanation of one of the most important probability distributions used in statistics: The Normal Distribution. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above. This resource covers the topics outlined in subunits 3.1.1 to 3.1.3.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 19”
Link: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 19” (YouTube)
Also available in:
iTunes U (Lecture 22)
Instructions: Watch “Lecture 19” up to 1:19:00. This video is the companion to Chapter 23, with the author of the text working through the materials. Please note that this is labeled “Lecture 22” on iTunesU. This resource covers the topics outlined in subunits 3.1.1 to 3.1.3.
Viewing this lecture and pausing to take notes should take approximately 2 hours.
Terms of Use: This video is licensed under a Creative Commons AttributionNoncommercialNo Derivative License. It is attributed to Philip Stark and the University of California. The original version can be found here.  Reading: U.S. Department of Commerce: NIST/SEMATECH eHandbook of Statistical Methods: “Cumulative Distribution Function of the Standard Normal Distribution”
Link: U.S. Department of Commerce: NIST/SEMATECH eHandbook of Statistical Methods: “Cumulative Distribution Function of the Standard Normal Distribution” (PDF)
Also Available in:
HTML
Instructions: Read “Cumulative Distribution Function of the Standard Normal Distribution” to learn how the normal distribution is graphed and how probabilities under the curve are computed from location X to Y on the curve using the table with probabilities for the normal distribution.
Reading this article should take approximately 30 minutes.
Terms of Use: The resource above is in the public domain.  Reading: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4th edition: “07 Introduction to the Normal Distribution”
Links: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4th edition: “07 Introduction to the Normal Distribution” (PDF)
Also Available in:
HTML
Instructions: Read Section 07 as it shows how the normal distribution is graphed and how probabilities under the curve are computed using Excel.
Reading this section should take approximately 1 hour.
Terms of Use: The resource above is released under a Creative Commons Attribution License. It is attributed to Dana Lee Ling, and the original version can be found here.  Web Media: Khan Academy's “Normal Distribution Problems: zscore” and “More Empirical Rule and Zscore Practice”
Links: Khan Academy's “Normal Distribution Problems: zscore” (YouTube) and “More Empirical Rule and Zscore Practice” (YouTube)
Instructions: Watch both lectures, and also try to work through the problems in each video. The first video “Normal Distribution Problems” will walk you through the process of finding the zscores, an important part of understanding this topic. The second video “More Empirical Rule and Zscore Practice” will walk you through the process of solving problems using the standard normal distribution, an important part of understanding this topic.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialShare Alike License. They are attributed to the Khan Academy.
 Web Media: YouTube: Khan Academy’s Statistics “Normal Distribution Problems: Qualitative Sense of Normal Distributions”

3.1.1 The Normal Curve
Note: The reading and lectures assigned below subunit 3.1 cover this topic. Make sure you know the properties of the Normal curve and how to get the probabilities using the Normal probability table.

3.1.2 The Central Limit Theorem
Note: The reading and lectures assigned below subunit 3.1 cover this topic. The Central Limit Theorem states that as nincreases this higher nleads any variable to follow a normal distribution.

3.1.3 Markov's and Chebyshev's Inequalities for Random Variables
Note: The reading and lectures assigned below subunit 3.1 cover this topic. Make sure you know the difference between these two concepts.

3.2 Spreadsheet Activity for Unit 3
 Activity: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4^{th} edition: “7.4 From an x Value to a Probability p and 7.5 Area to X” and The Saylor Foundation’s “Spreadsheet Activity”
Links: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4^{th} edition: “7.4 From an x Value to a Probability p and 7.5 Area to X” (PDF) and The Saylor Foundation’s “Spreadsheet Activity” (Open Office) or “Spreadsheet Activity” (Excel)
Also Available in:
HTML (7.4 From an x Value to a Probability p and 7.5 Area to X)
Instructions: Read through Sections 7.4 and 7.5 of the textbook. For this activity, work through the use of a spreadsheet to solve normal distribution probability problems. Be sure you understand how to use the “normdist” and “norminv” functions. The supporting spreadsheet files (links above to both Excel and Open Office versions) include a tab entitled “Starter File,” which contains everything you need to get started on the activity. Once you have worked through the activity, you can click on the “Solution File” tab to see how your finished spreadsheet should look.
Reading and completing this activity should take approximately 1 hour.
Terms of Use: This work is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Dana Lee Ling. The original version can be found here.
 Activity: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4^{th} edition: “7.4 From an x Value to a Probability p and 7.5 Area to X” and The Saylor Foundation’s “Spreadsheet Activity”

3.3 Assessments for Unit 3
 Assessment: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Practice: The Normal Distribution”
Link: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Practice: The Normal Distribution” (PDF)
Also Available in:
HTML
Instructions: Follow the instructions on the PDF to complete all five exercises. Each exercise has a solution you can check your work against by going to the HTML version and clicking “Show Solution”. You may also download this homework as a DOC by clicking on the link to the right in the HTML version.
Completing this assessment should take approximately 3 hours.
Terms of Use: This work is licensed under a Creative Commons Attribution 2.0 Generic License. It is attributed to Susan Dean and Barbara Illowsky. The original version can be found here. Please respect the copyright and terms of use.  Assessment: The Saylor Foundation’s “BUS204 Unit 3 Quiz”
Link: The Saylor Foundation’s “BUS204 Unit 3 Quiz” (HTML)
Instructions: Complete this assessment to gauge your understanding of the topics covered in this unit. The correct answers will be displayed when you click the “Submit” button.
Completing the quiz, and reviewing if necessary, should take approximately 2 hours.
 Assessment: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Practice: The Normal Distribution”

Unit 4: Sampling and Sampling Distributions
While you may not become a professional data gatherer, it is likely that you will need to compile data on a regular basis. When gathering data, you will not always have the luxury of collecting all available data. For example, economists cannot measure the entire unemployment of the population, so they must take a random sample instead. Likewise, in a manufacturing facility, quality control managers do not have the resources to test every product that comes off the line; it is simply not feasible. Instead, they take samples at various points during the production process to test the quality of the products the firm produces.
Unit 4 Time Advisory show close
There are a number of methods employed in sampling data. It is important that the sampling method fits the application. For example, marketing managers may wish to test a product on various groups of people. They may define these groups by age, race, geography, income, or any other factors. They then divide the population into these groups and take samples from each group in a process known as cluster sampling. If marketers do not properly divide the population, they may end up marketing to the wrong demographic and achieving poor sales.
Unit 4 Learning Outcomes show close

4.1 Sampling and Sampling Distributions
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 24: Sampling”
Link: University of California, Berkeley: Philip Stark's SticiGui’s “Chapter 24: Sampling” (HTML)
Instructions: Read Chapter 24 for an explanation of what sampling means in statistics and its possible biases when collecting data for a sample. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above. This resource covers the topics outlined in subunits 4.1.1 to 4.1.6.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 19” and “Lecture 20”
Links: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 19” and “Lecture 20” (YouTube)
Also available in:
iTunes U (Lectures 22 and 23)
Instructions: Watch “Lecture 19” from 1:19:00 to the end, and then watch “Lecture 20.” These video lectures are companions to Chapter 24, with the author of the text working through the materials. Please note that these are labeled “Lecture 22” and “Lecture 23,” respectively, on iTunesU. These resources cover the topics outlined in subunits 4.1.1 to 4.1.6.
Watching these lectures and pausing to take notes should take approximately 2 hours.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialNo Derivative License. They are attributed to Philip Stark and the University of California. The original versions can be found here and here.  Web Media: YouTube: Khan Academy’s Statistics “Sampling Distribution of the Sample Mean” and “Sampling Distribution of the Sample Mean 2”
Links: YouTube: Khan Academy’s Statistics “Sampling Distribution of the Sample Mean” (YouTube) and “Sampling Distribution of the Sample Mean 2” (YouTube)
Instructions: Please view both videos, which explain the nature of the sampling distribution and how it changes as the sample size changes.
Watching these lectures and pausing to take notes should take approximately 45 minutes.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 24: Sampling”

4.1.1 Parameters and Statistics
Note: The reading and lectures assigned below subunit 4.1 cover this topic. A parameter is a characteristic (such as the average) of a population under interest, whereas a statistic is a characteristic of a sample.

4.1.2 Why Sample?
Note: The reading and lectures assigned below subunit 4.1 cover this topic. Taking a sample that is representative of a population under interest is what the field of statistics is all about. It is almost impractical in real life to analyze all the observations belonging to a population.

4.1.3 Sample Surveys
Note: The reading and lectures assigned below subunit 4.1 cover this topic. Be aware that the rule in statistics is to take a sample that is representative of the entire population, meaning that sampling bias (such as taking a survey of only our friends in order to understand consumer behavior) should be avoided.

4.1.4 Bias in Surveys
Note: The reading and lectures assigned below subunit 4.1 cover this topic. Focus on how a researcher can introduce bias into a survey.

4.1.5 Sampling Designs
Note: The reading and lectures assigned below subunit 4.1 cover this topic. Focus on the different ways to draw observations for a sample as shown in the text under the section titled “Ways to Draw Samples.”

4.1.6 Sampling Distributions
Note: The reading and lectures assigned below subunit 4.1 cover this topic. Be sure to view the Khan Academy’s video for this section as it explains the meaning of distributions that apply to sample data.

4.2 Assessments for Unit 4
 Assessment: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Sampling and Data: Homework”
Link: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Sampling and Data: Homework” (PDF)
Also Available in:
HTML
Instructions: For this assessment, please work on problems 1, 3, 5, and 1929. To see a problem solution, go to the HTML version and click on the “Show Solution” link below the problem. You may also download this homework as a DOC by clicking on the links to the right in the HTML version.
Completing this assessment should take approximately 1 hour.
Terms of Use: This work is licensed under a Creative Commons Attribution 2.0 Generic License. It is attributed to Susan Dean and Barbara Illowsky. The original version can be found here. Please respect the copyright and terms of use.  Assessment: The Saylor Foundation’s “BUS204 Unit 4 Quiz”
Link: The Saylor Foundation’s “BUS204 Unit 4 Quiz” (HTML)
Instructions: Complete this assessment to gauge your understanding of the topics covered in this unit. The correct answers will be displayed when you click the “Submit” button.
Completing the quiz, and reviewing if necessary, should take approximately 1 hour and 30 minutes.
 Assessment: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Sampling and Data: Homework”

Unit 5: Estimation and Hypothesis Testing
Estimation is the process of making predictions based on the best available information. Businesses employ estimation in order to help managers make decisions regarding the future. For example, if the CFO estimates profits will be lower next year, the CEO will consider costcutting measures to make up for the loss. Normally, companies do not want to pursue aggressive costcutting because it usually comes in the form of layoffs, which are bad for employee morale.
Unit 5 Time Advisory show close
In order to make accurate estimates, companies use hypothesis testing. For example, assume the CFO thinks profits will be below 5% of revenue next year. His null hypothesis is that profits will be 5% or greater next year. The alternative hypothesis is that profits will not be 5% or greater next year. This seems counterintuitive but statistics proposes that a hypothesis cannot be proven true; it can only be rejected, or shown to be not true. Through the hypothesis testing process, the CFO will either reject or accept the null hypothesis. Hypothesis tests are always framed in this manner because, with imperfect information, nothing can be proven.
Note: The best nonbusiness analogy to hypothesis testing comes from the courtroom. In the United States, a defendant is presumed innocent until proven guilty. The null hypothesis in this scenario is innocent or not guilty. The alternative hypothesis is guilty. In order to find the defendant guilty, the jury must be offered enough evidence that suggests the defendant is guilty beyond a reasonable doubt. If the members of the jury make that decision, then they reject the null hypothesis. If the jury members decide they do not have enough evidence to make that judgment, then they must find the defendant not guilty. Notice not guilty does not mean the jury claims the defendant is innocent. The decision simply means the members of the jury do not have enough information to find the person guilty, so they err on the side of caution and fail to reject the null hypothesis. As an aside, in this example, beyond a reasonable doubt is analogous to the level of significance, which you will learn is crucial to hypothesis testing.
Unit 5 Learning Outcomes show close

5.1 Estimation
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 25: Estimating Parameters from Simple Random Samples”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 25: Estimating Parameters from Simple Random Samples” (HTML and Java)
Instructions: Read Chapter 25 to learn how to generalize for an entire population given sample data only and its statistics. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above. This resource covers the topics outlined in subunits 5.1.1 and 5.1.2.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 21”
Link: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 21” (YouTube)
Also available in:
iTunes U (Lecture 24)
Instructions: Watch “Lecture 21” up to 1:05. This video is the companion to Chapter 25, with the author of the text working through the materials. Please note that this is labeled “Lecture 24” on iTunesU. This resource covers the topics outlined in subunits 5.1.1 and 5.1.2.
Viewing this lecture and pausing to take notes should take approximately 1 hour 30 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNoncommercialNo Derivative License. It is attributed to Philip Stark and the University of California. The original version can be found here.
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 25: Estimating Parameters from Simple Random Samples”

5.1.1 Estimating Means and Percentages
Note: The reading and lecture assigned below subunit 5.1 cover this topic. This section is about knowing how to use the mean from the sample data to estimate a range for the real population mean. In terms of estimating percentages, the percentage of a given characteristic from the sample data is used to compute a range for the real population percentage.

5.1.2 The Sample Standard Deviation and Variance
Note: The reading and lecture assigned below subunit 5.1 cover this topic. Recall that the standard deviation and variance were introduced in subunit 1.3 “Measures of Spread and Data.”

5.2 Confidence Intervals
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 26: Confidence Intervals”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 26: Confidence Intervals” (HTML or Java)
Instructions: Read Chapter 26 to learn how to compute confidence intervals for the real population mean with the use of the “ttable” with probabilities. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 21” and “Lecture 22”
Links: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 21” (YouTube) and “Lecture 22” (YouTube)
Also available in:
iTunes U (Lectures 24 and 25)
Instructions: Watch “Lecture 21” from 1:05 to the end and “Lecture 22” up to 1:12:00. These video lectures are companions to Chapter 26, with the author of the text working through the materials. Please note that these are labeled “Lecture 24” and “Lecture 25” on iTunesU.
Watching these lectures and pausing to take notes should take approximately 2 hours.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialNo Derivative License. They are attributed to Philip Stark and the University of California. The original versions can be found here and here.  Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 30: Approximate Hypothesis Tests: the z Test and the t Test”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 30: Approximate Hypothesis Tests: the z Test and the t Test” (HTML and Java)
Instructions: Read Chapter 30, which will show you the difference in hypothesis testing between the z and t tests. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4th edition: “09 Confidence Intervals”
Links: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4th edition: “09 Confidence Intervals” (PDF)
Also Available in:
HTML
Instructions: Read Section 09 to learn how to compute confidence intervals for finding a range for the real population parameter using statistics from the sample data.
Reading this section should take approximately 1 hour.
Terms of Use: The resource above is released under a Creative Commons Attribution License. It is attributed to Dana Lee Ling, and the original version can be found here.
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 26: Confidence Intervals”

5.3 Hypothesis Testing: tTests
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 27: Hypothesis Testing – Does Chance Explain the Results?”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 27: Hypothesis Testing – Does Chance Explain the Results?” (HTML or Java)
Instructions: Read Chapter 27, which it introduces you to the concepts in hypothesis testing to test values of a true population parameter given sample statistics or to test and compare the statistics from two or more similar samples. Pay special attention to the terms: null hypothesis, alternative hypothesis, significance level, power of a test, and pvalues. These terms are widely used whenever a sample with data is analyzed. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above. This resource covers the topics outlined in subunits 5.3.1 to 5.3.8.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 22” and “Lecture 23”
Links: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 22” (YouTube) and “Lecture 23” (YouTube)
Also available in:
iTunes U (Lectures 25 and 26)
Instructions: Watch “Lecture 22” from 1:12 to the end and then watch “Lecture 23.” These video lectures are companions to Chapter 27, with the author of the text working through the materials. Please note that these are labeled “Lecture 25” and “Lecture 26” on iTunesU. This resource covers the topics outlined in subunits 5.3.1 to 5.3.8.
Watching these lectures and pausing to take note should take approximately 2 hours.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialNo Derivative License. They are attributed to Philip Stark and the University of California. The original versions can be found here and here.  Reading: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4th edition: “10 Hypothesis Testing”
Links: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4th edition: “10 Hypothesis Testing” (PDF)
Also Available in:
HTML
Instructions: Read Section 10 to learn how to conduct hypothesis testing for a population mean and a population proportion using one sample. This resource covers the topics outlined in subunits 5.3.1 to 5.3.8.
Reading this section should take approximately 1 hour.
Terms of Use: The resource above is released under a Creative Commons Attribution License. It is attributed to Dana Lee Ling, and the original version can be found here.  Web Media: YouTube: Khan Academy’s Statistics: “Hypothesis Testing and Pvalues”
Link: YouTube: Khan Academy’s Statistics: “Hypothesis Testing and Pvalues” (YouTube)
Instructions: View the lecture, which explains how to test a hypothesis. This resource covers the topics outlined in subunits 5.3.1 to 5.3.8.
Viewing this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNoncommercialShare Alike License. It is attributed to the Khan Academy.  Reading: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4th edition: “11 Testing the Two Sample Means with the tTest”
Link: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4th edition: “11 Testing the Two Sample Means with the tTest” (PDF)
Also Available in:
HTML
Instructions: Read Section 11 to learn how to conduct hypothesis testing for a population mean and a population proportion using two samples. This resource covers the topics outlined in subunits 5.3.1 to 5.3.8.
Reading this section should take approximately 1 hour.
Terms of Use: The resource above is released under a Creative Commons Attribution License. It is attributed to Dana Lee Ling, and the original version can be found here.
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 27: Hypothesis Testing – Does Chance Explain the Results?”

5.3.1 Examples of Hypothesis Testing Problems
Note: The reading and lectures assigned below subunit 5.3 cover this topic. Before covering this section from Chapter 27 under the section titled “Examples of Hypothesis Testing Problem,” make sure to read the first section about hypothesis testing. Hypothesis testing is the scientific procedure needed when testing data from a sample and when experiments are conducted to test their significance.

5.3.2 Significance Level and Power
Note: The reading and lectures assigned below subunit 5.3 cover this topic. In statistics, the significance level refers to the probability of concluding that the sample data give valid approximations for the real population parameters when in fact that is not true. The key is to choose a small significance level. This level is chosen by the data analyst but the most common one is the 0.05 significance level, which translates to using a 95% confidence level.

5.3.3 Test Statistics and Pvalues
Note: The reading and lectures assigned below subunit 5.3 cover this topic. Make sure to read Examples 272 and 273. Also, watch the video from the Khan Academy “Hypothesis Testing and Pvalues” as it shows you how to test a hypothesis.

5.3.4 Hypotheses about Parameters
Note: The reading and lectures assigned below subunit 5.3 cover this topic. In Chapter 27 under the section titled “Hypotheses about Parameters,” pay special attention to the concepts: rejection region, onesided, and twosided tests. Also, make sure to read the case study titled “Case Study: Employment Discrimination Arbitration” in order to understand how hypothesis testing is done in practice.

5.3.5 Population Parameters Testing Using One or Two Samples
Note: The reading and lectures assigned below subunit 5.3 cover this topic. In addition to reading Chapter 27 from the main text, read the sections titled “10 Hypothesis Testing” and “11 Testing the Two Sample Means with the tTest” in the reading from the College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org. Those sources will reinforce your understanding of the difference in hypothesis testing between one and two samples.

5.3.6 Caveats: The Meaning of Rejection, Statistical Significance and Practical Importance, and Interpreting Pvalues
Note: The reading and lectures assigned below subunit 5.3 cover this topic. In Chapter 27 from the main text, make sure to read the final section titled “Caveats,” which explains the most common problems one makes when conducting hypothesis testing.

5.4 Testing Equality of Two Percentages
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 29: Testing Equality of Two Percentages”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 29: Testing Equality of Two Percentages” (HTML and Java)
Instructions: Read Chapter 29 to learn how to compare data as a percent from two similar groups when you are analyzing categorical data. For example, suppose that you are analyzing the percent of low income women versus the percent of high income women that belong to one sample. Then, you want to compare those percentages to a different but similar sample of women. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Web Media: YouTube: Khan Academy’s Statistics: “Comparing Population Proportions 1” and “Comparing Population Proportions 2”
Link: YouTube: Khan Academy’s Statistics: “Comparing Population Proportions 1” (YouTube) and “Comparing Population Proportions 2” (YouTube)
Instructions: View the lectures, which explain how to compare the proportion of two different samples.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialShare Alike License. They are attributed to the Khan Academy.
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 29: Testing Equality of Two Percentages”

5.5 The Multinomial Distribution and the ChiSquared Test for Goodness of Fit
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 31: The Multinomial Distribution and the ChiSquared Test for Goodness of Fit”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 31: The Multinomial Distribution and the ChiSquared Test for Goodness of Fit” (HTML and Java)
Instructions: Read Chapter 31 to learn how to compare data as a percent from three or more similar groups when you are analyzing categorical data. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above.
Reading this chapter should take approximately 3 hours
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Web Media: YouTube: Khan Academy’s Statistics: “ChiSquare Distribution Introduction,” “Pearson's Chi Square Test (Goodness of Fit),” and “Contingency Table ChiSquare Test”
Link: YouTube: Khan Academy’s Statistics: “ChiSquare Distribution Introduction,” (YouTube) “Pearson's Chi Square Test (Goodness of Fit),” (YouTube) and “Contingency Table ChiSquare Test” (YouTube)
Instructions: Please view these three lectures, which explain how to conduct ChiSquare tests.
Watching these lectures and pausing to take notes should take approximately 1 hour.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialShare Alike License. They are attributed to the Khan Academy.
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 31: The Multinomial Distribution and the ChiSquared Test for Goodness of Fit”

5.6 Assessments for Unit 5
 Assessment: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Confidence Intervals: Homework” and “Hypothesis Testing – Single Mean and Single Proportion: Homework”
Links: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Confidence Intervals: Homework” (PDF) and “Hypothesis Testing – Single Mean and Single Proportion: Homework” (PDF)
Instructions: Select ten of the problems from each exercise set linked above. Note that not all problems have solutions attached, so please limit your choices to those that have solutions. To see a problem solution, go to the HTML versions and click on the “Show Solution” link below the problem. You may also download this homework as a DOC by clicking on the links to the right in the original versions below.
Completing these assessments should take approximately 3 hours.
Terms of Use: This work is licensed under a Creative Commons Attribution 2.0 Generic License. It is attributed to Susan Dean and Barbara Illowsky, and the original versions can be found here and here.  Assessment: The Saylor Foundation’s “BUS204 Unit 5 Quiz”
Link: The Saylor Foundation’s “BUS204 Unit 5 Quiz” (HTML)
Instructions: Complete this assessment to gauge your understanding of the topics covered in this unit. The correct answers will be displayed when you click the “Submit” button.
Completing the quiz, and reviewing if necessary, should take approximately 1 hour.
 Assessment: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Confidence Intervals: Homework” and “Hypothesis Testing – Single Mean and Single Proportion: Homework”

Unit 6: Correlation and Regression
If two data points move in the same direction, does that mean that one causes the other? How are we to analyze their correlation?
Unit 6 Time Advisory show close
Regression is an analysis of the relationship of one variable to another. A regression might identify, for example, the relationship between car speed and the number of fatal accidents. In this example, speed and number of accidents are the two variables; the number of accidents is said to be the dependent variable, because the number of accidents depends on the speed. Speed is considered the independent variable. While regressions can be calculated manually, a statistically significant dataset could take a long time to regress.
Regressions not only allow us to determine whether a relationship exists but also to identify how strong that relationship is. The measure of this relationship is known as the regression coefficient. If the regression coefficient is relatively low, then speed may not be the major factor in fatal accidents. Perhaps the major factor is the time of day, whether it rained or not, or if alcohol was involved. With multiple regression, a number of independent variables can be tested against the dependent variable at the same time. The regression coefficient would determine which variables have the strongest relationship with the dependent variable. In business, you will frequently use regression to predict future events. Though not an exact science, regression can be used to make reliable predictions if enough variables are identified. For example, first responders could use regression outputs to predict the number of fatal accidents in a given shift based on average travel speed, time of day, weather, and any other factors deemed significant. This unit will also stress the importance of determining the factors that most likely contribute to a dependent variable.
Regression is often used in finance. Investors often want to know the relationship between a stock’s performance and the overall performance of the market. By regressing the period returns of a stock with the returns of the market, investors can see the regression coefficient. This coefficient is known as a stock’s beta and is covered extensively in BUS202: Principles of Finance.
Unit 6 Learning Outcomes show close

6.1 Working with More Than One Variable
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 5: Multivariate Data and Scatterplots”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 5: Multivariate Data and Scatterplots” (HTML and Java)
Instructions: Read Chapter 5 to learn how to analyze the relationship between two variables. Two variables may be positively or negatively related when different pairs of data show the same pattern. For example, when incomes of individuals rise so does their consumption of goods and services; thus, income and consumption are considered to be positively related. As a person’s income rises, the number of bus rides this person takes falls; thus, income and bus riding are negatively related. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section. This resource covers the topics outlined in subunits 6.1.1 to 6.1.4.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 4” and “Lecture 5”
Links: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 4” (YouTube) and “Lecture 5” (YouTube)
Also available in:
iTunes U (Lectures 4 and 5)
Instructions: Watch "Lecture 4" from 50:00 to the end and then watch “Lecture 5” from the beginning until 38:00. These videos complement Chapter 5, with the author of the text working through the materials. This resource covers the topics outlined in subunits 6.1.1 to 6.1.4.
Watching these lectures and pausing to take notes should take approximately 1.5 hours.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialNo Derivative License. They are attributed to Philip Stark and the University of California. The original versions can be found here and here (YouTube).
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 5: Multivariate Data and Scatterplots”

6.1.1 Multivariate Data
Note: The reading and lectures assigned below subunit 6.1 cover this topic. Pay attention to bivariate data, which is about tracking two variables for each observation.

6.1.2 Scatterplots
Note: The reading and lectures assigned below subunit 6.1 cover this topic. Note that a scatterplot usually shows the dependent variable on the Yaxis and the independent variable on the Xaxis.

6.1.3 Outliers
Note: The reading and lectures assigned below subunit 6.1 cover this topic. Under the heading labeled “Describing Scatterplots,” review why an outlier, which is an unusual value, creates problems for getting summary statistics such as the mean.

6.1.4 Association
Note: The reading and lectures assigned below subunit 6.1 cover this topic. Be sure to revisit the section labeled “Scatterplots” and note how two variables are said to be linearly associated as their paired values form a straight line that either moves up or down.

6.2 Correlation and Association
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 7: Correlation and Association”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 7: Correlation and Association” (HTML and Java)
Instructions: Read Chapter 7 for a discussion on the difference between correlation and association between two variables. When two variables are said to be highly correlated, it does not mean that one is causing the other. Pay special attention to the formula for computing the correlation value. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above. This resource covers the topics outlined in subunits 6.2.1 to 6.2.3.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 5”
Link: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 5” (YouTube)
Also available in:
iTunes U (Lecture 5)
Instructions: Watch “Lecture 5” from 41:00 to the end. This video is the companion to Chapter 7, with the author of the text working through the materials. This resource covers the topics outlined in subunits 6.2.1 to 6.2.3.
Viewing this lecture and pausing to take notes should take approximately 1 hour.
Terms of Use: This video is licensed under a Creative Commons AttributionNoncommercialNo Derivative License. It is attributed to Philip Stark and the University of California. The original version can be found at here.  Reading: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Chapter 12: Linear Regression and Correlation, Section 6: The Correlation Coefficient”
Links: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Chapter 12: Linear Regression and Correlation, Section 6: The Correlation Coefficient” (PDF)
Instructions: Study this resource, which shows the formula for computing the correlation coefficient. It may be useful to save this resource for future reference to this formula. Note that the formula uses the Greek letter sigma, ∑, as the summation symbol. For instance, ∑ X_{i} = X_{1} + X_{2} + X_{3} when i = 1, 2, 3. This resource covers the topics outlined in subunits 6.2.1 to 6.2.3.
Reading this article should take approximately 30 minutes.
Terms of Use: This work is licensed under a Creative Commons Attribution 2.0 Generic License. It is attributed to Susan Dean and Barbara Illowsky, and the original version can be found here. Please respect the copyright and terms of use.
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 7: Correlation and Association”

6.2.1 The Correlation Coefficient
Note: The readings and lecture assigned below subunit 6.2 cover this topic. The correlation coefficient is a numerical measure between 1 and +1. It measures the strength of linear association between two variables. If it is close to 1, it means that two variables are strongly but negatively related. If it is close to +1, it means that two variables are strongly but positively related. Negative coefficients mean that two variables move in opposite directions, while positive coefficients mean that they move in the same direction. A coefficient of 0 means that there is no linear association between two variables. Make sure you understand the difference between correlation and causation as explained in that section of the text with the heading labeled “Correlation and Association.”

6.2.2 The Effect of Nonlinear Association
Note: The readings and lecture assigned below subunit 6.2 cover this topic. A nonlinear association is when the correlation coefficient is 0 (or very close to it from either side).

6.2.3 Computing the Correlation Coefficient
Note: The readings and lecture assigned below subunit 6.2 cover this topic. Make sure to read Chapter 12 by Dean and Illowsky to review how to compute the correlation coefficient when you are given n data points with each having a pair of X and Y values. Note that the formula uses the Greek letter sigma, ∑, as the summation symbol. For instance, ∑ X_{i} = X_{1} + X_{2} + X_{3} when i = 1, 2, 3.

6.3 Regression
 Reading: University of California, Berkeley: Philip Stark's SticiGui “Chapter 9: Regression”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 9: Regression” (HTML and Java)
Instructions: Read Chapter 9 to learn how to analyze X and Y data, where the X variable is considered the independent variable and Y the dependent variable. Regression analysis is used to determine how the X values affect the Y values by assuming that there is a linear relationship between them. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section above. This resource covers the topics outlined in subunits 6.3.1 to 6.3.5.
Reading this chapter should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 6”
Link: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 2” (YouTube)
Also available in:
iTunes U (Lecture 6)
Instructions: Watch “Lecture 6” from 3:50 to the 57:50. This video is the companion to Chapter 9, with the author of the text working through the materials. This resource covers the topics outlined in subunits 6.3.1 to 6.3.5.
Viewing this lecture and pausing to take notes should take approximately 2 hours.
Terms of Use: This video is licensed under a Creative Commons AttributionNoncommercialNo Derivative License. It is attributed to Philip Stark and the University of California. The original version can be found at here.
 Reading: University of California, Berkeley: Philip Stark's SticiGui “Chapter 9: Regression”

6.3.1 SD Line
Note: The reading and lecture assigned below subunit 6.3 cover this topic. Make sure to look at Figure 91 and focus on how the Standard Deviation (SD) line fits in an XY scatterplot.

6.3.2 Graph of Averages
Note: The reading and lecture assigned below subunit 6.3 cover this topic. Make sure to look at Figure 92 and focus on how average values of Y fit within class intervals of the X data.

6.3.3 Regression Line
Note: The reading and lecture assigned below subunit 6.3 cover this topic. Make sure to look at Figure 94 and focus on how the regression line is formed when the average values of Y are connected.

6.3.4 Estimating Using the Regression Line
Note: The reading and lecture assigned below subunit 6.3 cover this topic. The regression line is expressed this way: Y = aX + b, where a is the slope and b is the intercept of the line.

6.3.5 The Equation of the Regression Line
Note: The reading and lecture assigned below subunit 6.3 cover this topic. Make sure you know how to compute a and b given the equations in the text under the section labeled “The Equation of the Regression Line.”
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 11: Errors in Regression”
Link: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 11: Errors in Regression” (HTML and Java)
Instructions: This is an optional reading. Read Chapter 11 on errors in regression. Read through this chapter if you would like to experience the entire course as it was presented at University of California, Berkeley. There are several exercises and Java applets embedded in the text that are meant to further reinforce your learning. Do not skip these exercises! For instructions on how to navigate these exercises, see “Special Instructions on SticiGui Exercises and Java Applets” in the “Course Information” section.
Reading this article should take approximately 3 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 6” and “Lecture 7”
Link: YouTube: University of California, Berkeley: Philip Stark's Statistics 21: “Lecture 6” (YouTube) and “Lecture 7” (YouTube)
Also available in:
iTunes U (Lectures 6 and 7)
Instructions: These videos are optional. Watch “Lecture 6” from 57:50 to the end, and watch “Lecture 7” from the beginning to 47:00. These video lectures complement Chapter 11 with the author of the text working through the materials.
Watching these lectures and pausing to take notes should take approximately 1 hour 30 minutes.
Terms of Use: The videos above are licensed under a Creative Commons AttributionNoncommercialNo Derivative License. They are attributed to Philip Stark and the University of California. The original versions can be found here and here.
 Reading: University of California, Berkeley: Philip Stark's SticiGui: “Chapter 11: Errors in Regression”

6.4 Spreadsheet Activity for Unit 6
 Activity: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4^{th} edition: “04 Paired Data and Scatter Diagrams” and The Saylor Foundation’s “Spreadsheet Activity”
Links: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4^{th} edition: “04 Paired Data and Scatter Diagrams” (PDF) and The Saylor Foundation’s “Spreadsheet Activity” (Open Office) or “Spreadsheet Activity” (Excel)
Also Available in:
HTML (04 Paired Data and Scatter Diagrams)
Instructions: Read through Chapter 4 of the text. For this activity, you will review how a spreadsheet can be used to plot data, determine the slope and intercept of regression line, and draw the regression line. The instructions for creating the scatter graph and regression line are in Section 4.25. However, for this activity, we are solving for the problem presented in Section 4.4. The supporting spreadsheet files (links above to both Excel and Open Office versions) include a tab titled “Starter File,” which contains everything you need to get started on the activity. Once you have worked through the activity, you can click on the “Solution File” tab to see how your finished spreadsheet should look.
Completing this activity should take approximately 2 hours.
Terms of Use: This work is licensed under a Creative Commons Attribution 3.0 License. It is attributed to Dana Lee Ling and the original version can be found here.
 Activity: College of MicronesiaFSM: Dana Lee Ling's Introduction to Statistics Using OpenOffice.org, LibreOffice.org Calc, 4^{th} edition: “04 Paired Data and Scatter Diagrams” and The Saylor Foundation’s “Spreadsheet Activity”

6.5 Assessments for Unit 6
 Assessment: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Linear Regression and Correlation: Homework”
Link: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Linear Regression and Correlation: Homework” (PDF)
Also Available in:
HTML
Instructions: For this assessment, please work on the following problems: 1, 3, 5, 11, 15, 17, and 22. To see a problem solution, go the HTML version and click on the “Show Solution” link below the problem. You may also download this assessment as a DOC by clicking on the link to the right in the HTML version.
Completing this assessment should take approximately 3 hours.
Terms of Use: This work is licensed under a Creative Commons Attribution 2.0 Generic License. It is attributed to Susan Dean and Barbara Illowsky. The original version can be found here. Please respect the copyright and terms of use.  Assessment: The Saylor Foundation’s “BUS204 Unit 6 Quiz”
Link: The Saylor Foundation’s “BUS204 Unit 6 Quiz” (HTML)
Instructions: Complete this assessment to gauge your understanding of the topics covered in this unit. The correct answers will be displayed when you click the “Submit” button.
Completing the quiz, and reviewing if necessary, should take approximately 1 hour.
 Assessment: Connexions: Susan Dean and Barbara Illowsky’s Collaborative Statistics: “Linear Regression and Correlation: Homework”

Final Exam
 Final Exam: The Saylor Foundation's BUS204 Final Exam
Link: The Saylor Foundation's BUS204 Final Exam
Instructions: You must be logged into your Saylor Foundation School account in order to access this exam. If you do not yet have an account, you will be able to create one, free of charge, after clicking on the link above.
Note: While taking the final exam, you are welcome to make use of this Online Calculator (HTML).
 Final Exam: The Saylor Foundation's BUS204 Final Exam

NCCRS Credit Recommended Exam
 Optional Final Exam: The Saylor Foundation's “BUS204 Final Exam”
Link: The Saylor Foundation's "BUS204 Final Exam" (HTML)
Instructions: The above linked exam has been specially created as part of our National College Credit Recommendation Service (NCCRS) review program. Successfully passing this exam will make students eligible to receive a transcript with 3 hours of recommended college credit.
Note: While taking the final exam, you are welcome to make use of this Online Calculator (HTML).
Please note that because this exam has the possibility to be a creditbearing exam, it must be administered in a proctored environment, and is therefore password protected. Further information about Saylor's NCCRS program and the options and requirements for proctoring, can be found here. Please make sure to read this page carefully before attempting this exam.
If you choose to take this exam, you may want to first take the regular, certificatebearing BUS204 Final Exam as a practice test, which you can find above.
 Optional Final Exam: The Saylor Foundation's “BUS204 Final Exam”