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David Goldsman
This course covers two important methodologies in statistics – confidence intervals and hypothesis testing.
Confidence intervals are encountered in everyday life, and allow us to make probabilistic statements such as: “Based on the sample of observations we conducted, we are 95% sure that the unknown mean lies between A and B,” and “We are 95% sure that Candidate Smith’s popularity is 52% +/- 3%.” We begin the course by discussing what a confidence interval is and how it is used. We then formulate and interpret confidence intervals for a variety of probability distributions and their parameters.
Read more
This course covers two important methodologies in statistics – confidence intervals and hypothesis testing.
Confidence intervals are encountered in everyday life, and allow us to make probabilistic statements such as: “Based on the sample of observations we conducted, we are 95% sure that the unknown mean lies between A and B,” and “We are 95% sure that Candidate Smith’s popularity is 52% +/- 3%.” We begin the course by discussing what a confidence interval is and how it is used. We then formulate and interpret confidence intervals for a variety of probability distributions and their parameters.
Read more
This course covers two important methodologies in statistics – confidence intervals and hypothesis testing.
Confidence intervals are encountered in everyday life, and allow us to make probabilistic statements such as: “Based on the sample of observations we conducted, we are 95% sure that the unknown mean lies between A and B,” and “We are 95% sure that Candidate Smith’s popularity is 52% +/- 3%.” We begin the course by discussing what a confidence interval is and how it is used. We then formulate and interpret confidence intervals for a variety of probability distributions and their parameters.
Hypothesis testing allows us to pose hypotheses and test their validity in a statistically rigorous way. For instance, “Does a new drug result in a higher cure rate than the old drug?” or “Is the mean tensile strength of item A greater than that of item B?” The second half the course begins by motivating hypothesis tests and how they are used. We then discuss the types of errors that can occur with hypothesis testing, and how to design tests to mitigate those errors. Finally, we formulate and interpret hypothesis tests for a variety of probability distributions and their parameters.
Register for this course and see more details by visiting:
OpenCourser.com/course/kfkv34/probability
What's inside
Learning objectives
- Identify what a confidence interval is and how it is used
- Formulate and interpret confidence intervals for a variety of probability distributions and their parameters
- Determine what a hypothesis test is and how it is used
- Identify the types of errors that can occur with hypothesis testing, and how to design tests to mitigate those errors
- Formulate and interpret hypothesis tests for a variety of probability distributions and their parameters
- Upon completion of this course, learners will be able to:
- Identify what a confidence interval is and how it is used
- Formulate and interpret confidence intervals for a variety of probability distributions and their parameters
- Determine what a hypothesis test is and how it is used
- Identify the types of errors that can occur with hypothesis testing, and how to design tests to mitigate those errors
- Formulate and interpret hypothesis tests for a variety of probability distributions and their parameters
- Upon completion of this course, learners will be able to:
Syllabus
Traffic lights
Traffic lights
Read about what's good
what should give you pause and
possible dealbreakers
Studies confidence intervals and hypothesis testing, fundamental statistical methods
Employs clear and comprehensive course modules to guide learning
Taught by David Goldsman, an experienced and respected instructor in the field
Requiring a basic understanding of probability and statistics, this course may not be suitable for complete beginners
Covers a wide range of topics within confidence intervals and hypothesis testing, providing a solid foundation in these areas
Leverages the free text, "A First Course in Probability and Statistics," for additional support and reference
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Reviews summary
Rigorous statistical inference fundamentals
According to learners, this course offers a rigorous and well-structured exploration of confidence intervals and hypothesis testing. Many praise the instructor's clear explanations and the course's ability to demystify complex topics, building a strong theoretical foundation. Students consistently find the quizzes and exercises challenging yet effective for solidifying understanding. However, some learners note the course's strong theoretical emphasis means it provides fewer practical, software-based applications, and it assumes a solid mathematical and statistical background. It is therefore highly recommended for those seeking a deep, foundational understanding rather than immediate practical application with computational tools.
Quizzes are fair and challenging; textbook integration is seamless.
"The use of the FCPS textbook as a primary resource was excellent."
"The quizzes were fair, really testing understanding."
"The structure follows the textbook perfectly, making it easy to follow along."
Provides a strong, rigorous theoretical grounding.
"This course is essential for anyone serious about understanding statistical inference deeply."
"Recommended for those who want a deep dive into the underlying theory."
"Excellent and rigorous. This course provides a deep theoretical grounding in confidence intervals and hypothesis testing. The professor is a great explainer."
Material is presented logically with clear explanations.
"This course was incredibly well-structured and the instructor's explanations were crystal clear."
"Excellent course! The material is presented logically, building up complex ideas step by step."
"This course truly demystifies confidence intervals and hypothesis testing. The instructor explains complex topics in an accessible way."
Focuses less on practical application or software use.
"I found the course quite theoretical and less applied than I hoped."
"I wished there were more computational examples in a specific software (like R or Python) to complement the theory."
"I was expecting more emphasis on applying these concepts in data analysis software. It's good if you want to understand the 'why' behind the formulas, but less so for the 'how-to' in a practical setting."
Requires a solid background in math and statistics.
"It definitely requires a strong background in probability and calculus."
"It assumes a strong prior understanding of statistics which wasn't always clear. Not for beginners to the topic."
"Highly recommend if you have a solid math background."
Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Probability and Statistics IV: Confidence Intervals and Hypothesis Tests with these
activities:
Review fundamental probability and statistical concepts
Show steps
Reviewing these foundational concepts will help establish a solid basis for the course and enhance comprehension of more advanced material.
Browse courses on
Probability
Show steps
-
Review basic concepts of probability, including events, outcomes, and probability measures
-
Go over different probability distributions, such as binomial, normal, and Poisson distributions
-
Revisit fundamental statistical concepts, including mean, median, mode, and standard deviation
Read 'Mathematical Statistics with Applications' by Wackerly and Mendenhall
Show steps
This book provides a comprehensive treatment of the theoretical foundations and practical applications of statistics, enhancing your understanding of the concepts covered in the course.
View
Mathematical Statistics with Applications
on Amazon
Show steps
-
Read the assigned chapters corresponding to the course material
-
Take notes and highlight important concepts
-
Complete the practice exercises at the end of each chapter
Practice confidence interval calculations
Show steps
Engaging in practice drills will strengthen your understanding of the procedures involved in calculating and interpreting confidence intervals, enhancing your ability to apply these concepts in real-world situations.
Browse courses on
Confidence Intervals
Show steps
-
Solve practice problems on determining sample size for a given confidence level and margin of error
-
Practice calculating confidence intervals for different population parameters, such as mean and proportion
-
Interpret the results of confidence intervals, including the level of confidence and precision
Four other activities
Expand to see all activities and additional details
Show all seven activities
Participate in peer study groups
Show steps
Engaging in peer study sessions will provide opportunities to clarify concepts, discuss different perspectives, and reinforce your understanding through collaborative learning.
Show steps
-
Connect with classmates through discussion forums or social media groups
-
Organize regular study sessions to focus on specific topics or problem-solving
-
Take turns presenting concepts, leading discussions, and providing feedback to others
Create a comprehensive study guide
Show steps
Compiling a comprehensive study guide will help organize and reinforce your understanding of the course material, serving as a valuable resource for exam preparation and future reference.
Show steps
-
Gather notes, assignments, quizzes, and other course materials
-
Organize the materials into logical sections and subsections
-
Summarize key concepts, formulas, and examples in a concise and easy-to-understand manner
-
Include practice questions and exercises for self-assessment
Create a visual representation of hypothesis testing
Show steps
Creating a visual representation will aid in visualizing and comprehending the key elements and steps involved in hypothesis testing, bolstering your understanding of this crucial statistical technique.
Browse courses on
Hypothesis Testing
Show steps
-
Design a flowchart or infographic that outlines the process of hypothesis testing
-
Incorporate examples to illustrate the different types of hypotheses and their corresponding statistical tests
-
Explain the concepts of statistical significance and Type I and Type II errors
-
Present your visual representation to classmates or a mentor for feedback
Explore online tutorials on advanced statistical methods
Show steps
Seeking out and engaging with online tutorials will expose you to additional statistical techniques and concepts, expanding your knowledge and broadening your horizons in the field of statistics.
Browse courses on
Regression Analysis
Show steps
-
Identify reputable websites or platforms that offer tutorials on advanced statistical methods
-
Select topics that align with your interests or areas you want to improve
-
Follow the tutorials, taking notes and completing any practice exercises provided
Review fundamental probability and statistical concepts
Show steps
Reviewing these foundational concepts will help establish a solid basis for the course and enhance comprehension of more advanced material.
Browse courses on
Probability
Show steps
Show steps
Show steps
- Review basic concepts of probability, including events, outcomes, and probability measures
- Go over different probability distributions, such as binomial, normal, and Poisson distributions
- Revisit fundamental statistical concepts, including mean, median, mode, and standard deviation
Read 'Mathematical Statistics with Applications' by Wackerly and Mendenhall
Show steps
This book provides a comprehensive treatment of the theoretical foundations and practical applications of statistics, enhancing your understanding of the concepts covered in the course.
View
Mathematical Statistics with Applications
on Amazon
Show steps
Show steps
Show steps
- Read the assigned chapters corresponding to the course material
- Take notes and highlight important concepts
- Complete the practice exercises at the end of each chapter
Practice confidence interval calculations
Show steps
Engaging in practice drills will strengthen your understanding of the procedures involved in calculating and interpreting confidence intervals, enhancing your ability to apply these concepts in real-world situations.
Browse courses on
Confidence Intervals
Show steps
Show steps
Show steps
- Solve practice problems on determining sample size for a given confidence level and margin of error
- Practice calculating confidence intervals for different population parameters, such as mean and proportion
- Interpret the results of confidence intervals, including the level of confidence and precision
Four other activities
Expand to see all activities and additional details
Show all seven activities
Participate in peer study groups
Show steps
Engaging in peer study sessions will provide opportunities to clarify concepts, discuss different perspectives, and reinforce your understanding through collaborative learning.
Show steps
Show steps
Show steps
- Connect with classmates through discussion forums or social media groups
- Organize regular study sessions to focus on specific topics or problem-solving
- Take turns presenting concepts, leading discussions, and providing feedback to others
Create a comprehensive study guide
Show steps
Compiling a comprehensive study guide will help organize and reinforce your understanding of the course material, serving as a valuable resource for exam preparation and future reference.
Show steps
Show steps
Show steps
- Gather notes, assignments, quizzes, and other course materials
- Organize the materials into logical sections and subsections
- Summarize key concepts, formulas, and examples in a concise and easy-to-understand manner
- Include practice questions and exercises for self-assessment
Create a visual representation of hypothesis testing
Show steps
Creating a visual representation will aid in visualizing and comprehending the key elements and steps involved in hypothesis testing, bolstering your understanding of this crucial statistical technique.
Browse courses on
Hypothesis Testing
Show steps
Show steps
Show steps
- Design a flowchart or infographic that outlines the process of hypothesis testing
- Incorporate examples to illustrate the different types of hypotheses and their corresponding statistical tests
- Explain the concepts of statistical significance and Type I and Type II errors
- Present your visual representation to classmates or a mentor for feedback
Explore online tutorials on advanced statistical methods
Show steps
Seeking out and engaging with online tutorials will expose you to additional statistical techniques and concepts, expanding your knowledge and broadening your horizons in the field of statistics.
Browse courses on
Regression Analysis
Show steps
Show steps
Show steps
- Identify reputable websites or platforms that offer tutorials on advanced statistical methods
- Select topics that align with your interests or areas you want to improve
- Follow the tutorials, taking notes and completing any practice exercises provided
Career center
Learners who complete Probability and Statistics IV: Confidence Intervals and Hypothesis Tests will develop knowledge and skills
that may be useful to these careers:
Data Scientist
Data Scientist
A Data Scientist combines programming skills with knowledge of mathematics and statistics to extract meaningful insights from data. This course in Probability and Statistics IV can be a valuable aid in developing foundational knowledge for a career as a Data Scientist. By learning how to formulate and interpret confidence intervals and hypothesis tests, you can enhance your ability to analyze data, draw conclusions, and make informed decisions as a Data Scientist.
Statistician
Statistician
A Statistician collects, analyzes, interprets, and presents data. They use their knowledge of statistical methods to develop and test hypotheses, which can be used to make informed decisions in a variety of fields. This course in Probability and Statistics IV can provide you with a strong foundation in the principles of statistics, preparing you for a successful career as a Statistician.
Quantitative Analyst
Quantitative Analyst
A Quantitative Analyst (Quant) uses mathematical and statistical models to analyze financial data and make investment decisions. This course in Probability and Statistics IV can help you build the quantitative skills needed to succeed as a Quant. By learning how to formulate and interpret confidence intervals and hypothesis tests, you can enhance your ability to assess risk and make informed investment decisions.
Market Researcher
Market Researcher
A Market Researcher conducts research to understand consumer behavior and market trends. They use this information to help businesses make informed decisions about product development, marketing campaigns, and other business strategies. This course in Probability and Statistics IV can provide you with a strong foundation in the principles of statistics, which are essential for designing and conducting effective market research studies.
Business Analyst
Business Analyst
A Business Analyst uses data and statistical techniques to identify and solve business problems. They work with stakeholders to understand their needs, gather and analyze data, and develop recommendations for improvement. This course in Probability and Statistics IV can help you build the analytical skills needed to succeed as a Business Analyst. By learning how to formulate and interpret confidence intervals and hypothesis tests, you can enhance your ability to analyze data and make informed recommendations.
Actuary
Actuary
An Actuary uses mathematical and statistical techniques to assess risk and uncertainty. They work in a variety of fields, including insurance, finance, and healthcare. This course on Probability and Statistics IV can provide you with a strong foundation in the principles of statistics, which are essential for success as an Actuary.
Data Engineer
Data Engineer
A Data Engineer designs and builds the infrastructure that stores and manages data. They work with data scientists and other stakeholders to ensure that data is accessible, reliable, and secure. This course on Probability and Statistics IV may be useful for a Data Engineer who wants to build a foundation in statistical concepts and methods.
Epidemiologist
Epidemiologist
An Epidemiologist investigates the causes and patterns of disease and other health problems in populations. They use statistical methods to analyze data and develop strategies for prevention and control. This course on Probability and Statistics IV may be useful for an Epidemiologist who wants to build a foundation in statistical concepts and methods.
Forensic Scientist
Forensic Scientist
A Forensic Scientist uses scientific methods to analyze evidence and provide expert testimony in legal proceedings. They use statistical methods to interpret data and draw conclusions about the evidence. This course on Probability and Statistics IV may be useful for a Forensic Scientist who wants to build a foundation in statistical concepts and methods.
Operations Research Analyst
Operations Research Analyst
An Operations Research Analyst uses mathematical and statistical techniques to solve complex problems in business and industry. They work with stakeholders to identify and define problems, collect and analyze data, and develop recommendations for improvement. This course on Probability and Statistics IV may be useful for an Operations Research Analyst who wants to build a foundation in statistical concepts and methods.
Risk Manager
Risk Manager
A Risk Manager identifies, assesses, and mitigates risks to an organization. They use statistical methods to analyze data and develop strategies for risk management. This course on Probability and Statistics IV may be useful for a Risk Manager who wants to build a foundation in statistical concepts and methods.
Quality Control Manager
Quality Control Manager
A Quality Control Manager ensures that products and services meet quality standards. They use statistical methods to analyze data and identify areas for improvement. This course on Probability and Statistics IV may be useful for a Quality Control Manager who wants to build a foundation in statistical concepts and methods.
Technical Writer
Technical Writer
A Technical Writer creates and maintains technical documentation, such as user manuals, product descriptions, and training materials. They use statistical methods to analyze data and develop clear and concise documentation. This course on Probability and Statistics IV may be useful for a Technical Writer who wants to build a foundation in statistical concepts and methods.
Project Manager
Project Manager
A Project Manager plans, executes, and closes projects. They use statistical methods to track progress and identify risks. This course in Probability and Statistics IV may be useful for a Project Manager who wants to build a foundation in statistical concepts and methods.
Software Engineer
Software Engineer
A Software Engineer designs, develops, and tests software applications. They use statistical methods to analyze data and identify trends. This course in Probability and Statistics IV may be useful for a Software Engineer who wants to build a foundation in statistical concepts and methods.
For more career information including salaries, visit:
OpenCourser.com/course/kfkv34/probability
Reading list
We've selected 15 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Probability and Statistics IV: Confidence Intervals and Hypothesis Tests.
Provides a comprehensive overview of pattern recognition and machine learning. It covers topics such as supervised learning, unsupervised learning, and reinforcement learning.
Provides a comprehensive overview of probability, random variables, and stochastic processes. It valuable resource for students and practitioners who want to develop a deep understanding of these topics.
Save
Provides a comprehensive overview of Markov chains and stochastic processes. It valuable resource for students and practitioners who want to develop a deep understanding of these topics.
Provides a comprehensive overview of time series analysis. It valuable resource for students and practitioners who want to develop a deep understanding of this topic.
Save
Provides a comprehensive overview of forecasting methods. It covers topics such as time series analysis, regression analysis, and machine learning.
Provides a comprehensive overview of statistical learning methods. It covers topics such as linear regression, logistic regression, and support vector machines.
Provides a comprehensive overview of statistical inference, covering topics such as point estimation, hypothesis testing, and confidence intervals. It valuable resource for students and practitioners who want to deepen their understanding of statistical methods.
Provides a solid foundation in mathematical statistics, covering topics such as probability theory, random variables, and statistical inference. It valuable resource for students and practitioners who want to develop a strong understanding of the mathematical underpinnings of statistics.
Provides a clear and concise introduction to probability and stochastic processes. It is suitable for students and practitioners who want to learn the basics of these subjects.
Provides a clear and concise introduction to probability and mathematical statistics. It is suitable for students and practitioners who want to learn the basics of these subjects.
Provides a practical introduction to time series analysis. It covers topics such as data analysis, forecasting, and model selection.
Save
Provides a clear and concise introduction to stochastic processes. It is suitable for students and practitioners who want to learn the basics of this subject.
Provides a clear and concise introduction to stochastic processes. It is suitable for students and practitioners who want to learn the basics of this subject.
Provides a practical introduction to probability and statistics for engineers and scientists. It covers topics such as data analysis, probability distributions, and statistical inference.
Provides a clear and concise introduction to probability and statistics for engineers. It covers topics such as probability distributions, statistical inference, and regression analysis.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/kfkv34/probability
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Effort
6 to 10 hours per week for 4 weeks
Level
Intermediate
Via
edX
Institution
The Georgia Institute of Technology
Instructor
David Goldsman
Sessions
August 17, 2026
- January 1, 2027
May 11, 2026
- August 9, 2026
January 5, 2026
- May 10, 2026
August 18, 2025
- January 1, 2026
Language
English
Transcript
English
This course belongs to a
collection
called
Statistics, Confidence Intervals and Hypothesis Tests. It's comprised of two courses:
- Probability and Statistics III: A Gentle Introduction to Statistics
- Probability and Statistics IV: Confidence Intervals and Hypothesis Tests (viewing)
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