— MA121: Introduction to Statistics —

• Unit 1
• Unit 2
• Unit 3
• Unit 4
• Unit 5
• Unit 6
• Final Exam
• All Units

Unit Outline show close

Unit 1: Statistics and Data  

In today’s technologically advanced world, we have access to large volumes of data. The first step of data analysis is to accurately summarize all of this data, both graphically and numerically, so that we can understand what the data reveals. To be able to use and interpret the data correctly is essential to making informed decisions. For instance, when you see a survey of opinion about a certain TV program, you may be interested in the proportion of those people who indeed like the program.  
 
In this unit, you will learn about descriptive statistics, which are used to summarize and display data. After completing this unit, you will know how to present your findings once you have collected data. For example, suppose you want to buy a new mobile phone with a particular type of a camera. Suppose you are not sure about the prices of any of the phones with this feature, so you access a website that provides you with a sample data set of prices, given your desired features. Looking at all of the prices in a sample can sometimes be confusing. A better way to compare this data might be to look at the median price and the variation of prices. The median and variation are two ways out of several ways that you can describe data. You can also graph the data so that it is easier to see what the price distribution looks like.
 
In this unit, you will study precisely this; namely, you will learn both numerical and graphical ways to describe and display your data. You will understand the essentials of calculating common descriptive statistics for measuring center, variability, and skewness in data. You will learn to calculate and interpret these measurements and graphs.
 
Descriptive statistics are, as their name suggests, descriptive. They do not generalize beyond the data considered. Descriptive statistics illustrate what the data shows. Numerical descriptive measures computed from data are called statistics. Numerical descriptive measures of the population are called parameters. Inferential statistics can be used to generalize the findings from sample data to a broader population.

Unit 1 Time Advisory   show close


Unit 1 Learning Outcomes   show close


1.1 The Science of Statistics and Its Importance  

1.1.1 What is Statistics?  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 1, Section 2: What Are Statistics?” and “Section 3: Importance of Statistics”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 1, Section 2: What Are Statistics?” (HTML) and “Section 3: Importance of Statistics” (HTML)
   
  Instructions: Read sections 2 and 3 from chapter 1. Section 2 providesa brief introduction to the field of statistics and some relevant examples. Section 3 presentsmore examples of how statistics can lend credibility to making arguments. Also, complete the questions in these sections.
   
  Reading these sections and answering the questions should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.1.2 Descriptive and Inferential Statistics  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 1, Section 4: Descriptive Statistics” and “Section 5: Inferential Statistics”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 1, Section 4: Descriptive Statistics” (HTML) and “Section 5: Inferential Statistics” (HTML)
   
  Instructions: Read sections 4 and 5 from chapter 1, and then complete the questions at the end of each section. Section 4 introduces descriptive statistics by using examples and discusses the difference between descriptive and inferential statistics. Section 5 talks about samples and populations, explains how one can identify biased samples, and defines differential statistics. 
   
  Reading these sections and answering the questions should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Reading: Introductory Statistics: “Chapter 1, Section 1: Basic Definitions and Concepts”

  Link: Introductory Statistics: “Chapter 1, Section 1: Basic Definitions and Concepts” (PDF)
   
  Instructions: Read section 1 from chapter 1 on pages 4–10 to further enhance your understanding of the elements of descriptive and inferential statistics. This section will introduce some of the key concepts in statistics and has numerous exercise and examples. Complete the odd-numbered exercises before checking the answers.
   
  Reading this section and completing the exercises should take approximately 45 minutes.
   
  Terms of Use: This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-Share-Alike 3.0 License without attribution as requested by the work’s original creator or licensee.

• Interactive Lab: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 1, Introduction – Section 6: Sampling Demonstration”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 1, Introduction – Section 6: Sampling Demonstration” (HTML)
   
  Instructions: Follow the instructions to run the random sampling simulation. You will learn the difference between random sampling and stratified sampling.
   
  Completing this interactive lab should take approximately 30 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.1.3 Types of Data and Their Collection  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 1, Section 7: Variables” and “Chapter 6, Section 4: Data Collection”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 1, Section 7: Variables”(HTML) and “Chapter 6, Section 4: Data Collection” (HTML)
   
  Instructions: Read section 7 from chapter 1 and section 4 from chapter 6. Also, complete the questions at the end of each section. Section 7 will introduce several types of data and their distinguishing features. You will also learn about independent and dependent variables. Section 4 will explain how common data can be coded and collected. 
   
  Reading these sections and answering the questions should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Reading: Introductory Statistics: “Chapter 1, Section 3: Presentation of Data”

  Link: Introductory Statistics: “Chapter 1, Section 3: Presentation of Data” (PDF)
   
  Instructions: Study section 3 from chapter 1 on pages 13 and 14. This reading talks about ways that data can be presented. Attempt the odd-numbered exercises on page before checking the answers.
   
  Reading this section and completing the exercises should take approximately 30 minutes.
   
  Terms of Use: This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-Share-Alike 3.0 License without attribution as requested by the work’s original creator or licensee.

1.2 Methods for Describing Data  

1.2.1 Graphical Methods for Describing Quantitative Data  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 2, Section 3: Quantitative Variables,” “Section 4: Stem and Leaf Displays,” “Section 5: Histograms,” “Section 6: Frequency Polygons,” “Section 7: Box Plots,” “Section 9: Bar Charts,” and “Section 10: Line Graphs”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 2, Section 3: Quantitative Variables” (HTML), “Section 4: Stem and Leaf Displays” (HTML), “Section 5: Histograms” (HTML), “Section 6: Frequency Polygons” (HTML), “Section 7: Box Plots” (HTML), “Section 9: Bar Charts” (HTML) and “Section 10: Line Graphs” (HTML)
   
  Instructions: Read sections 3–7, 9, and 10 from chapter 2. Also, complete the questions at the end of each section. Section 3 provides an overview of the available methods to portray distributions of quantitative variables. Section 4 introduces you to the stem and leaf plot. In sections 5 and 6, you will learn how to capture the frequency of your data. Section 7 discusses box plots for the purpose of identifying outliers and for comparing distributions. Section 9 discusses bar charts for quantitative variables. Section 10 talks about the method of line graphs, which is based on bar graphs.
   
  Reading these sections and answering the questions should take approximately 3 hours.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Reading: Introductory Statistics: “Chapter 2, Section 1: Three Popular Data Displays”

  Link: Introductory Statistics: “Chapter 2, Section 1: Three Popular Data Displays” (PDF)
   
  Instructions: Read section 1 from chapter 2 on pages 16–29. This reading further elaborates on ways of describing data. In particular, you will learn about the relative frequency histogram. Complete the odd-numbered exercises on before checking the answers.
   
  Reading this section and completing the exercises should take approximately 1 hour and 15 minutes.
   
  Terms of Use: This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-Share-Alike 3.0 License without attribution as requested by the work’s original creator or licensee.

• Interactive Lab: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 2, Graphing Distributions – Section 8: Box Plot Demo”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 2, Graphing Distributions – Section 8: Box Plot Demo” (HTML)
   
  Instructions: Watch the video demo in this section, and follow the instructions to run the simulation. You will learn which measure of central tendency will balance a distribution.
   
  Completing this interactive lab should take approximately 30 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.2.2 Numerical Measures of Central Tendency and Variability  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 3, Section 2: Central Tendency,” “Section 4: Measures of Central Tendency,” “Section 8: Median and Mean,” “Section 12: Variability,” and “Section 13: Measures of Variability” (HTML)

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 3, Section 2: Central Tendency” (HTML), “Section 4: Measures of Central Tendency” (HTML), “Section 8: Median and Mean” (HTML), “Section 12: Variability” (HTML), and “Section 13: Measures of Variability” (HTML)
   
  Instructions: Read sections 2, 4, 8, 12, and 13 from chapter 3. Also, complete the questions at the end of each section. Section 2 defines the concept of central tendency. Section 4 introduces mean, median, and mode in the context of examples. Section 8 further elaborates on median and mean and discusses their strengths and weaknesses in measuring the central tendency. Section 12 addresses the concept of variability. Section 13 discusses range, interquartile range, variance, and the standard deviation.  
   
  Reading these sections and answering the questions should take approximately 3 hours.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Reading: Introductory Statistics: “Chapter 2, Section 2: Measures of Central Location and Section 3: Measures of Variability”

  Link: Introductory Statistics: “Chapter 2, Section 2: Measures of Central Location and Section 3: Measures of Variability” (PDF)
   
  Instructions: Read sections 2 and 3 from chapter 2 on pages 29–61. Section 2.2 further elaborates on mean, median, and mode – both at the population level and sample level. This section contains many interesting examples and exercises. Section 2.3 talks about range, variance, and standard deviation using many examples. Complete the odd-numbered problems in the exercise sets for each section before checking the answers.
   
  Reading these sections and completing the exercises should take approximately 3 hours.
   
  Terms of Use: This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-Share-Alike 3.0 License without attribution as requested by the work’s original creator or licensee.

• Web Media: Khan Academy’s “Statistics Intro: Mean, Median, and Mode”

  Link: Khan Academy’s “Statistics Intro: Mean, Median, and Mode” (YouTube)
   
  Instructions: Watch this video, which begins with a discussion on descriptive statistics and inferential statistics and then talks about mean, median, and mode.
   
  Watching this video and pausing to take notes should take approximately 30 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

• Web Media: Khan Academy’s “Example: Finding Mean, Median, and Mode”

  Link: Khan Academy’s “Example: Finding Mean, Median, and Mode” (YouTube)
   
  Instructions: Watch this video, which gives examples on finding the mean, median, and mode.
   
  Watching this video and pausing to take notes should take approximately 15 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

• Web Media: Khan Academy’s “Sample Mean versus Population Mean”

  Link: Khan Academy’s “Sample Mean versus Population Mean” (YouTube)
   
  Instructions: Watch this video, which focuses on sample mean and population mean.
   
  Watching this video and pausing to take notes should take approximately 30 minutes.
  
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here. 

• Web Media: Khan Academy’s “Variance of Population”

  Link: Khan Academy’s “Variance of a Population” (YouTube)
   
  Instructions: Watch this video, which discusses variance of a population.
   
  Watching this video and pausing to take notes should take approximately 30 minutes.
  
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here. 

• Web Media: Khan Academy’s “Sample Variance”

  Link: Khan Academy’s “Sample Variance” (YouTube)
   
  Instructions: Watch this video on sample variance.
   
  Watching this lecture and pausing to take notes should take approximately 30 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

• Web Media: Khan Academy’s “Review and Intuition of Why We Divide n-1 for the Unbiased Sample Variance”

  Link: Khan Academy’s “Review and Intuition of Why We Divide n-1 for the Unbiased Sample Variance” (YouTube)
   
  Instruction: Watch this video, which discusses unbiased sample variance.
   
  Watching this video and pausing to take notes should take approximately 30 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

1.2.3 Methods for Describing Relative Standing  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 1, Section 8: Percentiles”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 1, Section 8: Percentiles” (HTML)
                                          
  Instructions: Read section 8 of chapter 1. Also, complete the questions at the end of the section. This reading discusses percentiles, which are useful for describing relative standings of observations in a dataset. This reading presents several definitions, so make sure to take notes.
   
  Reading this section should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.2.4 Methods for Describing Bivariate Relationships  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 4, Section 3: Values of the Pearson Correlation,” “Section 5: Properties of Pearson’s r,” and “Section 6: Computing Pearson’s r”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 4, Section 3: Values of the Pearson Correlation” (HTML), “Section 5: Properties of Pearson’s r” (HTML), and “Section 6: Computing Pearson’s r” (HTML)
   
  Instructions: Read sections 3, 5, and 6 from chapter 4. Also,complete the questions at the end of each section. Section 3 introduces Pearson’s correlation and explains what the typical values represent. Section 5 further elaborates on the properties of r, particularly the fact that it is invariant under linear transformation. Section 6 introduces several formulas that can be used to compute Pearson’s correlation.
   
  Reading these sections and answering the questions should take approximately 1 hour and 30 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Web Media: Sophia: Al Greene’s “Scatter Plot/Bivariate Data”

  Link: Sophia: Al Greene’s “Scatter Plot/Bivariate Data” (Flash)
   
  Instructions: Watch this video tutorial to learn how to create the scatter plot for bivariate data, using two variables x and y. It may be useful to review the definitions on this webpage.
   
  Watching this tutorial, pausing to take notes, and reviewing the definitions should take approximately 30 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Al Greene, and the original version can be found here.

• Interactive Lab: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 4, Describing Bivariate Data – Section 7: Restriction of Range Demo”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 4, Describing Bivariate Data – Section 7: Restriction of Range Demo” (HTML)
   
  Instructions: Watch the video demo, and follow the instructions to run the simulation. From the demonstration, you will learn how range restriction can affect the correlation between two variables.
   
  Completing this interactive lab should take approximately 30 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

Unit 2: Elements of Probability and Random Variables  

Probabilities affect our everyday lives. In this unit, you will learn about probability and its properties, how probability behaves, and how to calculate and use it. You will study the fundamentals of probability and will work through examples that cover different types of probability questions. These basic probability concepts will provide a foundation for understanding more statistical concepts, for example, interpreting polling results. Though you may have already encountered concepts of probability, after this unit, you will be able to formally and precisely predict the likelihood of an event occurring given certain constraints.
 
Probability theory is a discipline that was created to deal with chance phenomena. For instance, before getting a surgery, a patient wants to know the chances that the surgery might fail; before taking medication, you want to know the chances that there will be side effects; before leaving your house, you want to know the chance that it will rain today. Probability is a measure of likelihood that takes on values between 0 and 1, inclusive, with 0 representing impossible events and 1 representing certainty. The chances of events occurring fall between these two values. 
 
The skill of calculating probability allows us to make better decisions. Whether you are evaluating how likely it is to get more than 50% of the questions correct on a quiz if you guess randomly; predicting the chance that the next storm will arrive by the end of the week; or exploring the relationship between the number of hours students spend at the gym and their performance on an exam, an understanding of the fundamentals of probability is crucial.
 
We will also talk about random variables. A random variable describes the outcomes of a random experiment. A statistical distribution describes the numbers of times each possible outcome occurs in a sample. The values of a random variable can vary with each repetition of an experiment. Intuitively, a random variable, summarizing certain chance phenomenon, takes on values with certain probabilities. A random variable can be classified as being either discrete or continuous, depending on the values it assumes. Suppose you count the number of people who go to a coffee shop between 4 p.m. and 5 p.m. and the amount of waiting time that they spend in that hour. In this case, the number of people is an example of a discrete random variable and the amount of waiting time they spend is an example of a continuous random variable. 

Unit 2 Time Advisory   show close


Unit 2 Learning Outcomes   show close


2.1 Classical Probability Model  

2.1.1 Events, Sample Spaces, and Probability  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 5, Section 2: Introduction to Probability” and “Section 3: Basic Concepts”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 5, Section 2: Introduction to Probability” (HTML) and “Section 3: Basic Concepts” (HTML)
   
  Instructions: Read sections 2 and 3 from chapter 5. Also, complete the questions at the end of each section. Section 2 talks about experiments for which outcomes are equally likely to occur and also discusses the frequency approach to assign probabilities. Section 3 focuses on the concept of events and also touches upon the issue of conditional probability. 
  
  Reading these sections and answering the questions should take approximately 4 hours.
  
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Reading: Introductory Statistics: “Chapter 3: Basic Concepts of Probability”

  Link: Introductory Statistics: “Chapter 3: Basic Concepts of Probability” (PDF)
   
  Instructions: Study chapter 3 on pages 98–158 to learn about basic concepts of probability. Section 1 discusses spaces, events, and their probabilities using many examples. Section 2 elaborates on sets operations, including complements, intersections, and unions using Venn diagrams. Section 3 introduces conditional probability and talks about independent events. Complete the odd-numbered exercises for each section before checking the answers.
   
  Studying this chapter and completing the exercises should take approximately 6 hours.
   
  Terms of Use: This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-Share-Alike 3.0 License without attribution as requested by the work’s original creator or licensee.

2.1.2 Counting Rules  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 5, Section 6: Permutations and Combinations”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 5, Section 6: Permutations and Combinations” (HTML)
   
  Instructions: Read section 6 from chapter 5. Also, complete the questions at the end of this section. Section 6 introduces formulas for combinations and permutations, which are useful to compute probabilities.
   
  Reading this section and answering the questions should take approximately 45 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Web Media: Khan Academy’s “Probability with Playing Cards and Venn Diagrams”

  Link: Khan Academy’s “Probability with Playing Cards and Venn Diagrams” (YouTube)
   
  Instruction: Watch this video, which introduces Venn diagrams in the context of playing cards.
   
  Watching this video and pausing to take notes should take approximately 30 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

• Web Media: Khan Academy’s “Addition Rule for Probability”

  Link: Khan Academy’s “Addition Rule for Probability” (YouTube)
   
  Instructions: Watch this video, which talks about the addition rule for probability. 
   
  Watching this video and pausing to take notes should take approximately 30 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

2.2 Random Variables and Distributions  

2.2.1 Common Discrete Random Variables  

• Reading: Introductory Statistics: “Chapter 4, Section 1: Random Variables and Section 2: Probability Distributions for Discrete Random Variables”

  Link: Introductory Statistics: “Chapter 4, Section 1: Random Variables and Section 2: Probability Distributions for Discrete Random Variables” (PDF)
  
  Instructions: Read sections 1 and 2 from chapter 4 on pages 159–185. Section 1 defines discrete and continuous random variables. Section 2 introduces the distributions for discrete random variables. This section also talks about the mean and variance calculations. Complete the odd-numbered exercises for each section before checking the answers.
   
  Studying these sections and completing the exercises should take approximately 3 hours.
   
  Terms of Use: This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-Share-Alike 3.0 License without attribution as requested by the work’s original creator or licensee.

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 5, Section 8: Binomial Distributions,” “Section 10: Poisson Distributions,” and “Section 11: Multinomial Distribution”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 5, Section 8: Binomial Distributions” (HTML), “Section 10: Poisson Distributions” (HTML), and “Section 11: Multinomial Distribution” (HTML)
   
  Instructions: Read sections 8, 10, and 11 from chapter 5. Also, complete the questions at the end of each section. Section 8 talks about binomial probabilities, discusses how to compute their cumulatives, and introduces the mean and standard deviation. Section 10 introduces the Poisson probability formula. Section 11 defines multinomial outcomes and discusses how to compute probabilities by using the multinomial distribution.
   
  Reading these sections and answering the questions should take approximately 4 hours.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Web Media: Khan Academy’s “Binomial Distribution”

  Link: Khan Academy’s “Binomial Distribution” (YouTube)
   
  Instructions: Watch these videos on binomial distributions. These videos introduce binomial probabilities and show how to graph them, and elaborate on binomial distribution in the context of basketball examples.
   
  Watching these videos and pausing to take notes should take approximately 1 hour and 30 minutes.
   
  Terms of Use: These resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. They are attributed to Khan Academy.

• Web Media: Khan Academy’s “Expected Value of Binomial Distribution”

  Link: Khan Academy’s “Expected Value of Binomial Distribution” (YouTube)
   
  Instructions: Watch this video, which explains how to compute the mean of a binomial distribution.
   
  Watching this video and pausing to take notes should take approximately 30 minutes.
  
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

2.2.2 Normal Distribution  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 7, Section 3: History,” “Section 4: Areas of Normal Distributions,” “Section 6: Standard Normal,” and “Section 7: Normal Approximation to the Binomial”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 7, Section 3: History” (HTML), “Section 4: Areas of Normal Distributions” (HTML), “Section 6: Standard Normal” (HTML), and “Section 7: Normal Approximation to the Binomial” (HTML)
   
  Instructions: Read sections 3, 4, 6, and 7 from chapter 7. Also, complete the questions at the end of each section. Section 3 briefly talks about the history of both the normal distribution and the central limit theorem, and this section also discusses the relation of normal distributions to errors. Section 4 discusses ways of computing the areas under the normal curve. Section 6 discusses the standard normal distribution and the related areas under the standard normal curve. Regarding the calculation of areas, Section 6 also discusses how to translate from non-standard normal to standard normal. Section 7 addresses how to compute (cumulative) binomial probabilities by using normal approximations.
   
  Reading these sections and answering the questions should take approximately 1 hour and 30 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Interactive Lab: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 7, Normal Distribution – Section 5: Varieties Demonstration”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 7, Normal Distribution – Section 5: Varieties Demonstration” (HTML)
   
  Instructions: Follow the instructions to run the simulation to see the relationship between the mean and standard deviation of a distribution and its shape. 
   
  Completing this interactive lab should take approximately 30 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Reading: Introductory Statistics: “Chapter 5, Section 2: The Standard Normal Distribution”

  Link: Introductory Statistics: “Chapter 5, Section 2: The Standard Normal Distribution” (PDF)
   
  Instructions: Read section 2 from chapter 5 on pages 215–225. This section talks about standard normal curve and how to compute certain areas underneath the curve. This section also contains numerous exercises and examples. Complete the odd-numbered exercises for this section before checking the answers.
   
  Reading this section and completing the exercises should take approximately 1 hour and 30 minutes.
   
  Terms of Use: This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-Share-Alike 3.0 License without attribution as requested by the work’s original creator or licensee.

• Web Media: Khan Academy’s “Introduction to the Normal Distribution”

  Link: Khan Academy’s “Introduction to the Normal Distribution” (YouTube)
   
  Instructions: Watch this video on normal distribution. This video introduces normal distribution and its density curve and explains how to read the areas underneath the normal curve. It also touches on the central limit behavior.  
   
  Watching this video and pausing to take notes should take approximately 1 hour.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

Unit 3: Sampling Distributions  

The concept of sampling distribution lies at the very foundation of statistical inference. It is best to introduce sampling distribution using an example here. Suppose you want to estimate a parameter of a population, say the population mean. There are two natural estimators: 1. sample mean, which is the average value of the data set; and 2. median, which is the middle number when the measurements are arranged in ascending (or descending) order. In particular, for a sample of even size n, the median is the mean of the middle two numbers. But which one is better, and in what sense? This involves repeated sampling, and you want to choose the estimator that would do better on average. It is clear that different samples may give different sample means and medians; some of them may be closer to the truth than the others. Consequently, we cannot compare these two sample statistics or, in general, any two sample statistics on the basis of their performance with a single sample. Instead, you should recognize that sample statistics are themselves random variables; therefore, sample statistics should have frequency distributions by taking into account all possible samples. In this unit, you will study the sampling distribution of several sample statistics. This unit will show you how the central limit theorem can help to approximate sampling distributions in general.  

Unit 3 Time Advisory   show close


Unit 3 Learning Outcomes   show close


3.1 The Concept of Sampling Distributions  

3.1.1 Continuous Random Variables  

• Reading: Introductory Statistics: “Chapter 5, Section 1: Continuous Random Variables, Section 3: Probability Computations for General Normal Random Variables, and Section 4: Areas of Tails of Distributions”

  Link: Introductory Statistics: “Chapter 5, Section 1: Continuous Random Variables, Section 3: Probability Computations for General Normal Random Variables, and Section 4: Areas of Tails of Distributions” (PDF)
   
  Instructions: From chapter 5, read section 1 on pages 204–214 and sections 3 and 4 on pages 225–251. Section 1 talks about how to describe continuous distributions and compute related probabilities, including some basic facts about the normal distribution. Section 3 talks about how to compute probabilities related to any normal random variable. This section has many examples illustrating the usage of z-score transformations. Section 4 defines tail probabilities and illustrates how to find them. Complete the odd-numbered exercises at the end of each section before checking the answers.
   
  Reading these sections and completing the exercises should take approximately 3 hours and 30 minutes.
   
  Terms of Use: This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-Share-Alike 3.0 License without attribution as requested by the work’s original creator or licensee.

3.1.2 Definition and Interpretation  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 9, Section 2: Introduction”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 9, Section 2: Introduction” (HTML)
   
  Instructions: Read section 2 from chapter 9. Also, complete the questions at the end. Section 2 introduces sampling distribution by using a concrete, discrete example, followed by a continuous example. This section also discusses sampling distributions’ relationship to inferential statistics.
   
  Reading this section and answering the questions should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

3.1.3 Sampling Distributions Properties  

• Interactive Lab: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 9, Section 3: Basic Demo,” “Section 4: Sample Size Demo,” and “Section 5: CLT Demo”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 9, Section 3: Basic Demo” (HTML), “Section 4: Sample Size Demo” (HTML), and “Section 5: CLT Demo” (HTML)
   
  Instructions: Watch the videos for sections 3–5 from chapter 9, and follow the instructions to run the simulations for each section. Section 3 further illustrates the concept of sampling distribution by using video demos. Section 4 demonstrates how the sampling distributions may depend on the sample sizes and the properties of populations. Section 5 discusses the central limit behavior when the sample size increases.
   
  Completing this interactive lab should take approximately 4 hours.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

3.2 Sampling Distributions for Common Statistics  

3.2.1 The Sampling Distribution of Sample Mean  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 9, Section 6: Sampling Distribution of the Mean” and “Section 7: Differences between Means”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 9, Section 6: Sampling Distribution of the Mean” (HTML) and “Section 7: Differences between Means” (HTML)
   
  Instructions: Read sections 6 and 7 from chapter 9. Also, complete the questions at the end of each section. Section 6 discusses the mean and variance of the sampling distribution of the mean. This section also shows how central limit theorem can help to approximate the corresponding sampling distributions. Section 7 talks about the properties of the sampling distribution for differences between means by giving the formulas of both mean and variance for the sampling distribution. Using the central limit theorem, it also talks about how to compute the probability of a difference between means being beyond a specified value.
   
  Reading these sections and answering the questions should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Reading: Introductory Statistics: “Chapter 6, Section 1: The Mean and Standard Deviation of the Sample Mean and Section 2: The Sampling Distribution of the Sample Mean”

  Link: Introductory Statistics: “Chapter 6, Section 1: The Mean and Standard Deviation of the Sample Mean and Section 2: The Sampling Distribution of the Sample Mean” (PDF)
   
  Instructions: Read sections 1 and 2 from chapter 6 on pages 252–270. Section 1 presents several concrete examples to calculate the exact distributions of the sample mean. Based on these distributions, the corresponding means and standard deviations are computed for demonstrations. Section 2 concerns the sampling distributions of the sample means when the sample size is large. The case when the population is normal is also considered. The central limit theorem is used for large sample approximations. Complete the odd-numbered exercises at the end of each section before checking the answers.
   
  Reading these sections and completing the exercises should take approximately 2 hours.
   
  Terms of Use: This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-Share-Alike 3.0 License without attribution as requested by the work’s original creator or licensee.

• Web Media: Khan Academy’s “Central Limit Theorem”

  Link: Khan Academy’s “Central Limit Theorem” (YouTube)
   
  Instructions: Watch this video, which explains how the central limit theorem can help to approximate the sampling distributions of sample means.
   
  Watching this video and pausing to take notes should take approximately 30 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

• Web Media: Khan Academy’s “Sampling Distribution of the Mean”

  Link: Khan Academy’s “Sampling Distribution of the Mean” (YouTube)
   
  Instructions: Watch this video on the sampling distribution of sample means.
   
  Watching this video and pausing to take notes should take approximately 30 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

• Web Media: Khan Academy’s “Standard Error of the Mean”

  Link: Khan Academy’s “Standard Error of the Mean” (YouTube)
   
  Instructions: Watch this video, which explains the standard errors of the sampling distribution.
   
  Watching this video and pausing to take notes should take approximately 30 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

3.2.2 The Sampling Distribution of Pearson’s r  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 9, Section 8: Sampling Distribution of r”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 9, Section 8: Sampling Distribution of r” (HTML)
   
  Instructions: Read section 8 from chapter 9. Also, complete the questions at the end. Section 8 talks about how the shape of the sampling distribution of Pearson correlation deviates from normality and then discusses how to transform r to a normally distributed quantity. Furthermore, this section talks about how to calculate the probability of obtaining an r above a specified value.
   
  Reading this section and answering the questions should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

3.2.3 The Sampling Distribution of the Sample Proportion  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 9, Section 9: Sampling Distribution of p”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 9, Section 9: Sampling Distribution of p” (HTML)
   
  Instructions: Read section 9 from chapter 9. Also, complete the questions at the end. Section 9 introduces the mean and standard deviation of the sampling distribution of p, and this section discusses the relationship between the sampling distribution of p and the normal distribution.
   
  Reading this section and answering the questions should take approximately 45 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Web Media: Sophia: Tracy P’s “Determining Standard Deviation”

  Link: Sophia: Tracy P’s “Determining Standard Deviation” (Flash)
   
  Instructions: To enhance your understanding, watch this video on determining standard deviation.
   
  Watching the video several times as needed and pausing to take notes should take approximately 15 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

Unit 4: Estimation with Confidence Intervals  

In this unit, you will learn how to use the central limit theorem and confidence intervals, the latter of which enables you to estimate unknown population parameters. The central limit theorem provides us with a way to make inferences from samples of non-normal populations. This theorem states that given any population, as the sample size increases, the sampling distribution of the means approaches a normal distribution. This powerful theorem allows us to assume that given a large enough sample, the sampling distribution will be normally distributed. 
 
You will also learn about confidence intervals, which provide you with a way to estimate a population parameter. Instead of giving just a one-number estimate of a variable, a confidence interval gives a range of likely values for it. This is useful, because point estimates will vary from sample to sample, so an interval with certain confidence level is better than a single point estimate. After completing this unit, you will know how to construct such confidence intervals and the level of confidence.  

Unit 4 Time Advisory   show close


Unit 4 Learning Outcomes   show close


4.1 Point Estimators and Their Characteristics  

4.1.1 Sample Statistics and Parameters  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 10, Section 2: Introduction” and “Section 3: Degrees of Freedom”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 10, Section 2: Introduction” (HTML) and “Section 3: Degrees of Freedom” (HTML)
   
  Instructions: Read sections 2 and 3 from Chapter 10. Also, complete the questions in each section. Section 2 explains the basic concepts of sample statistics and population parameters as well as the basic goal of estimation for which point estimates and interval estimates are introduced. Section 3 talks about the degree of freedom, which is defined as the number of independent pieces of information on which a point estimate is based. Section 3 also talks about variance, a quantity depending on the degrees of freedom.
   
  Reading these sections and answering the questions should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

4.1.2 Bias and Sampling Variability  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 10, Section 4: Characteristics of Estimators”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 10, Section 4: Characteristics of Estimators” (HTML)
   
  Instructions: Read section 4 from Chapter 10. Also, complete the questions at the end. Section 4 discusses two important characteristics used as point estimates of parameters: bias and sampling variability.Bias refers to whether an estimator tends to over or underestimate the parameter. Sampling variability refers to how much the estimate varies from sample to sample.
   
  Reading this section and answering the questions should take approximately 30 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Interactive Lab: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 10, Section 5: Bias and Variability Simulation”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 10, Section 5: Bias and Variability Simulation” (HTML)
   
  Instructions: Select the “Show Simulation” button to launch the simulation. Follow the general instructions to complete the simulation. This simulation demonstrates bias and variability. Please note that you may ignore this website's reference to questions that you must answer before accessing this simulation, and you do not need to answer any questions as part of this resource.
   
  Completing this interactive lab should take approximately 2 hours.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

4.2 Confidence Intervals  

4.2.1 Confidence Intervals for Mean  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 10, Section 7: Confidence Intervals Introduction,” “Section 8: Confidence Interval for Mean,” “Section 9: t-Distribution,” and “Section 11: Confidence Intervals on Difference between Means”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 10, Section 7: Confidence Intervals Introduction” (HTML) “Section 8: Confidence Interval for Mean” (HTML), “Section 9: t-Distribution” (HTML), and “Section 11: Confidence Intervals on Difference between Means” (HTML)
   
  Instructions: Read sections 7, 8, 9, and 11 from Chapter 10. Also, answer the questions at the end of each section. Section 7 explains the need for confidence intervals and why a confidence interval is not the probability the interval contains the parameter. Section 8 explains how to compute a confidence interval on the mean when sigma is unknown and needs to be estimated. For this purpose, it also explains when to use t-distribution or a normal distribution. Section 9 states the difference between the shape of the t distribution and the normal distribution, and this section also explains how this difference is affected by degrees of freedom. Section 11 explains the procedure to compute a confidence interval on the difference between means.
   
  Reading these sections and answering the questions should take approximately 2.5 hours.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.

• Interactive Lab: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 10, Section 10: Confidence Interval Simulation”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 10, Section 10: Confidence Interval Simulation” (HTML)
   
  Instructions: Review the illustrated instructions, and follow the general instructions to complete this simulation. This interactive lab will help you develop a basic understanding of the properties of a sampling distribution, based on the properties of the population.
   
  Completing this interactive lab should take approximately 1.5 hours.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Interactive Lab: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 12, Section 3: t Distribution Demo”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 12, Section 3: t Distribution Demo” (HTML)
   
  Instructions: Watch the video demo, and follow the instructions to run the simulation in order to see how the degrees of freedom affect the difference between t and normal distributions.
   
  Completing this interactive lab should take approximately 15 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

4.2.2 Confidence Intervals for Correlation and Proportion  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 10, Section 12: Correlation” and “Section 13: Proportion”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 10, Section 12: Correlation” (HTML) and “Section 13: Proportion” (HTML)
   
  Instructions: Read sections 12 and 13 from Chapter 10. Also, complete the questions at the end of each section. Section 12 shows how to compute a confidence interval for Pearson’s correlation; the solution lies in using Fisher’s z transformation. Section 13 explains the procedure to compute confidence intervals for population proportions, where the sampling distribution needs a normal approximation.
   
  Reading these sections and answering the questions should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.

• Web Media: Khan Academy’s “Confidence Interval Example”

  Link: Khan Academy’s “Confidence Interval Example” (YouTube)
   
  Instruction: Watch this video on confidence intervals. This video concerns confidence intervals for means in general. This video also explains the standard errors of the sampling distributions.
   
  Watching this video and pausing to take notes should take approximately 45 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

• Web Media: Khan Academy’s “Small Sample Size Confidence Intervals”

  Link: Khan Academy’s “Small Sample Size Confidence Intervals” (YouTube)
  
  Instructions: Watch this video on confidence intervals. This video focuses on the setting of small sample size. This video also explains the standard errors of the sampling distributions.
   
  Watching this video lecture and pausing to take notes should take approximately 30 minutes.
  
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

Unit 5: Hypothesis Test  

A hypothesis test involves collecting and evaluating data from a sample. The data gathered and evaluated is then used to make a decision as to whether or not the data supports the claim that is made about the population. This unit will teach you how to conduct hypothesis tests and how to identify and differentiate between the errors associated with them. 
 
Many times, you need answers to questions in order to make efficient decisions. For example, a restaurant owner might claim that his restaurant’s food costs 30% less than other restaurants in the area, or a phone company might claim that its phones last at least one year more than phones from other companies. In order to decide whether it would be more affordable to eat at the restaurant that “costs 30% less” or another restaurant in the area, or in order to decide which phone company to choose based on the durability of the phone, you will have to collect data to justify these claims. The process of hypothesis testing is a way of decision-making. In this unit, you will learn to establish your assumptions through null and alternative hypotheses. The null hypothesis is the hypothesis that is assumed to be true and the hypothesis you hope to nullify, while the alternative hypothesis is the research hypothesis that you claim to be true. This means that you need to conduct the correct tests to be able to accept or reject the null hypothesis. You will learn how to compare sample characteristics to see whether there is enough data to accept or reject the null hypothesis.

Unit 5 Time Advisory   show close


Unit 5 Learning Outcomes   show close


5.1 Elements of Hypothesis Testing  

5.1.1 Setting up Hypotheses  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 11, Section 2: Introduction,” “Section 4: Type I and II Errors,” and “Section 5: One- and Two-Tailed Tests”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 11, Section 2: Introduction” (HTML), “Section 4: Type I and II Errors” (HTML), and “Section 5: One- and Two-Tailed Tests” (HTML)
   
  Instructions: Read sections 2, 4, and 5 from Chapter 11, and complete the questions at the end of each section. Section 2 discusses the logic behind hypothesis testing using concrete examples and explains how to set up null and alternative hypothesis. Section 4 explains what Type I and II errors are and how they can occur. Section 5 introduces one-tailed and two-tailed tests and explains which one should be used for the testing purpose.
   
  Reading these sections and completing the questions should take approximately 1.5 hours.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

5.1.2 Interpreting Hypotheses Testing Results  

• Reading: Introductory Statistics: “Chapter 8, Section 3: The Observed Significance of a Test“

  Link: Introductory Statistics: “Chapter 8, Section 3: The Observed Significance of a Test”(PDF)
   
  Instructions: Read section 3 from Chapter 8 on pages 356–367. This section explains what the observed significance of a test is; in particular, this reading tells us how to compute it and use it in the p-value approach. Study the examples, and complete the odd-numbered exercises at the end of the section before checking the answers.
   
  Reading this section and completing the exercises should take approximately 1.25 hours.
   
  Terms of Use: This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-Share-Alike 3.0 License without attribution as requested by the work’s original creator or licensee.

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 11, Section 6: Significant Results” and “Section 7: Non-Significant Results”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 11, Section 6: Significant Results” (HTML) and “Section 7: Non-Significant Results” (HTML)
   
  Instructions: Read sections 6 and 7 from Chapter 11, and complete the questions at the end of each section. Section 6 discusses whether rejection of the null hypothesis should be an all-or-none proposition. Section 7 discusses how to interpret non-significant results; for example, it explains why the null hypothesis should not be accepted, or accepted with caution. This section also describes how a non-significant result can increase confidence that the null hypothesis is false.
   
  Reading these sections and completing the questions should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Reading: Missouri State University: David W. Stockburger’s Introductory Statistics: Concepts, Models, and Applications: “Errors in Hypothesis Testing”

  Link: Missouri State University: David W. Stockburger’s Introductory Statistics: Concepts, Models, and Applications: “Errors in Hypothesis Testing” (HTML)
   
  Instructions: Read this section, which talks about two types of errors in hypothesis testing, using numerous examples.
   
  Studying this section should take approximately 45 minutes.
   
  Terms of Use: This resource is in the public domain.

• Web Media: Khan Academy’s “Hypothesis Testing and P-Values”

  Link: Khan Academy’s “Hypothesis Testing and P-Values” (YouTube)
   
  Instruction: Watch this video on hypothesis testing. In particular, this video talks about using examples to set up hypothesis and compute p-values.
   
  Watching this video and pausing to take notes should take approximately 30 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

• Web Media: Khan Academy’s “One-Tailed and Two-Tailed Tests”

  Link: Khan Academy’s “One-Tailed and Two-Tailed Tests” (YouTube)
   
  Instructions: Watch this video on hypothesis testing. In particular, this video distinguishes one-tailed and two-tailed tests.
   
  Watching this video and pausing to take notes should take approximately 15 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

5.1.3 Steps in Hypothesis Testing and Its Relation to Confidence Intervals  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 11, Section 8: Steps in Hypothesis Testing” and “Section 9: Confidence Intervals”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 11, Section 8: Steps in Hypothesis Testing” (HTML) and “Section 9: Confidence Intervals” (HTML)
   
  Instructions: Read sections 8 and 9 from Chapter 11. Also, complete the questions at the end of each section. Section 8 lists four key steps in hypothesis testing. Section 9 explains the close relationship between confidence intervals and significance tests. 
   
  Reading these sections and answering the questions should take approximately 45 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Web Media: Sophia: Al Greene’s “Hypothesis Testing”

  Link: Sophia: Al Greene’s “Hypothesis Testing” (YouTube)
   
  Instructions: Watch the videos titled “Significance Level in Hypothesis Testing” and “Hypothesis Testing Example.” The first video shows you how to make a decision in a hypothesis test based on the significance level of critical values. The second video provides an example of a left tailed hypothesis test.
   
  Watching these videos and pausing to take notes should take approximately 30 minutes.
  
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Al Greene, and the original versions can be found here.

5.2 Tests of Population Means  

5.2.1 Testing Single Mean  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 12, Section 2: Single Mean”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 12, Section 2: Single Mean” (HTML)
   
  Instructions: Read section 2 from Chapter 12. This section shows how to test the null hypothesis that the population mean is equal to some hypothesized value, using a very concrete example. In this example, all the main elements of hypothesis testing come in to play a role. There are 9 questions at the end of the section to help your understanding of the material.
   
  Reading this section and answering the questions should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Reading: Introductory Statistics: “Chapter 8, Section 2: Large Sample Tests for a Population Mean, Section 4: Small Sample Tests for a Population Mean, and Section 5: Large Sample Tests for a Population Proportion”

  Link: Introductory Statistics: “Chapter 8, Section 2: Large Sample Tests for a Population Mean, Section 4: Small Sample Tests for a Population Mean, and Section 5: Large Sample Tests for a Population Proportion” (PDF)
   
  Instructions:Read the section 2 on page 346–356, and then read sections 4 and 5 on pages 368–393. Complete the odd-numbered problems at the end of each section before checking your answers.
   
  Section 2 talks about how to use the central limit theorem to test a population mean when the sample size is large. It also addresses how to interpret the test results in the application background. Section 4 discusses testing a population mean when the sample size is small. This section outlines a five-step testing procedure and then illustrates this procedure with an example. Study the example carefully and complete the relevant exercises and applications. Section 5 talks about large sample tests for a population proportion. Both the critical value and p-value approach are introduced based on a standardized test statistic. Once again, this section illustrates the five-step testing procedure in Examples 12–15.  
   
  Reading these sections and completing the exercises should take approximately 3 hours.
   
  Terms of Use: This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-Share-Alike 3.0 License without attribution as requested by the work’s original creator or licensee.

5.2.2 Testing the Difference between Two Means  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 12, Section 4: Difference between Two Means”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 12, Section 4: Difference between Two Means” (HTML)
   
  Instructions: Read section 4 from Chapter 12. Also, answer the questions at the end of this section. This section covers how to test for differences between means from two separate groups of subjects. This reading presents an example of opinions on animal research, and the main interest is to test for gender difference at the population level. The detailed testing procedure is carried out by using the standard steps in hypothesis testing.
   
  Reading this section and answering the questions should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Web Media: Khan Academy’s “Difference of Sample Means Distribution”

  Link: Khan Academy’s “Difference of Sample Means Distribution” (YouTube)
   
  Instruction: Watch this video on the difference of means. This lecture talks about the difference of sample means distribution.
   
  Watching this video and pausing to take notes should take approximately 30 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original versions can be found here.

• Web Media: Khan Academy’s “Hypothesis Tests for Difference of Means”

  Link: Khan Academy’s “Hypothesis Tests for Difference of Means” (YouTube)
   
  Instructions: Watch this video on the difference of means. In particular, this video addresses some of the testing issues for the difference of means.
   
  Watching this video and pausing to take notes should take approximately 30 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original versions can be found here.

5.3 Chi-Square Distribution (Optional)  

This optional subunit will introduce you to chi-distributions and their applications, including testing goodness of fit.

• Optional Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 17, Section 2: Chi-Square Distribution” and “Chapter 17, Section 3: One-Way Tables (Testing Goodness of Fit)” (HTML)

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 17, Section 2: Chi-Square Distribution” and “Chapter 17, Section 3: One-Way Tables (Testing Goodness of Fit)” (HTML)
   
  Instructions: Read these two sections, which discuss chi-square distributions and how to test goodness of fit. Also, answer the questions at the end of each section. While these sections are optional, studying them may help you if you wish to take the credit-aligned exam that is linked with this course.
   
  Reading these sections and answering the questions should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Optional Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 17, Section 5: Contingency Tables” (HTML)

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 17, Section 5: Contingency Tables” (HTML)
   
  Instructions: Read this section, which discusses contingency tables, and answer the questions at the end of the section. While this section is optional, studying it may help you if you wish to take the credit-aligned exam that is linked with this course.
   
  Reading this and answering the questions should take approximately 30 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Optional Web Media: Khan Academy’s “Chi-square Distribution Introduction”, “Pearson's Chi Square Test (Goodness of Fit)”, and “Contingency Table Chi-Square Test”

  Link: Khan Academy’s “Chi-square Distribution Introduction”, “Pearson's Chi Square Test (Goodness of Fit)”, and “Contingency Table Chi-Square Test” (YouTube)
  
  Instructions: Watch these videos, which discuss chi-square distributions, goodness of fit, and contingency tables. While these videos are optional, studying these topics may help you if you are interested in taking the credit-aligned exam that is linked with this course.
   
  Watching these videos and pausing to take notes should take approximately 1 hour.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to the Khan Academy.

5.4 Comparing the Proportions of Populations (Optional)  

• Optional Web Media: Khan Academy’s “Comparing Population Proportions 1”, “Comparing Population Proportions 2”, and “Hypothesis Test Comparing Population Proportions”

  Link: Khan Academy’s “Comparing Population Proportions 1”, “Comparing Population Proportions 2”, and “Hypothesis Test Comparing Population Proportions” (YouTube)
  
  Instructions: Watch these videos, which discuss comparing population proportions. While these videos are optional, studying these topics may help you if you are interested in taking the credit-aligned exam that is linked with this course.
   
  Watching these videos and pausing to take notes should take approximately 1 hour.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to the Khan Academy.

Unit 6: Linear Regression  

In this unit, we will discuss situations in which the mean of a population, treated as a variable, depends on the value of another variable. One of the main reasons why we conduct such analyses is to understand how two variables are related to each other. The most common type of relationship is a linear relationship. For example, you may want to know what happens to one variable when you increase or decrease the other variable. You want to answer questions such as, “Does one variable increase as the other increases, or does the variable decrease?” For example, you may want to determine how the mean reaction time of rats depends on the amount of drug in bloodstream. 
 
In this unit, you will also learn to measure the degree of a relationship between two or more variables. Both correlation and regression are measures for comparing variables. Correlation quantifies the strength of a relationship between two variables and is a measure of existing data. On the other hand, regression is the study of the strength of a linear relationship between an independent and dependent variable and can be used to predict the value of the dependent variable when the value of the independent variable is known.

Unit 6 Time Advisory   show close


Unit 6 Learning Outcomes   show close


6.1 The Regression Model  

6.1.1 Scatter Plot of Two Variables and Regression Line  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 14, Section 2: Introduction to Linear Regression”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 14, Section 2: Introduction to Linear Regression” (HTML)
   
  Instructions: Read section 2 from Chapter 14. Also, answer the questions at the end. Section 2 defines simple linear regression, introduces scatter plot to reveal linear patterns, and then talks about prediction error. This section also talks about how to compute regression line by minimizing squared errors.
   
  Reading this section and answering the questions should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Reading: Missouri State University: David W. Stockburger’s Introductory Statistics: Concepts, Models, and Applications: “Regression Models”

  Link: Missouri State University: David W. Stockburger’s Introductory Statistics: Concepts, Models, and Applications: “Regression Models” (HTML)
   
  Instructions: Read this section on regression models. This section elaborates more on regression models by discussing least squares criterion and confidence intervals.
   
  Reading this section should take approximately 1.5 hours.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Interactive Lab: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 14, Section 3: Linear Fit Demo”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 14, Section 3: Linear Fit Demo” (HTML)
   
  Instructions: Watch the video demo, and follow the instructions to launch the simulation. Section 3 is devoted to linear fit demonstration; this simulation allows you to change the regression line and examine the effects on the errors of prediction.
   
  Completing this interactive lab should take approximately 1.5 hours.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

6.1.2 Correlation Coefficient  

• Reading: Missouri State University: David W. Stockburger’s Introductory Statistics: Concepts, Models, and Applications: “Correlation”

  Link: Missouri State University: David W. Stockburger’s Introductory Statistics: Concepts, Models, and Applications: “Correlation” (HTML)
   
  Instructions: Read this section on correlation. You will learn the interpretation and calculation of correlation coefficient, correlation matrix, and the relation between correlation and causation.  
   
  Reading this section should take approximately 1 hour.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Reading: Introductory Statistics: “Chapter 10, Section 2: The Linear Correlation Coefficient”

  Link: Introductory Statistics: “Chapter 10, Section 2: The Linear Correlation Coefficient” (PDF)
   
  Instructions: Read section 2 of Chapter 10 on pages 485–499 for a discussion on linear correlation. You will learn what the linear correlation coefficient is, how to compute it, and what it tells us about the relationship between two variables x and y.   
   
  Reading this section and completing the exercises should take approximately 1.25 hours.
   
  Terms of Use: This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-Share-Alike 3.0 License without attribution as requested by the work’s original creator or licensee.

6.1.3 Sums of Squares  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 14, Section 4: Partitioning Sums of Squares”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 14, Section 4: Partitioning Sums of Squares” (HTML)

   

  Instructions: Read section 4 from Chapter 14. Also, answer the questions at the end of the section. Section 4 further discusses the sums of squares, including partitioning sum of squares into sums of squares predicted and sum of squares error. 

   

  Reading this section and answering the questions should take approximately 45 minutes.

   

  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Web Media: Khan Academy’s “Squared Error of Regression Line”

  Link: Khan Academy’s “Squared Error of Regression Line” (YouTube)
   
  Instruction: Watch this video, which talks about the squared error of regression line.
   
  Watching this video and pausing to take notes should take 15 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

• Web Media: Khan Academy’s “Regression Line Example”

  Link: Khan Academy’s “Regression Line Example” (YouTube)
   
  Instructions: Watch this video, which talks about the least squares estimates of both the intercept and the slope. This video also shows how to compute them by using examples. 
   
  Watching this video and pausing to take notes should take approximately 30 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to Khan Academy, and the original version can be found here.

6.2 Fitting the Model  

6.2.1 Standard Errors of the Least Squares Estimates  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 14, Section 5: Standard Error of the Estimate”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 14, Section 5: Standard Error of the Estimate” (HTML)
   
  Instructions: Read section 5 from Chapter 14. Also, answer the questions at the end. Section 5 discusses how to compute the standard error of the estimate based on errors of prediction as well as how to compute the standard error of the estimate based on a sample.
   
  Reading this section and answering the questions should take approximately 45 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

6.2.2 Statistical Inference for the Slope and Correlation  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 14, Section 7: Inferential Statistics for b and r”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 14, Section 7: Inferential Statistics for b and r” (HTML)
   
  Instructions: Read section 7 from Chapter 14. Also, answer the questions at the end. Section 7 starts with assumptions on the errors that are necessary for statistical inference. Then, this reading shows an example of a significance test for the slope. This section also talks about constructing confidence intervals for the slope. Then, it closes with a significance test for the correlation.
   
  Reading this section and answering the questions should take approximately 45 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Reading: Introductory Statistics: “Chapter 10, Section 5: Statistical Inference about Slope”

  Link: Introductory Statistics: “Chapter 10, Section 5: Statistical Inference about Slope” (PDF)
   
  Instructions: Read section 5 from Chapter 10 on pages 520–532. This section further details two types of inferences on the slope parameter, considering both confidence intervals and hypothesis testing. Complete the odd-numbered exercises at the end of the section before checking your answers.
   
  Reading this section and answering the questions should take approximately 1.5 hours.
   
  Terms of Use: This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-Share-Alike 3.0 License without attribution as requested by the work’s original creator or licensee.

6.2.3 Influential Observations  

• Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 14, Section 8: Influential Observations”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 14, Section 8: Influential Observations” (HTML)
   
  Instructions: Read section 8 from Chapter 14. Also, answer the questions at the end. Section 8 discusses the notion of influence and describes what makes a point influential. It further introduces the concepts of leverage and distance, which are useful to detect influential observations.   
   
  Reading this section and answering the questions should take approximately 45 minutes.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Reading: Introductory Statistics “Chapter 10, Section 8: A Complete Example”

  Link: Introductory Statistics: “Chapter 10, Section 8: A Complete Example” (PDF)
   
  Instructions: Read section 8 from Chapter 10 on pages 551–560. This section presents a complete example on linear regression, starting from presenting the data, then proceeds to a scatter plot to identify the linear pattern, and fits a linear model using least squares estimation. This reading also addresses some statistical inferences on both correlation coefficient and slope parameter. Complete the odd-numbered exercises at the end of the section before checking the answers.
   
  Reading this section and completing the exercises should take approximately 1 hour.
   
  Terms of Use: This text was adapted by The Saylor Foundation under a Creative Commons Attribution-NonCommercial-Share-Alike 3.0 License without attribution as requested by the work’s original creator or licensee.

6.3 ANOVA (Optional)  

This optional subunit will teach you about “Analysis of Variance" (abbreviated ANOVA), which is used for hypothesis tests involving more than two averages. ANOVA is about examining the amount of variability in the y variable and trying to see where that variability is coming from. You will study the simplest form of ANOVA, called single factor or one-way ANOVA. Finally, you will briefly study the F distribution, used for ANOVA, and the test of two variances.

• Optional Reading: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 15: ANOVA”

  Link: Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study: “Chapter 15: ANOVA” (HTML)
   
  Instructions: Read this chapter and complete the questions at the end of each section. While these sections are optional, studying ANOVA may help you if you are interested in taking the credit-aligned exam that is linked with this course.
   
  Reading these sections and answering the questions should take approximately 3 hours.
   
  Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

• Optional Web Media: Khan Academy’s “ANOVA 1: Calculating SST (total sum of squares)”, “ANOVA 2: Calculating SSW and SSB (total sum of squares within and between)”, and “ANOVA 3: Hypothesis test with F-statistic”

  Link: Khan Academy’s “ANOVA 1: Calculating SST (total sum of squares)”, “ANOVA 2: Calculating SSW and SSB (total sum of squares within and between)”, and “ANOVA 3: Hypothesis test with F-statistic” (YouTube)
  
  Instructions: Watch these videos, which discuss each of the steps in ANOVA. While these videos are optional, studying ANOVA may help you if you are interested in taking the credit-aligned exam that is linked with this course.
   
  Watching these videos and pausing to take notes should take approximately 45 minutes.
   
  Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to the Khan Academy.

Final Exam  

• Final Exam: The Saylor Foundation’s “MA121 Final Exam”

  Link: The Saylor Foundation’s “MA121 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 the link.
  
  Note: This exam has been designed as a practice exam for both the credit bearing StraighterLine Introduction to Statistics MAT202 exam, and the Thomas Edison State College Principles of Statistics (STA-201-TE) TECEP exam.
  
  You can register for the StraighterLine exam here. Please note that unlike The Saylor Foundation practice exam for this course, which is free, the StraighterLine version will cost $25.00, plus a $99.00 montly subscription fee. Passing this exam will make students eligible for 3 hours of college credit, transferrable to numerous colleges and universities.
  
  You can register for the TECEP exam here. Please note that the TECEP exam will cost $102.00 for in-state New Jersey residents, or $108.00 for out-of-state/international students. Passing this exam will earn students 3 hours of college credit, which can be applied to a Thomas Edison State College degree program, or potentially transfered to another college.
  
  To read more about the partnerships with StraighterLine and Thomas Edison State College, and to learn more about credit transfer opportunities and procedures for this course, go here.