This course is part of the Data Science Foundations: Statistical Inference Specialization

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Jem Corcoran

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Part of the Master of Science in Electrical Engineering degree
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Data Science Foundations: Statistical Inference SpecializationUniversity of Colorado Boulder

About this Course

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This course will focus on theory and implementation of hypothesis testing, especially as it relates to applications in data science. Students will learn to use hypothesis tests to make informed decisions from data. Special attention will be given to the general logic of hypothesis testing, error and error rates, power, simulation, and the correct computation and interpretation of p-values. Attention will also be given to the misuse of testing concepts, especially p-values, and the ethical implications of such misuse.
This course can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) degree offered on the Coursera platform. The MS-DS is an interdisciplinary degree that brings together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the MS-DS is ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://www.coursera.org/degrees/master-of-science-data-science-boulder.

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Course 3 of 3 in the

Data Science Foundations: Statistical Inference Specialization

Intermediate Level

Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R

Approx. 36 hours to complete

English

What you will learn

Define a composite hypothesis and the level of significance for a test with a composite null hypothesis.
Define a test statistic, level of significance, and the rejection region for a hypothesis test. Give the form of a rejection region.
Perform tests concerning a true population variance.
Compute the sampling distributions for the sample mean and sample minimum of the exponential distribution.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Course 3 of 3 in the

Data Science Foundations: Statistical Inference Specialization

Intermediate Level

Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R

Approx. 36 hours to complete

English

Instructor

Instructor rating

4.87/5 (9 Ratings)

Jem Corcoran

Offered by

University of Colorado Boulder

Start working towards your Master's degree

This course is part of the 100% online Master of Science in Electrical Engineering from University of Colorado Boulder. If you are admitted to the full program, your courses count towards your degree learning.

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Syllabus - What you will learn from this course

Week1

Week 1

2 hours to complete

Start Here!

2 hours to complete

3 readings

8 hours to complete

Fundamental Concepts of Hypothesis Testing

8 hours to complete

6 videos (Total 70 min), 11 readings, 2 quizzes

6 videos

What is Hypothesis Testing?3mTypes of Hypotheses14mNormal Computations23mErrors in Hypothesis Testing7mTest Statistics and Significance14mA First Test4m

11 readings

What is Hypothesis Testing?5mTypes of Hypotheses10mVideo Slides for Types of Hypotheses10mNormal Computations10mVideo Slides for Normal Computations10mErrors in Hypothesis Testing10mVideo Slides for Errors in Hypothesis Testing10mTest Statistics and Significance10mVideo Slides for Test Statistics and Level of Significance10mA First Test10mVideo Slides for A First Test10m

1 practice exercise

Introduction to Hypothesis Testing30m

Week2

Week 2

8 hours to complete

Composite Tests, Power Functions, and P-Values

8 hours to complete

7 videos (Total 125 min), 7 readings, 2 quizzes

7 videos

Composite Hypotheses and Level of Significance16mOne-Tailed Tests20mPower Functions13mHypothesis Testing with P-Values21mTwo Tailed Tests12mCLT: A Brief Review16mHypothesis Tests for Proportions23m

7 readings

Video Slides for Composite Hypotheses and Level of Significance10mVideo Slides for One-Tailed Tests10mVideo Slides for Power Functions10mVideo Slides for Hypothesis Testing with P-Values10mVideo Slides for Two-Tailed Tests10mVideo Slides for CLT: A Brief Review10mVideo Slides for Hypothesis Tests for Proportions10m

1 practice exercise

Constructing Tests30m

Week3

Week 3

8 hours to complete

t-Tests and Two-Sample Tests

8 hours to complete

7 videos (Total 140 min), 7 readings, 2 quizzes

7 videos

The t and Chi-Squared Distributions41mThe Sample Variance for the Normal Distribution23mt-Tests18mTwo Sample Tests for Means15mTwo Sample t-Tests for a Difference of Means17mWelch's t-Test and Paired Data13mComparing Population Proportions8m

7 readings

Video Slides for the t and Chi-Squared Distributions10mVideo Slides for the Sample Variance and the Normal Distribution10mVideo Slides for t-Tests10mVideo Slides for Two Sample Tests for Means10mVideo Slides for Differences in Population Means10mVideo Slides for Welch's Test and Paired Data10mVideo Slides for Comparing Population Proportions10m

1 practice exercise

More Hypothesis Tests!30m

Week4

Week 4

4 hours to complete

Beyond Normality

In this module, we will consider some problems where the assumption of an underlying normal distribution is not appropriate and will expand our ability to construct hypothesis tests for this case. We will define the concept of a “uniformly most powerful” (UMP) test, whether or not such a test exists for specific problems, and we will revisit some of our earlier tests from Modules 1 and 2 through the UMP lens. We will also introduce the F-distribution and its role in testing whether or not two population variances are equal.

4 hours to complete

6 videos (Total 118 min), 6 readings, 2 quizzes

6 videos

Properties of the Exponential Distribution13mTwo Tests27mBest Tests22mUMP Tests10mA Test for the Variance of the Normal Distribution12mThe F-Distribution and a Ratio of Variances31m

6 readings

Video Slides for Properties of the Exponential Distribution10mVideo Slides for Two Hypothesis Tests for the Exponential10mVideo Slides for Best Tests10mVideo Slides for UMP Tests10mVideo Slides for a Normal Variance Test10mVideo Slides for an F-Distribution and a Ratio of Variances10m

2 practice exercises

Best Tests and Some General Skills30mUniformly Most Powerful Tests and F-Tests30m

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TOP REVIEWS FROM STATISTICAL INFERENCE AND HYPOTHESIS TESTING IN DATA SCIENCE APPLICATIONS

by RKOct 26, 2022

In-depth course on Hypothesis testing. Course instructor is quite engaging.

by GVJul 27, 2022

Loved the material. Content looks quite convincing and well explained!

View all reviews

About the Data Science Foundations: Statistical Inference Specialization

This program is designed to provide the learner with a solid foundation in probability theory to prepare for the broader study of statistics. It will also introduce the learner to the fundamentals of statistics and statistical theory and will equip the learner with the skills required to perform fundamental statistical analysis of a data set in the R programming language.

This specialization can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) degree offered on the Coursera platform. The MS-DS is an interdisciplinary degree that brings together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the MS-DS is ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://www.coursera.org/degrees/master-of-science-data-science-boulder. Logo adapted from photo by Christopher Burns on Unsplash.

Data Science Foundations: Statistical Inference

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Statistical Inference and Hypothesis Testing in Data Science Applications

About this Course

What you will learn

Define a composite hypothesis and the level of significance for a test with a composite null hypothesis.

Define a test statistic, level of significance, and the rejection region for a hypothesis test. Give the form of a rejection region.

Perform tests concerning a true population variance.

Compute the sampling distributions for the sample mean and sample minimum of the exponential distribution.