PSYCH201/MA121: Introduction to Statistics « Saylor.org – Free Online Courses Built by Professors

Introduction to Statistics

Purpose of Course show close

In this course, we will look at the properties behind the basic concepts of probability and statistics and focus on applications of statistical knowledge. We will learn how statistics and probability work together. The subject of statistics involves the study of methods for collecting, summarizing, and interpreting data. Statistics formalizes the process of making decisions—and this course is designed to help you cultivate statistic literacy so that you can use this knowledge to make better decisions. Note that this course has applications in sciences, economics, computer science, finance, psychology, sociology, criminology, and many other fields. Every day, we read articles and reports in print or online. After finishing this course, you should be comfortable asking yourself whether the articles make sense. You will be able to extract information from the articles and display that information effectively. You will also be able to understand the basics of how to draw statistical conclusions. This course will begin with descriptive statistics and the foundation of statistics. You will then learn about probability and random distributions, the latter of which enables us to work with several aspects of random events and their applications. Finally, we will examine a number of ways to investigate the relationships between various characteristics of data. By the end of this course, you should have a grasp on what statistics represent, how to use them to organize and display data, and how to test the data to make effective conclusions.

Learning Outcomes show close

Upon successful completion of the course, the student will be able to:

Define the meaning of descriptive statistics and statistical inference.
Distinguish between a population and a sample.
Explain the purpose of measures of location, variability, and skewness.
Calculate probabilities.
Explain the difference between how probabilities are computed for discrete and continuous random variables.
Recognize and understand discrete probability distribution functions, in general.
Identify confidence intervals for means and proportions.
Explain how the central limit theorem applies in inference.
Calculate and interpret confidence intervals for one population average and one population proportion.
Differentiate between Type I and Type II errors.
Conduct and interpret hypothesis tests.
Compute regression equations for data.
Use regression equations to make predictions.
Conduct and interpret ANOVA (Analysis of Variance).

Course Requirements show close

In order to take this course, you must:

√ Have access to a computer

√ Have continuous broadband internet access

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

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

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

√ Be competent in the English language

√ Access to a calculator.

√ Have read the Saylor Student Handbook.

Preliminary Information

Course Resources

You may either proceed through the resource boxes below to encounter distinct chapters and videos as they should be read and viewed in the context of the course, or you may click to download all course materials now.

Course Videos (zipped mp4's, 1.6 Gb)
Course Pack (PDF, 16.6 Mb)

Unit Outline show close

1 Data and Descriptive Statistics
1.1 Introduction to Statistics
1.1.1 Statistics, Probability, and Key Terms
1.1.2 Data and Sampling
1.1.3 Variation and Frequency
1.2 Descriptive Statistics: Displaying Data
1.2.1 Stem and Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
1.2.2 Histograms
1.2.3 Box Plots
1.3 Descriptive Statistics: Measures
1.3.1 Measures of Location
1.3.2 Measures of Center
1.3.3 Skewness and the Mean, Median, and Mode
1.3.4 Measures of Spread

2 Probability Topics
2.1 Probability Overview
2.1.1 Probability Topics
2.1.2 Probability Terminology
2.2 Independent and Mutually Exclusive Events
2.3 Two Basic Rules of Probability
2.3.1 The Multiplication Rule
2.3.2 The Addition Rule
2.4 Contingency Tables, Venn Diagrams, and Tree Diagrams

3 Random Variables and Distributions
3.1 Discrete Random Variables and Discrete Probability Distributions
3.1.1 Probability Distribution Functions
3.1.2 Expected Value and Standard Deviation
3.1.3 Common Discrete Probability Distributions
3.2 Continuous Random Variables
3.2.1 Continuous Probability Functions
3.2.2 Uniform Distribution
3.2.3 Exponential Distribution
3.3 Normal Distribution
3.3.1 The Standard Normal Distribution
3.3.2 Z-scores
3.3.3 Areas to the Left and Right of X
3.3.4 Calculations of Probabilities

4 Central Limit Theorem and Confidence Intervals
4.1 The Central Limit Theorem
4.1.1 The Central Limit Theorem for Sample Means (Averages)
4.1.2 The Central Limit Theorem for Sums
4.1.3 Using the Central Limit Theorem
4.2 Confidence Intervals
4.2.1 Confidence Interval, Single Population Mean, Population Standard Deviation Known, Normal
4.2.2 Confidence Interval, Single Population Mean, Standard Deviation Unknown, Student-T
4.2.3 Confidence Interval for a Population Proportion

5 Hypothesis Testing
5.1 Hypothesis Testing: Single Mean and Single Proportion
5.1.1 Null and Alternate Hypotheses
5.1.2 Type I and Type II Errors
5.1.3 Distribution for Hypothesis Testing and More
5.2 Hypothesis Testing: Two Means, Paired Data, Two Proportions
5.2.1 Comparing Two Independent Population Means with Unknown Population Standard Deviations
5.2.2 Comparing Two Independent Population Means with Known Population Standard Deviations
5.2.3 Comparing Two Independent Population Proportions
5.2.4 Matched or Paired Samples
5.3 Chi-Square Distribution
5.3.1 Notation and Facts
5.3.2 Goodness-of-Fit Test
5.3.3 Test of Independence
5.3.4 Test of a Single Variance (Optional)

6 Correlation, Regression, and ANOVA
6.1 Linear Regression
6.1.1 Linear Equations, Slope, and Y-intercept
6.1.2 Scatter Plots
6.1.3 The Regression Equation
6.2 Correlation
6.2.1 The Correlation Coefficient
6.2.2 Prediction
6.2.3 Outliers
6.3 F-Distribution and ANOVA
6.3.1 ANOVA
6.3.2 The F Distribution and the F Ratio
6.3.3 Test of Two Variances

7 Final Exam

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Unit 1: Data and Descriptive Statistics

In today's world we access and use large volumes of data every day. The first step of data analysis is to accurately summarize this data, both graphically and numerically, so that we can understand what the data is saying. To be able to use and interpret data correctly is essential to making informed decisions. In this unit you will learn about descriptive statistics, which is used to summarize and display data. After completing this unit, you will know what you can do to present data that you have collected.

For example, suppose you are interested in buying a new mobile phone with a particular type of a camera. Suppose you are not sure about the price of any of the phones with this feature, so you log on to a website that provides you with a sample data set of prices, given your requirements. Now, looking at all the prices in the sample can sometimes be confusing. A better way to compare might be to look at the median price and the variation of prices. The median and variation are two 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 numerical and graphical ways to describe and display data. You will understand the principles of calculating common descriptive statistics for measuring center, variability, and skewness in data. You will learn to not only calculate but to interpret these measurements and graphs.

Descriptive statistics describe what the data show. Numerical descriptive measures computed from data are called statistics. Numerical descriptive measures of the population, however, are called parameters. Remember: Descriptive statistics are, as their name suggests, “descriptive.” They do not generalize beyond the data considered. Inferential statistics can be used to generalize the findings from sample data to a broader population.

Time Advisory show close

Learning Outcomes show close

1.1 Introduction to Statistics

1.1.1 Statistics, Probability, and Key Terms

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 1: Sampling and Data: “Section 1: Sampling and Data,” “Section 2: Statistics,” “Section 3: Probability,” and “Section 4: Key Terms”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 1: Sampling and Data: “Section 1: Sampling and Data” (PDF), “Section 2: Statistics” (PDF), “Section 3: Probability” (PDF), and “Section 4: Key Terms” (PDF)

Instructions: Please click on the links above, and read these sections in their entirety. Sections 1 and 2 provide a brief introduction to the field of statistics and the concepts of statistics. Section 3 introduces the concepts of probability, including some real-world examples. Finally, Section 4 presents a number of key terms related to statistical sampling and data. These readings should take you approximately one hour to complete.

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1.1.2 Data and Sampling

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 1: Sampling and Data: “Section 5: Data” and “Section 6: Sampling”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 1: Sampling and Data: “Section 5: Data” (PDF) and “Section 6: Sampling” (PDF)

Instructions: Please click on the links above, and read these sections in their entirety. Section 5 discusses the initial concepts of qualitative data, quantitative continuous data, and quantitative discrete data as used in statistics. Section 6 introduces the concept of statistical sampling. These readings should take you approximately 30 minutes to complete.

Terms of Use: This work is licensed under a Creative Commons Attribution 2.0 Generic License. It is attributed to Barbara Illowsky and Susan Dean, and the original version can be found here.

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1.1.3 Variation and Frequency

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 1: Sampling and Data: “Section 7: Variation,” “Section 8: Answers and Rounding Off,” and “Section 9: Frequency”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 1: Sampling and Data: “Section 7: Variation” (PDF), “Section 8: Answers and Rounding Off” (PDF), and “Section 9: Frequency” (PDF)

Instructions: Please click on the links above, and read these sections in their entirety. Section 7 will briefly discuss statistical variability within data and samples, Section 8 is a brief review of how you should round your answers, and Section 9 will introduce the concepts of frequency, relative frequency, and cumulative relative frequency. These readings should take you approximately one hour to complete.

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Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 1: Sampling and Data”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 1: Sampling and Data” (YouTube)

Instructions: Please click on the link above and view the lecture titled “Lecture 1: Sampling and Data” (28:52 minutes). This lecture will review the topics from Chapter 1.

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Assessment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 1 Practice: Sampling and Data”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 1: Practice: Sampling and Data” (PDF)

Instructions: Please solve problems 1-6 under the section titled “Key Terms” and problems 7-12 under the section titled “Discussion Questions.” Next, click on the hyperlink titled “Homework” and solve problems 1, 3, 5, 7, 9, 11, 16, 19, 21, and 25-27. To check your solutions, go to the end of the document. This assessment should take approximately two hours to complete.

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1.2 Descriptive Statistics: Displaying Data

1.2.1 Stem and Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Section 1: Descriptive Statistics,” “Section 2: Displaying Data,” “Section 3: Stem and Leaf Graphs (Stemplots), Line Graphs and Bar Graphs”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Section 1: Descriptive Statistics” (PDF), “Section 2: Displaying Data” (PDF), “Section 3: Stem and Leaf Graphs (Stemplots), Line Graphs and Bar Graphs” (PDF)

Instructions: Please click on the links above, and read these sections in their entirety. Section 1 provides an overview of the chapter, and in Section 2 you will see the ways graphs and charts can be used to provide visual representations of data. Section 3 introduces the use of stem-and-leaf graphs, line graphs, and bar graphs for describing a set of data visually. These readings should take you approximately one hour to complete.

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Lecture: Khan Academy’s Statistics: “Reading Pictographs,” “Reading Bar Graphs,” “Reading Line Graphs,” “Reading Pie Graphs (Circle Graphs),” “Stem-and-leaf Plots,” and “Misleading Line Graphs”
Link: Khan Academy’s Statistics: “Reading Pictographs” (YouTube), “Reading Bar Graphs” (YouTube), “Reading Line Graphs” (YouTube), “Reading Pie Graphs (Circle Graphs)” (YouTube), “Stem-and-leaf Plots” (YouTube), and “Misleading Line Graphs” (YouTube)

Instructions: Please view all six lectures in their entirety. First, view the first five lectures (approximately 16:50 minutes); these explain how to read different types of graphs and show examples of each type of graph. Then, watch the last video titled “Misleading Line Graphs” (4:53 minutes), which will give an example of a misleading line graph and how it can distort patterns and trends. Viewing these lectures and taking notes should take approximately 30 minutes to complete.

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1.2.2 Histograms

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Section 4: Histograms”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Section 4: Histograms” (PDF)

Instructions: Please click the link above and read the section in its entirety. Section 4 introduces a method of displaying data called a histogram. This reading should take you approximately 30 minutes to complete.

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1.2.3 Box Plots

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Section 5: Box Plots”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Section 5: Box Plots” (PDF)

Instructions: Please click the link above and read the section in its entirety. Section 5 discusses box plots, which give a good graphical image of the concentration a given data set. This reading should take you approximately 30 minutes to complete.

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Lecture: Khan Academy’s Statistics: “Box-and-Whisker Plots” and “Reading Box-and-Whisker Plots”
Link: Khan Academy’s Statistics: “Box-and-Whisker Plots” (YouTube) and “Reading Box-and-Whisker Plots” (YouTube)

Instructions: Please click the above link and view the lecture titled “Box-and-Whisker Plots” (10:05 minutes). In this video, you will learn about box plots, which give a good graph of the concentration of the data. Then, view the lecture titled “Reading Box-and-Whisker Plots” (3:18 minutes) to learn how to read and interpret a box plot. Viewing these lectures should take approximately 15 minutes to complete.

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1.3 Descriptive Statistics: Measures

1.3.1 Measures of Location

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Section 6: Measures of the Location of the Data”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Section 6: Measures of the Location of the Data” (PDF)

Instructions: Please click the link above and read the section in its entirety. Section 6 explains percentiles and quartiles. This reading, including the examples and problems, should take you approximately one hour to complete.

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1.3.2 Measures of Center

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Section 7: Measures of the Center of the Data”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Section 7: Measures of the Center of the Data” (PDF)

Instructions: Please click the link above and read the section in its entirety. Section 7 discusses ways to measure descriptive statistical information using the center of the data. This reading should take you approximately 30 minutes to complete.

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Lecture: Khan Academy’s Statistics: “The Average” and “Sample vs. Population Mean”
Link: Khan Academy’s Statistics: “The Average” (YouTube) and “Sample vs. Population Mean” (YouTube)

Instructions: Please click the link above and view lecture titled “The Average” in its entirety (12:35 minutes). This lecture provides an introduction to descriptive statistics and central tendency as well as ways to measure the average of a set using median, mean, and mode. Then, view the lecture titled “Sample vs. Population Mean” in its entirety (6:42 minutes). This lecture discusses the difference between the mean of a sample and the mean of a population. Viewing these lectures and taking notes as necessary should take approximately 20 minutes to complete.

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Lecture: Khan Academy’s Statistics: “Mean, Median, and Mode” and “Range and Mid-range”
Link: Khan Academy’s Statistics: “Mean, Median, and Mode” (YouTube) and “Range and Mid-range” (YouTube)

Instructions: Please view the linked lecture titled “Mean, Median, and Mode” (3:55 minutes). In this lecture, you will learn about some of the most widely used measures central tendency. Then, view the lecture titled “Range and Mid-range” (2:03 minutes) to learn how to calculate range and mid-range for a given data set. Viewing these lectures and taking notes should take less than 15 minutes to complete.

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1.3.3 Skewness and the Mean, Median, and Mode

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Section 8: Skewness and the Mean, Median, and Mode”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Section 8: Skewness and the Mean, Median, and Mode” (PDF)

Instructions: Please read the section linked above in its entirety. Section 8 discusses skewness and symmetry and how it relates to the mean, median, and mode. This reading should take you approximately 30 minutes to complete.

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1.3.4 Measures of Spread

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Section 9: Measures of the Spread of the Data”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics “Section 9: Measures of the Spread of the Data” (PDF)

Instructions: Please read the section above in its entirety. Section 9 explains standard deviation as a measure of variation in data. This reading should take you approximately 30 minutes to complete.

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Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 2: Descriptive Statistics”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 2: Descriptive Statistics” (YouTube)

Instructions: Please view the linked lecture titled “Video Lecture 2: Descriptive Statistics” (27:51 minutes) to learn how to measure and display data. You will learn how to display data numerically and graphically as well as different measures of data.

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Lecture: Khan Academy’s Statistics: “Variance of a Population,” “Sample Variance,” “Standard Deviation,” and “Alternate Variance Formulas”
Link: Khan Academy’s Statistics: “Variance of a Population” (YouTube), “Sample Variance” (YouTube), “Standard Deviation” (YouTube), and “Alternate Variance Formulas” (YouTube)

Instructions: Please view all four lectures in their entirety. First, view “Variance of a Population” (12:23 minutes). Second, watch “Sample Variance” (12:23 minutes), which explains how to estimate the variance of a population using the variance of a sample. Then, watch the video titled “Standard Deviation” (13:07 minutes), which will provide a review for what you have learned so far as well as an introduction to the standard deviation. Finally, view “Alternate Variance Formulas” (12:17 minutes) to learn alternates for the variance of a population. You should dedicate approximately one hour to viewing these lectures and taking notes.

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Assessment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Practice 1: Center of the Data” and “Practice 2: Spread of the Data”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 2: Descriptive Statistics: “Practice 1: Center of the Data” (PDF) and “Practice 2: Spread of the Data” (PDF)

Instructions: Please solve all the problems in these two sections. Next, click on the hyperlink titled “Homework” (PDF) and solve problems 1, 3, 5, 7, 9, 12, 14, 15, 17, 21, and 24-30. To check your solutions, go to the end of the document. This assessment should take you approximately three hours to complete.

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Unit 2: Probability Topics

After you have learned to describe and display data, how can you use the sample data to draw conclusions about the populations? To answer this question, you need probability, a subject we will explore over the course of this unit.

If you open a newspaper, you are likely to read headlines like: “Should risky medical procedures be allowed?”; “30% chance of a hurricane this weekend”; “Analysts expect the gas prices to increase this summer”; and “Two brothers meet by accident after being separate for more than 20 years.” All of these topics deal with everyday life and all of them have to do with probability.

The world seems to be full of apparently unpredictable events. Probability theory is a tool that was created to deal with such events more effectively. For example, before getting a surgery, patients want to know the probability that the surgery might fail; before taking medication, we want to know the probability that there will be side effects; before leaving the house, we want to know the probability that it will rain today. Probability deals with the likelihood of an event occurring. It is a measure that takes on values between 0 and 1, inclusive, with 0 representing impossible events and 1 representing certainty. The ability to calculate probability allows us to make better decisions.

Probabilities affect our everyday lives. In this unit you will learn what probability and its properties are, 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 problems. These basic probability concepts will provide a foundation for understanding more statistical concepts. You probably already (intuitively) use concepts from probability, but this unit will help you formally and precisely predict the likelihood of an event occurring given certain constraints.

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 likelihood 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. Make sure you spend time on this unit. Your goal will be to become comfortable with the basic machinery of probability theory and its applications.

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Learning Outcomes show close

2.1 Probability Overview

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 3: Probability Topics: “Section 1: Probability Topics” and “Section 2: Terminology”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 3: Probability Topics: “Section 1: Probability Topics” (PDF) and “Section 2: Terminology” (PDF)

Instructions: Please read the sections linked above in their entirety. Section 1 introduces the concept of probability, and Section 2 defines key terms related to probability. Please note that these readings cover sub-subunits 2.1.1 and 2.1.2. These readings should take you approximately one hour to complete.

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2.1.1 Probability Topics

Note: This topic is covered by the reading assigned in subunit 2.1. In particular, please focus on the Section 1 reading of Illowsky and Dean’s Collaborative Statistics.

2.1.2 Probability Terminology

Note: This topic is covered by the reading assigned in subunit 2.1. In particular, please focus on the Section 2 reading of Illowsky and Dean’s Collaborative Statistics.

2.2 Independent and Mutually Exclusive Events

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 3: Probability Topics: “Section 3: Independent and Mutually Exclusive Events”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Section 3: Independent and Mutually Exclusive Events” (PDF)

Instructions: Please read the entire section linked above in its entirety. Section 3 explains the concept of independent events, where the probability of event A does not have any effect on the probability of event B, and mutually exclusive events, where events A and B cannot occur at the same time. This reading should take you approximately one hour to complete.

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2.3 Two Basic Rules of Probability

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 3: Probability Topics: “Section 4: Two Basic Rules of Probability”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Section 4: Two Basic Rules of Probability” (PDF)

Instructions: Please read the entire section linked above in its entirety. Section 4 introduces the multiplication and addition rules used when calculating probabilities. Please note that this reading covers the topics outlined in sub-subunits 2.3.1 and 2.3.2. This reading, including examples and problems, should take you approximately one hour to complete.

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2.3.1 The Multiplication Rule

Note: This topic is covered by the reading assigned in subunit 2.3. Focus on the explanation of the multiplication rule as well as the examples and sample problems provided.

2.3.2 The Addition Rule

Note: This topic is covered by the reading assigned in subunit 2.3. Focus on the explanation of the multiplication rule as well as the examples and sample problems provided.

2.4 Contingency Tables, Venn Diagrams, and Tree Diagrams

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 3: Probability Topics: “Section 5: Contingency Tables,” “Section 6: Venn Diagrams,” and “Section 7: Tree Diagrams”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 3: Probability Topics: “Section 5: Contingency Tables” (PDF), “Section 6: Venn Diagrams” (PDF), and “Section 7: Tree Diagrams” (PDF)

Instructions: Please read these sections linked above in their entirety. Section 5 introduces the contingency table as a way of determining conditional probabilities. Section 6 discusses Venn diagrams, and Section 7 explains the utility of tree diagrams as a method for making some probability problems easier to solve. These readings should take approximately two hours to complete.

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Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 3: Probability Topics”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 3: Probability Topics” (YouTube)

Instructions: Please view the linked lecture titled “Video Lecture 3: Probability Topics” (28:05 minutes), in which you will learn about elementary probability theory.

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Assessment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 3: Probability Topics: “Practice 1: Contingency Tables” and “Practice 2: Calculating Probabilities”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 3: Probability Topics: “Practice 1: Contingency Tables” (PDF) and “Practice 2: Calculating Probabilities” (PDF)

Instructions: Please click on the links above titled “Practice 1: Contingency Tables” and “Practice 2: Calculating Probabilities.” Please solve all the problems in these two sections. Next, click on the link titled “Homework” and solve problems 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, and 28-32. To check your solutions, go to the end of the document. This assessment should take you approximately four hours to complete.

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Unit 3: Random Variables and Distributions

In the last unit, you learned how to calculate probabilities in the framework of sample spaces, outcomes, and events. In this unit, you will build on those ideas and learn about random variables. A random variable describes the outcomes of a statistical 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 is an observable that 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 4:00 pm and 5:00 pm and the amount of money 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 money they spend is an example of a continuous random variable.

In this unit, you will study probability problems involving random distributions. You will also learn about both discrete and continuous random variables and their applications. Finally, you will study an important example of a continuous distribution, the normal distribution, which is a bell-shaped distribution used widely across many disciplines.

A note from the textbook: “The values of discrete and continuous random variables can be ambiguous. For example, if X is equal to the number of miles (to the nearest mile) you drive to work, then X is a discrete random variable. You count the miles. If X is the distance you drive to work, then you measure values of X, and X is a continuous random variable. How the random variable is defined is very important.”[1]

[1] Illowsky, Barbara and Susan Dean. Collaborative Statistics. Connexions. Accessed March 22, 2010, http://cnx.org/content/col10522/1.38/.

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3.1 Discrete Random Variables and Discrete Probability Distributions

3.1.1 Probability Distribution Functions

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 4: Discrete Random Variables: “Section 1: Discrete Random Variables” and “Section 2: Probability Distribution Function (PDF) for a Discrete Random Variable”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 4: Discrete Random Variables: “Section 1: Discrete Random Variables” (PDF) and “Section 2: Probability Distribution Function (PDF) for a Discrete Random Variable” (PDF)

Instructions: Please read through each section thoroughly. Be sure to complete the activities or problems included in each reading. Section 1 provides an introduction to discrete random variables, and Section 2 examines the discrete probability distribution function and its characteristics. These readings should take you approximately 45 minutes to complete.

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Lecture: Khan Academy’s Statistics: “Introduction to Random Variables” and “Probability Density Functions”
Link: Khan Academy’s Statistics: “Introduction to Random Variables” (YouTube) and “Probability Density Functions” (YouTube)

Instructions: Please view the linked lecture titled “Introduction to Random Variables” (12:04 minutes). This lecture will provide an introduction to random variables and probability distribution functions. Then, view the “Probability Density Functions” lecture (10:02 minutes) to learn about probability density functions for continuous random variables. Viewing these lectures and taking notes should take you approximately 30 minutes to complete.

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3.1.2 Expected Value and Standard Deviation

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 4: Discrete Random Variables: “Section 3: Mean or Expected Value and Standard Deviation”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Section 3: Mean or Expected Value and Standard Deviation” (PDF)

Instructions: Please read the section linked above in its entirety. Section 3 explores the Law of Large Numbers. This reading should take you approximately 30 minutes to complete.

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Lecture: Khan Academy’s Statistics: “Expected Value: E(X)”
Link: Khan Academy’s Statistics: “Expected Value: E(X)” (YouTube)

Instructions: Please view the lecture in its entirety (approximately 15 minutes). In this lecture you will learn how to calculate expected value.

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3.1.3 Common Discrete Probability Distributions

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 4: Discrete Random Variables: “Section 4: Common Discrete Probability Distribution Functions,” “Section 5: Binomial,” “Section 6: Geometric (optional),” “Section 7: Hypergeometric (optional),” and “Section 8: Poisson”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 4: Discrete Random Variables: “Section 4: Common Discrete Probability Distribution Functions” (PDF), “Section 5: Binomial” (PDF), “Section 6: Geometric (optional)” (PDF), “Section 7: Hypergeometric (optional)” (PDF), and “Section 8: Poisson” (PDF)

Instructions: Please read the sections linked above in their entirety. Section 5 introduces characteristics of a binomial experiment and the binomial probability distribution function. Section 6 describes the geometric experiment and the geometric probability distribution. Section 7 describes the properties of a hypergeometric experiment and hypergeometric probability distribution. Section 8 describes the characteristics of a Poisson experiment and the Poisson probability distribution. These readings, including examples, should take you approximately three hours to complete.

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Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 4: Discrete Distributions”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 4: Discrete Distributions” (YouTube)

Instructions: Please view the linked lecture titled “Lecture 4: Discrete Distributions” (26:47 minutes) to learn about discrete random variables.

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Assessment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 4: Discrete Random Variables: “Practice 1: Discrete Distribution,” “Practice 2: Binomial Distribution,” “Practice 3: Poisson Distribution,” “Practice 4: Geometric Distribution,” and “Practice 5: Hypergeometric Distribution”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 4: Discrete Random Variables: “Practice 1: Discrete Distribution” (PDF), “Practice 2: Binomial Distribution” (PDF), “Practice 3: Poisson Distribution” (PDF), “Practice 4: Geometric Distribution” (PDF), and “Practice 5: Hypergeometric Distribution” (PDF)

Instructions: Click on the above links and solve all the problems in these sections. Next, click on the link titled “Homework” and solve problems 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 29, and 31. To check your solutions, go to the end of the document. Please solve all of the problems before checking the solutions. This assessment should take you approximately four hours to complete.

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Lecture: Khan Academy’s Statistics: “Binomial Distribution 1,” “Binomial Distribution 2,” “Binomial Distribution 3,” and “Binomial Distribution 4”
Link: Khan Academy’s Statistics: “Binomial Distribution 1” (YouTube), “Binomial Distribution 2” (YouTube), “Binomial Distribution 3” (YouTube), and “Binomial Distribution 4” (YouTube)

Instructions: Please view all four lectures in their entirety (approximately 47 minutes total). In the first three lectures, you will learn about the binomial distribution. In the fourth lecture, you will learn to use excel to visualize the basketball binomial distribution presented in the third video. You should dedicate approximately one hour to viewing and taking notes on these lectures.

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Lecture: Khan Academy’s Statistics: “Expected Value of Binomial Distribution”
Link: Khan Academy’s Statistics: “Expected Value of Binomial Distribution” (YouTube)

Instructions: Please view the lecture in its entirety (approximately 17 minutes). In this lecture, you will learn about the expected value of a binomial distributed random variable.

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Lecture: Lecture: Khan Academy’s Statistics: “Poisson Process 1” and “Poisson Process 2”
Link: Khan Academy’s Statistics: “Poisson Process 1” (YouTube) and “Poisson Process 2” (YouTube)

Instructions: Please view both lectures in their entirety (approximately 24 minutes total). In these lectures, you will learn about the Poisson processes and the Poisson distribution and its derivation.

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3.2 Continuous Random Variables

3.2.1 Continuous Probability Functions

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 5: Continuous Random Variables: “Section 1: Continuous Random Variables” and “Section 2: Continuous Probability Functions”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 5: Continuous Random Variables: “Section 1: Continuous Random Variables” (PDF) and “Section 2: Continuous Probability Functions” (PDF)

Instructions: Please read the sections linked above in their entirety. These sections introduce the continuous probability function. These readings should take you approximately one hour to complete.

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3.2.2 Uniform Distribution

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 5: Continuous Random Variables: “Section 3: The Uniform Distribution”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Section 3: The Uniform Distribution” (PDF)

Instructions: Please read the section linked above in its entirety. Section 3 describes the properties of the uniform distribution. This reading, including examples and problems, should take you approximately one hour to complete.

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3.2.3 Exponential Distribution

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 5: Continuous Random Variables: “Section 4: The Exponential Distribution”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 5: Continuous Random Variables: “Section 4: The Exponential Distribution” (PDF)

Instructions: Please read the section linked above in its entirety. Section 4 introduces the properties of the exponential distribution. This reading should take you approximately one hour to complete.

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Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 5: Continuous Random Variables”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 5: Continuous Random Variables” (YouTube)

Instructions: Please view the linked lecture titled “Lecture 5: Continuous Random Variables” (27:22 minutes) to learn about continuous random variables and to study two specific continuous random variables.

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Assessment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 5: Continuous Random Variables: “Practice 1: Uniform Distribution” and “Practice 2: Exponential Distribution”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 5: Continuous Random Variables: “Practice 1: Uniform Distribution” (PDF) and “Practice 2: Exponential Distribution” (PDF)

Instructions: Click on the links above titled “Practice 1: Uniform Distribution” and “Practice 2: Exponential Distribution.” Please solve all the problems in these two sections. Next, click on the link titled “Homework” and solve problems 3, 5, 7, 9, 11, 13, and 15-20. To check your solutions, go to the end of the document. Please solve all of the problems before checking the solutions. This assessment should take you approximately three and a half hours to complete.

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3.3 Normal Distribution

3.3.1 The Standard Normal Distribution

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 6: The Normal Distribution: “Section 1: The Normal Distribution” and “Section 2: The Standard Normal Distribution”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 6: The Normal Distribution: “Section 1: The Normal Distribution” (PDF) and “Section 2: The Standard Normal Distribution” (PDF)

Instructions: Please read the sections linked above in their entirety. These sections will introduce an important distribution, known as the normal distribution. These readings should take you approximately one hour to complete.

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Lecture: Khan Academy’s Statistics: “Law of Large Numbers”
Link: Khan Academy’s Statistics: “Law of Large Numbers” (YouTube)

Instructions: Please view the lecture in its entirety (9:00 minutes). In this lecture, you will learn about the law of large numbers. You should dedicate approximately 15 minutes to viewing this lecture and taking notes.

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Lecture: Khan Academy’s Statistics: “Normal Distribution Excel Exercise,” “Introduction to Normal Distribution,” and “Normal Distribution Problems: Qualitative Sense of Normal Distributions”
Link: Khan Academy’s Statistics: “Normal Distribution Excel Exercise” (YouTube), “Introduction to Normal Distribution” (YouTube), and “Normal Distribution Problems: Qualitative Sense of Normal Distributions” (YouTube)

Instructions: Please view the lectures linked above. In the lecture titled “Normal Distribution Excel Exercise” (26 minutes), you will see a presentation on a spreadsheet, which will show that the normal distribution approximates the binomial distribution for a large number of trials. Please view the other two lectures on normal distribution in their entirety (approximately 37 minutes total). You should dedicate approximately one and a half hours viewing and taking notes on the lectures.

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3.3.2 Z-scores

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 6: The Normal Distribution: “Section 3: Z-scores”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 6: The Normal Distribution: “Section 3: Z-scores” (PDF)

Instructions: Please read the section linked above in its entirety. Section 3 introduces the Z-score, which tells you how many standard deviations the value X lays above (to the right of) or below (to the left of) the mean. This reading should take you approximately 30 minutes to complete.

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Lecture: Khan Academy’s Statistics: “Normal Distribution Problems: Z-score,” “Normal Distribution Problems: Empirical Rule,” and “Standard Normal Distribution and the Empirical Rule”
Link: Khan Academy’s Statistics: “Normal Distribution Problems: Z-score” (YouTube), “Normal Distribution Problems: Empirical Rule” (YouTube), and “Standard Normal Distribution and the Empirical Rule” (YouTube)

Instructions: Please view the lectures linked above in their entirety (approximately 26 minutes total). In these lecture, you will learn about Z-scores and how to use the empirical rule (the 68-95-99.7 rule) to estimate probabilities for normal distributions.

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3.3.3 Areas to the Left and Right of X

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 6: The Normal Distribution: “Section 4: Areas to the Left and Right of x”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 6: The Normal Distribution: “Section 4: Areas to the Left and Right of x” (PDF)

Instructions: Please read the section linked above in its entirety. Section 4 shows you how to interpret probability as the area under a curve. This reading should take you less than 30 minutes to complete.

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3.3.4 Calculations of Probabilities

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 6: The Normal Distribution: “Section 5: Calculations of Probabilities”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 6: The Normal Distribution: “Section 5: Calculations of Probabilities” (PDF)

Instructions: Please read the section linked above in its entirety. Section 5 provides examples in which you will use the normal distribution to calculate probabilities. This reading, including examples and problems, should take you approximately 30 minutes to complete.

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Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 6: The Normal Distribution”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 6: The Normal Distribution” (YouTube)

Instructions: Please view the lecture titled “Lecture 6: The Normal Distribution” (26:32 minutes) to learn about the normal distribution.

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Assessment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 6: The Normal Distribution: “Practice: The Normal Distribution”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 6: The Normal Distribution: “Practice: The Normal Distribution” (PDF)

Instructions: Click on the above link titled “Practice: The Normal Distribution.” Please solve all the problems in this section. Next, click on the link titled “Homework” and solve problems 1, 3, 5, 7, 9, 11, and 12-19. To check your solutions, go to the end of the document. Please solve all of the problems before checking the solutions. This assessment should take you approximately two hours to complete.

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Unit 4: Central Limit Theorem and Confidence Intervals

In this unit, you will learn how to use the central limit theorem and confidence intervals, the latter of which enable us to estimate unknown population parameters. The central limit theorem provides us a way to make inference from samples of non-normal populations. This theorem states that given any population (regardless of whether or not it is a normal distribution), as the sample size increases, the sampling distribution of the means approaches a normal distribution. It is a powerful theorem because it allows us to assume that given a large enough sample, the sampling distribution will be normally distributed. The central limit theorem is one of the most important ideas in statistics, so be sure to spend time on it.

You will also learn about confidence intervals, which provide 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 sample results will vary from sample to sample, so a range of values is better than a one-number estimate. After completing this unit, you will know how to construct confidence intervals and calculate their margin of error. You will learn to how to come up with a range of values for a parameter and the level of confidence for the intervals.

For example, suppose you want to know the amount of soda that an average high school student in New York drinks per day. The average volume of soda for the entire population of New York high school students who drink soda is the parameter you are trying to estimate. Suppose you take a random sample and find out the average amount is 0.5 liters. Then, you also want to know how much you expect the average to vary from one sample to the next, with a certain level of confidence. The number that you use to represent this precision, i.e. to measure how close you expect your results to be to the truth, is called the margin of error.

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4.1 The Central Limit Theorem

4.1.1 The Central Limit Theorem for Sample Means (Averages)

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 7: The Central Limit Theorem: “Section 1: The Central Limit Theorem” and “Section 2: The Central Limit Theorem for Sample Means (Averages)”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 7: The Central Limit Theorem: “Section 1: The Central Limit Theorem” (PDF) and “Section 2: The Central Limit Theorem for Sample Means (Averages)” (PDF)

Instructions: Please read the sections linked above in their entirety. These sections will provide an introduction to the Central Limit Theorem, one of the most important concepts in the course. These readings should take you approximately 30 minutes to complete.

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Lecture: Khan Academy’s Statistics: “Central Limit Theorem”
Link: Khan Academy’s Statistics: “Central Limit Theorem” (YouTube)

Instructions: Please view the lecture in its entirety (approximately 10 minutes). This lecture will provide an introduction to the central limit theorem and the sampling distribution of the mean. You should spend less than 15 minutes viewing and taking notes on the lecture.

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Lecture: Khan Academy’s Statistics: “Sampling Distribution of the Sample Mean” and “Sampling Distribution of the Sample Mean 2”
Link: Khan Academy’s Statistics: “Sampling Distribution of the Sample Mean” (YouTube) and “Sampling Distribution of the Sample Mean 2” (YouTube)

Instructions: Please view both lectures, which discuss the sampling distribution of the sample mean, in their entirety (approximately 11 minutes and 13 minutes, respectively). You should spend approximately 30 minutes viewing and taking notes on the lectures.

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Lecture: Khan Academy’s Statistics: “Standard Error of the Mean” and “Sampling Distribution Example Problem”
Link: Khan Academy’s Statistics: “Standard Error of the Mean” (YouTube) and “Sampling Distribution Example Problem” (YouTube)

Instructions: Please view both lectures in their entirety (approximately 30 minutes total). These lectures will discuss the standard error of the mean, i.e. the standard deviation of the sampling distribution of the sample mean, and work out an example.

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4.1.2 The Central Limit Theorem for Sums

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 7: The Central Limit Theorem: “Section 3: The Central Limit Theorem for Sums”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 7: The Central Limit Theorem: “Section 3: The Central Limit Theorem for Sums” (PDF)

Instructions: Please read the section linked above in its entirety. Section 3 will explain the central limit theorem for sums, which says that if you keep drawing larger and larger samples and taking their sums, the sums form their own normal distribution (the sampling distribution). This reading should take you approximately 30 minutes to complete.

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4.1.3 Using the Central Limit Theorem

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 7: The Central Limit Theorem: “Section 4: Using the Central Limit Theorem”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 7: The Central Limit Theorem: “Section 4: Using the Central Limit Theorem” (PDF)

Instructions: Please read the section linked above in its entirety. Section 4 covers how and when to use the Central Limit Theorem. This reading, including examples and problems, should take you approximately one hour to complete.

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Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 7: The Central Limit Theorem”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 7: The Central Limit Theorem” (YouTube)

Instructions: Please view the lecture titled “Video Lecture 7: The Central Limit Theorem” (26:04 minutes) to study the Central Limit Theorem.

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Assessment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 7: The Central Limit Theorem: “Practice: The Central Limit Theorem”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 7: The Central Limit Theorem: “Practice: The Central Limit Theorem” (PDF)

Instructions: Click on the link titled “Practice: The Central Limit Theorem.” Please solve all the problems in this section. Next, click on the link titled “Homework” and solve problems 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19-25. To check your solutions, go to the end of the document. Please solve all of the problems before checking the solutions. This assessment should take you approximately two and a half hours to complete.

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4.2 Confidence Intervals

4.2.1 Confidence Interval, Single Population Mean, Population Standard Deviation Known, Normal

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 8: Confidence Intervals: “Section 1: Confidence Intervals” and “Section 2: Confidence Interval, Single Population Mean, Population Standard Deviation Known, Normal”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 8: Confidence Intervals: “Section 1: Confidence Intervals” (PDF) and “Section 2: Confidence Interval, Single Population Mean, Population Standard Deviation Known, Normal” (PDF)

Instructions: Please read the sections linked above in their entirety. Section 1 introduces the idea of a confidence interval, which is an estimate for an unknown population parameter. Section 2 explains how to construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known. These readings should take you approximately one hour to complete.

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Lecture: Khan Academy’s Statistics: “Confidence Interval 1”
Link: Khan Academy’s Statistics: “Confidence Interval 1” (YouTube)

Instructions: Please view the lecture in its entirety (approximately 14 minutes). In this lecture, you will learn to estimate the probability that the true population mean lies within a given range around a sample mean.

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Lecture: Khan Academy’s Statistics: “Margin of Error 1” and “Margin of Error 2”
Link: Khan Academy’s Statistics: “Margin of Error 1” (YouTube) and “Margin of Error 2” (YouTube)

Instructions: Please view both lectures in their entirety (approximately 25 minutes total). In these lectures, you will learn to find the 95% confidence interval for a problem.

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Lecture: Khan Academy’s Statistics: “Confidence Interval Example”
Link: Khan Academy’s Statistics: “Confidence Interval Example” (YouTube)

Instructions: Please view the lecture linked above (approximately 19 minutes). In this lecture, you will work out a confidence interval example.

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4.2.2 Confidence Interval, Single Population Mean, Standard Deviation Unknown, Student-T

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 8: Confidence Intervals: “Section 3: Confidence Interval, Single Population Mean, Standard Deviation Unknown, Student-T”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 8: Confidence Intervals: “Section 3: Confidence Interval, Single Population Mean, Standard Deviation Unknown, Student-T” (PDF)

Instructions: Please read the section linked above in its entirety. Section 3 explains how to construct a confidence interval for a single population mean μ, where the population standard deviation is unknown, using a Student-T distribution. This reading should take you approximately 30 minutes to complete.

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Lecture: Khan Academy’s Statistics: “Small Sample Size Confidence Intervals” and “Small Sample Hypothesis Test”
Link: Khan Academy’s Statistics: “Small Sample Size Confidence Intervals” (YouTube) and “Small Sample Hypothesis Test” (YouTube)

Instructions: Please view both lectures in their entirety (approximately 21 minutes total). These lectures will discuss constructing small size confidence intervals using t-distributions. You should spend approximately 30 minutes viewing and taking notes on these lectures.

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4.2.3 Confidence Interval for a Population Proportion

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 8: Confidence Intervals: “Section 4: Confidence Interval for a Population Proportion”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 8: Confidence Intervals: “Section 4: Confidence Interval for a Population Proportion” (PDF)

Instructions: Please read the section linked above in its entirety. Section 4 explains how to construct a confidence interval for a population proportion. This reading should take you approximately one hour to complete.

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Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 8: Confidence Intervals”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 8: Confidence Intervals” (YouTube)

Instructions: Please view the lecture titled “Video Lecture 8: Confidence Intervals” (27:57 minutes) to study confidence intervals, which are used to estimate a parameter.

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Assessment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 8: Confidence Intervals: “Practice 1: Confidence Intervals for Averages, Known Population Standard Deviation,” “Practice 2: Confidence Intervals for Averages, Unknown Population Standard Deviation,” and “Practice 3: Confidence Intervals for Proportions”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 8: Confidence Intervals: “Practice 1: Confidence Intervals for Averages, Known Population Standard Deviation” (PDF), “Practice 2: Confidence Intervals for Averages, Unknown Population Standard Deviation” (PDF), and “Practice 3: Confidence Intervals for Proportions” (PDF)

Instructions: Click on the link titled “Practice 1: Confidence Intervals for Averages, Known Population Standard Deviation” and solve problems 1-13. Next, click on the links titled “Practice 2: Confidence Intervals for Averages, Unknown Population Standard Deviation” to solve problems 1-11 and “Practice 3: Confidence Intervals for Proportions” to solve problems 1-13. Finally, click on the link titled “Homework” and solve problems 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, and 21. To check your solutions, go to the end of the document. Please solve all of the problems before checking the solutions. This assessment should take you approximately three and a half hours to complete.

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Unit 5: Hypothesis Testing

One of the major goals in statistics is to use the information you collect from a sample to get a better idea of the entire population in which you are interested. In this unit, you will learn about hypothesis testing, which will enable you to achieve that goal.

A hypothesis test involves collecting and evaluating data from a sample to make a decision as to whether or not that data supports a claim made about a population. This unit will also teach you how to conduct hypothesis tests and 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. The process of hypothesis testing is a way making decisions about claims like these. In this unit, you will learn to establish your assumptions through null and alternative hypotheses. Then, you will learn to compare sample characteristics to assumptions to see whether there is enough data to accept or reject the null hypothesis. The null hypothesis is, at first, assumed to be true and the one you hope to nullify, while the alternative hypothesis is a 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. The unit concludes with an introduction to Chi-distributions and their applications.

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5.1 Hypothesis Testing: Single Mean and Single Proportion

5.1.1 Null and Alternate Hypotheses

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 9: Hypothesis Testing: Single Mean and Single Proportion: “Section 1: Hypothesis Testing: Single Mean and Single Proportion” and “Section 2: Null and Alternate Hypotheses”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 9: Hypothesis Testing: Single Mean and Single Proportion: “Section 1: Hypothesis Testing: Single Mean and Single Proportion” (PDF) and “Section 2: Null and Alternate Hypotheses” (PDF)

Instructions: Please read the sections linked above in their entirety. Section 1 briefly introduces the process of hypothesis testing. Section 2 discusses the null hypothesis and the alternate hypothesis. These readings should take you approximately 30 minutes to complete.

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5.1.2 Type I and Type II Errors

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 9: Hypothesis Testing: Single Mean and Single Proportion: “Section 3: Outcomes and the Type I and Type II Errors”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 9: Hypothesis Testing: Single Mean and Single Proportion: “Section 3: Outcomes and the Type I and Type II Errors” (PDF)

Instructions: Please read the section linked above in its entirety. Section 3 explains the types of errors that can occur while performing a hypothesis test. This reading should take you less than 30 minutes to complete.

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Lecture: Khan Academy’s Statistics: “Type I Errors”
Link: Khan Academy’s Statistics: “Type I Errors” (YouTube)

Instructions: Please watch the brief video lecture (3:24 minutes). This lecture will discuss Type I Errors. Viewing this lecture and taking notes should take you less than 15 minutes.

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5.1.3 Distribution for Hypothesis Testing and More

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 9: Hypothesis Testing: Single Mean and Single Proportion: “Section 4: Distribution Needed for Hypothesis Testing,” “Section 5: Assumption,” “Section 6: Rare Events,” “Section 7: Using the Sample to Support One of the Hypotheses,” “Section 8: Decision and Conclusion,” and “Section 9: Additional Information”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 9: Hypothesis Testing: Single Mean and Single Proportion: “Section 4: Distribution Needed for Hypothesis Testing” (PDF) “Section 5: Assumption” (PDF), “Section 6: Rare Events” (PDF), “Section 7: Using the Sample to Support One of the Hypotheses” (PDF), “Section 8: Decision and Conclusion” (PDF), and “Section 9: Additional Information” (PDF)

Instructions: Please read the sections linked above in their entirety. The first three sections discuss assumptions about particular distributions associated with hypothesis testing. Section 7 explains how to use the sample to calculate the actual probability of getting the test result, called the p-value. Section 8 discusses how to make a decision about whether to reject or not reject the null hypothesis. These readings should take you approximately one and a half hours to complete.

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Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 9: Hypothesis Testing with a Single Mean”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 9: Hypothesis Testing with a Single Mean” (YouTube)

Instructions: Please view the lecture titled “Video Lecture 9: Hypothesis Testing with a Single Mean” (28:58 minutes) to learn how to perform hypothesis tests for a single mean.

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Assessment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 9: Hypothesis Testing: Single Mean and Single Proportion: “Practice 1: Single Mean, Known Population Standard Deviation,” “Practice 2: Single Mean, Unknown Population Standard Deviation,” and “Practice 3: Single Proportion”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 9: Hypothesis Testing: Single Mean and Single Proportion: “Practice 1: Single Mean, Known Population Standard Deviation” (PDF), “Practice 2: Single Mean, Unknown Population Standard Deviation” (PDF), and “Practice 3: Single Proportion” (PDF)

Instructions: Click on the above links solve all the problems in each practice lesson. Next, click on the link titled “Homework” and solve problems 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, and 27. To check your solutions, go to the end of the document. Please complete all assigned exercises before checking the solutions. This assessment should take you approximately three hours to complete.

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Lecture: Khan Academy’s Statistics: “Large Sample Proportion Hypothesis Testing”
Link: Khan Academy’s Statistics: “Large Sample Proportion Hypothesis Testing” (YouTube)

Instructions: Please view the entire video lecture (14:30 minutes). This lecture will discuss large sample proportion hypothesis testing.

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Lecture: Khan Academy’s Statistics: “Difference of Sample Means Distribution”
Link: Khan Academy’s Statistics: “Difference of Sample Means Distribution” (YouTube)

Instructions: Please view the entire lecture (approximately 12 minutes). This lecture will discuss the difference of sample means distribution.

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Lecture: Khan Academy’s Statistics: “Confidence Interval of Difference of Means”
Link: Khan Academy’s Statistics: “Confidence Interval of Difference of Means” (YouTube)

Instructions: Please watch the entire lecture (approximately 16 minutes). This lecture will discuss confidence interval of difference of means.

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5.2 Hypothesis Testing: Two Means, Paired Data, Two Proportions

5.2.1 Comparing Two Independent Population Means with Unknown Population Standard Deviations

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions: “Section 1: Hypothesis Testing: Two Population Means and Two Population Proportions” and “Section 2: Comparing Two Independent Population Means with Unknown Population Standard Deviations”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions: “Section 1: Hypothesis Testing: Two Population Means and Two Population Proportions” (PDF) and “Section 2: Comparing Two Independent Population Means with Unknown Population Standard Deviations” (PDF)

Instructions: Please read the sections linked above in their entirety. These sections discuss how to compare two independent population means with unknown population standard deviations. These readings, including examples and problems, should take you approximately one hour to complete.

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5.2.2 Comparing Two Independent Population Means with Known Population Standard Deviations

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions: “Section 3: Comparing Two Independent Population Means with Known Population Standard Deviations”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions: “Section 3: Comparing Two Independent Population Means with Known Population Standard Deviations” (PDF)

Instructions: Please read the section linked above in its entirety. Section 3 provides an overview of hypothesis testing in situations where there are two independent population means and known population standard deviations in statistics. This reading should take you approximately 30 minutes to complete.

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5.2.3 Comparing Two Independent Population Proportions

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions: “Section 4: Comparing Two Independent Population Proportions”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions: “Section 4: Comparing Two Independent Population Proportions” (PDF)

Instructions: Please read the section linked above in its entirety. Section 4 discusses how to compare two population parameters. This reading should take you approximately 30 minutes to complete.

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Lecture: Khan Academy’s Statistics: “Comparing Population Proportions 1,” “Comparing Population Proportions 2,” and “Hypothesis Test Comparing Population Proportions”
Link: Khan Academy’s Statistics: “Comparing Population Proportions 1” (YouTube), “Comparing Population Proportions 2” (YouTube), and “Hypothesis Test Comparing Population Proportions” (YouTube)

Instructions: Please view these three video lectures in their entirety (approximately 27 minutes total). These lectures will discuss comparing population proportions and hypothesis test comparing population proportions.

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5.2.4 Matched or Paired Samples

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions: “Section 5: Matched or Paired Samples”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions: “Section 5: Matched or Paired Samples” (PDF)

Instructions: Please read the section linked above in its entirety. Section 5 provides an overview of hypothesis testing for matched or paired samples. This reading should take you approximately 30 minutes to complete.

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Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 10: Hypothesis Testing with Two Means
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 10: Hypothesis Testing with Two Means” (YouTube)

Instructions: Please view the lecture titled “Video Lecture 10: Hypothesis Testing with Two Means” (28:51 minutes) to continue studying hypothesis testing, with a focus on testing two means and two proportions.

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Lecture: Khan Academy’s Statistics: “Hypothesis Test for Difference of Means”
Link: Khan Academy’s Statistics: “Hypothesis Test for Difference of Means” (YouTube)

Instructions: Please view the above lecture in its entirety (10 minutes). It discusses hypothesis tests for difference of means.

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Assessment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions: “Practice 1: Hypothesis Testing for Two Proportions” and “Practice 2: Hypothesis Testing for Two Averages”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions: “Practice 1: Hypothesis Testing for Two Proportions” (PDF) and “Practice 2: Hypothesis Testing for Two Averages” (PDF)

Instructions: Click on the above links and solve all the problems in the practice lessons. Next, click on the link titled “Homework” and solve problems 1, 5, 7, 9, 11, 15, 17, 21, 23, 27, 29, 33, 35, and 43-48. To check your solutions, go to the end of the document. Please attempt all of the assigned problems before checking your answers against the solutions.

This assessment should take you approximately three hours.

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5.3 Chi-Square Distribution

5.3.1 Notation and Facts

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 11: The Chi-Square Distribution: “Section 1: The Chi-Square Distribution,” “Section 2: Notation,” and “Section 3: Facts About the Chi-Square Distribution”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 11: The Chi-Square Distribution: “Section 1: The Chi-Square Distribution” (PDF), “Section 2: Notation” (PDF), and “Section 3: Facts About the Chi-Square Distribution” (PDF)

Instructions: Please read the sections linked above in their entirety. These sections provide and introduction to the Chi-square distribution. These readings should take you approximately 45 minutes to complete.

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Lecture: Khan Academy’s Statistics: “Chi-Square Distribution Introduction,” “Pearson's Chi Square Test (Goodness of Fit),” and “Contingency Table Chi-Square Test”
Link: Khan Academy’s Statistics: “Chi-Square Distribution Introduction” (YouTube), “Pearson's Chi Square Test (Goodness of Fit)” (YouTube), and “Contingency Table Chi-Square Test” (YouTube)

Instructions: Please view all three video lectures in their entirety (approximately 40 minutes total). These lectures will provide an introduction to the Chi-square distribution as well as the Chi-square test.

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5.3.2 Goodness-of-Fit Test

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 11: The Chi-Square Distribution: “Section 4: Goodness-of-Fit Test”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 11: The Chi-Square Distribution: “Section 4: Goodness-of-Fit Test” (PDF)

Instructions: Please read the section linked above in its entirety. Section 4 describes how the Chi-square distribution is used to conduct the goodness-of-fit test. This reading should take you approximately one hour to complete.

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5.3.3 Test of Independence

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 11: The Chi-Square Distribution: “Section 5: Test of Independence”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 11: The Chi-Square Distribution: “Section 5: Test of Independence” (PDF)

Instructions: Please read the linked section in its entirety. Section 5 describes how the Chi-square distribution can be used to test for independence. This reading should take you approximately 30 minutes to complete.

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5.3.4 Test of a Single Variance (Optional)

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 11: The Chi-Square Distribution: “Section 6: Test of a Single Variance (Optional)”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 11: The Chi-Square Distribution: “Section 6: Test of a Single Variance (Optional)” (PDF)

Instructions: Please read the linked section in its entirety. Section 6 provides an overview on Chi-square distribution tests of variance. This reading should take you approximately 30 minutes to complete.

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Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 11: The Chi-Square Distribution”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 11: The Chi-Square Distribution” (YouTube)

Instructions: Please view the linked lecture titled “Video Lecture 11: The Chi-Square Distribution” (26:16 minutes) to study the Chi-square distribution and its properties.

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Assessment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 11: The Chi-Square Distribution: “Practice 1: Goodness-of-Fit Test,” “Practice 2: Contingency Tables,” and “Practice 3: Test of a Single Variance”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 11: The Chi-Square Distribution: “Practice 1: Goodness-of-Fit Test” (PDF), “Practice 2: Contingency Tables” (PDF), and “Practice 3: Test of a Single Variance” (PDF)

Instructions: Click on the above solve all the problems in each practice lesson. Next, click on the link titled “Homework” and solve the odd numbered problems from 3-37. To check your solutions, go to the end of the document. Please solve all of the problems before checking the solutions. This assessment should take you approximately three hours to complete.

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Unit 6: Correlation, Regression, and ANOVA

One of the main reasons you will conduct analysis is in order to understand how two variables are related to one another. 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 increase as the other increases, or does it decrease?” For example, how does drinking soda relate to weight gain for teenagers? Does drinking more soda really relate to more weight gain? In this unit, you will learn to measure the degree of a relationship between two or more variables. Both correlation and regression are measures for comparing variables. However, they are quite different from one another. Correlation quantifies the strength of a relationship between two variables and is a measure of existing data. Regression, on the other hand, 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 unknown. A note of caution: Be careful to not automatically interpret correlation and regression as establishing cause-and-effect relationships!

Also, you will learn about a method called 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.

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6.1 Linear Regression

6.1.1 Linear Equations, Slope, and Y-intercept

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 12: Linear Regression and Correlation: “Section 1: Linear Regression and Correlation,” “Section 2: Linear Equations,” and “Section 3: Slope and Y-Intercept of a Linear Equation”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 12: Linear Regression and Correlation: “Section 1: Linear Regression and Correlation ” (PDF), “Section 2: Linear Equations” (PDF), and “Section 3: Slope and Y-Intercept of a Linear Equation” (PDF)

Instructions: Please read the sections linked above in their entirety. Section 1 introduces the idea of bivariate and multivariate data. Section 2 discusses linear equations, and Section 3 discusses the slope and Y-intercept of a linear equation. These readings should take you approximately one hour to complete.

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6.1.2 Scatter Plots

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 12: Linear Regression and Correlation: “Section 4: Scatter Plots”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 12: Linear Regression and Correlation: “Section 4: Scatter Plots” (PDF)

Instructions: Please read the section linked above in its entirety. Section 4 introduces scatter plots, which are a way to display the relation between two variables, X and Y. This reading should take you less than 30 minutes to complete.

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6.1.3 The Regression Equation

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 12: Linear Regression and Correlation: “Section 5: The Regression Equation”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 12: Linear Regression and Correlation: “Section 5: The Regression Equation” (PDF)

Instructions: Please read the section linked above in its entirety. Section 5 explains how to find and graph the regression equation. This reading should take you approximately 30 minutes to complete.

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Lecture: Khan Academy’s Statistics: “Covariance and the Regression Line”
Link: Khan Academy’s Statistics: “Covariance and the Regression Line” (YouTube)

Instructions: Please view the video lecture in its entirety (approximately 15 minutes). This lecture discusses covariance, variance, and the slope of the regression.

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6.2 Correlation

6.2.1 The Correlation Coefficient

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 12: Linear Regression and Correlation: “Section 6: The Correlation Coefficient”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 12: Linear Regression and Correlation: “Section 6: The Correlation Coefficient” (PDF)

Instructions: Please read the section linked above in its entirety. Section 6 introduces the correlation coefficient, which is a numerical measure of the strength of association between the independent variable, X, and the dependent variable, Y. This reading should take you approximately 30 minutes to complete.

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Lecture: Khan Academy’s Statistics: “Correlation and Causality”
Link: Khan Academy’s Statistics: “Correlation and Causality” (YouTube)

Instructions: Please view the entire video lecture (10:25 minutes). This lecture discusses correlation and causality. Viewing this lecture and taking notes should take you approximately 15 minutes to complete.

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6.2.2 Prediction

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 12: Linear Regression and Correlation: “Section 8: Prediction”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 12: Linear Regression and Correlation: “Section 8: Prediction” (PDF)

Instructions: Please read the section linked above in its entirety. Section 8 explains how to predict using the regression equation. This reading should take you approximately 30 minutes to complete.

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6.2.3 Outliers

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 12: Linear Regression and Correlation: “Section 9: Outliers”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 12: Linear Regression and Correlation: “Section 9: Outliers” (PDF)

Instructions: Please read the section linked above in its entirety. Section 9 discusses how to identify outliers. This reading should take you approximately 30 minutes to complete.

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Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 12: Linear Regression and Correlation”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 12: Linear Regression and Correlation” (YouTube)

Instructions: Please view the lecture titled “Lecture 12: Linear Regression and Correlation” (27:21 minutes) to study linear regression and bivariate data.

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Assessment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 12: Linear Regression and Correlation “Practice: Linear Regression”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 12: Linear Regression and Correlation: “Practice: Linear Regression” (PDF)

Instructions: Click on the above link and solve the problems. Next, click on the link titled “Homework” and solve problems 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, and 21-25. To check your solutions, go to the end of the document. Please solve all of the problems before checking the solutions. This assessment should take you approximately two and a half hours to complete.

Terms of Use: This work is licensed under a Creative Commons Attribution 2.0 Generic License. It is attributed to Barbara Illowsky and Susan Dean, and the original version can be found here.
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6.3 F-Distribution and ANOVA

6.3.1 ANOVA

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 13: F Distribution and ANOVA: “Section 1: F Distribution and ANOVA” and “Section 2: ANOVA”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 13: F Distribution and ANOVA: “Section 1: F Distribution and ANOVA” (PDF) and “Section 2: ANOVA” (PDF)

Instructions: Please read the sections linked above in their entirety. These sections describe the assumptions needed for implementing an ANOVA and how to set up the hypothesis test for the ANOVA. These reading should take you approximately 30 minutes to complete.

Terms of Use: This work is licensed under a Creative Commons Attribution 2.0 Generic License. It is attributed to Barbara Illowsky and Susan Dean, and the original version can be found here.
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6.3.2 The F Distribution and the F Ratio

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 13: F Distribution and ANOVA: “Section 3: The F Distribution and the F Ratio” and “Section 4: Facts about the F Distribution”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 13: F Distribution and ANOVA: “Section 3: The F Distribution and the F Ratio” (PDF) and “Section 4: Facts about the F Distribution” (PDF)

Instructions: Please read the sections linked above in their entirety. Section 3 describes how to calculate the F-ratio and F-distribution based on the hypothesis test for the ANOVA, and Section 4 states the factors associated with F-distributions. These readings should take you approximately one hour to complete.

Terms of Use: This work is licensed under a Creative Commons Attribution 2.0 Generic License. It is attributed to Barbara Illowsky and Susan Dean, and the original version can be found here.
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Lecture: Khan Academy’s Statistics: “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 Statistics: “ANOVA 1: Calculating SST (Total Sum of Squares)” (YouTube), “ANOVA 2: Calculating SSW and SSB (Total Sum of Squares Within and Between)” (YouTube), and “ANOVA 3: Hypothesis Test with F-Statistic” (YouTube)

Instructions: Please view the three lectures, which discuss ANOVA, in their entirety (approximately 30 minutes total).

Terms of Use: This video is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike United States License 3.0. It is attributed to the Khan Academy.
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6.3.3 Test of Two Variances

Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 13: F Distribution and ANOVA: “Section 5: Test of Two Variances”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 13: F Distribution and ANOVA: “Section 5: Test of Two Variances” (PDF)

Instructions: Please read the section linked above in its entirety. Section 5 provides the assumptions to be considered in order to calculate a test of two variances and how to execute the test of two variances. This reading should take you approximately 30 minutes to complete.

Terms of Use: This work is licensed under a Creative Commons Attribution 2.0 Generic License. It is attributed to Barbara Illowsky and Susan Dean, and the original version can be found here.
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Assessment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 13: F Distribution and ANOVA: “Practice: ANOVA”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Chapter 13: F Distribution and ANOVA: “Practice: ANOVA” (PDF)

Instructions: Click on the above link and solve the problems. Next, click on the link titled “Homework” and solve problems 1, 3, 5, and 7. To check your solutions, go to the end of the document. Please solve all of the problems before checking the solutions. This assessment should take you approximately two hours to complete.

Terms of Use: This work is licensed under a Creative Commons Attribution 2.0 Generic License. It is attributed to Barbara Illowsky and Susan Dean, and the original version can be found here.
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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.
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