University of Colorado Boulder
Statistical Inference and Hypothesis Testing in Data Science Applications
University of Colorado Boulder

Statistical Inference and Hypothesis Testing in Data Science Applications

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

Taught in English

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Jem Corcoran

Instructor: Jem Corcoran

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Course

Gain insight into a topic and learn the fundamentals

4.7

(37 reviews)

Intermediate level

Recommended experience

38 hours (approximately)
Flexible schedule
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Progress towards a degree

What you'll 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.

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Assessments

6 quizzes

Course

Gain insight into a topic and learn the fundamentals

4.7

(37 reviews)

Intermediate level

Recommended experience

38 hours (approximately)
Flexible schedule
Learn at your own pace
Progress towards a degree

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This course is part of the Data Science Foundations: Statistical Inference Specialization
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There are 6 modules in this course

Welcome to the course! This module contains logistical information to get you started!

What's included

6 readings1 app item1 discussion prompt1 ungraded lab

In this module, we will define a hypothesis test and develop the intuition behind designing a test. We will learn the language of hypothesis testing, which includes definitions of a null hypothesis, an alternative hypothesis, and the level of significance of a test. We will walk through a very simple test.

What's included

6 videos12 readings1 quiz1 programming assignment2 ungraded labs

In this module, we will expand the lessons of Module 1 to composite hypotheses for both one and two-tailed tests. We will define the “power function” for a test and discuss its interpretation and how it can lead to the idea of a “uniformly most powerful” test. We will discuss and interpret “p-values” as an alternate approach to hypothesis testing.

What's included

7 videos8 readings1 quiz1 programming assignment1 ungraded lab

In this module, we will learn about the chi-squared and t distributions and their relationships to sampling distributions. We will learn to identify when hypothesis tests based on these distributions are appropriate. We will review the concept of sample variance and derive the “t-test”. Additionally, we will derive our first two-sample test and apply it to make some decisions about real data.

What's included

7 videos8 readings1 quiz1 programming assignment1 ungraded lab

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.

What's included

6 videos7 readings2 quizzes

In this module, we develop a formal approach to hypothesis testing, based on a “likelihood ratio” that can be more generally applied than any of the tests we have discussed so far. We will pay special attention to the large sample properties of the likelihood ratio, especially Wilks’ Theorem, that will allow us to come up with approximate (but easy) tests when we have a large sample size. We will close the course with two chi-squared tests that can be used to test whether the distributional assumptions we have been making throughout this course are valid.

What's included

5 videos7 readings1 quiz1 programming assignment1 ungraded lab

Instructor

Instructor ratings
4.9 (12 ratings)
Jem Corcoran
University of Colorado Boulder
6 Courses25,247 learners

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Recommended if you're interested in Probability and Statistics

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4.7

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