GTx: Probability and Statistics IV: Confidence Intervals and Hypothesis Tests

This course covers two important methodologies in statistics – confidence intervals and hypothesis testing. Confidence intervals allow us to make probabilistic statements such as: “We are 95% sure that Candidate Smith’s popularity is 52% +/- 3%.” 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?"

Confidence Intervals and Hypothesis Testing

An Intermediate-Level Course by GTx

Course Description

This intermediate-level course, offered by GTx, delves into two crucial statistical methodologies: confidence intervals and hypothesis testing. It's an essential part of the Professional Certificate in Statistics, Confidence Intervals and Hypothesis Tests program, designed to equip learners with advanced skills in data analysis and statistics.

The course begins by exploring confidence intervals, a concept frequently encountered in everyday life. Students will learn how to make probabilistic statements based on sample observations, such as estimating a candidate's popularity within a certain range. The second half of the course focuses on hypothesis testing, teaching students how to pose and validate hypotheses in a statistically rigorous manner. This knowledge is applicable in various fields, from drug efficacy studies to material strength comparisons.

What You Will Learn

Understand and apply confidence intervals in real-world scenarios
Formulate and interpret confidence intervals for various probability distributions and their parameters
Grasp the concept of hypothesis testing and its practical applications
Identify and mitigate different types of errors in hypothesis testing
Design and interpret hypothesis tests for various probability distributions and their parameters
Utilize statistical software like Excel and R for data analysis

Prerequisites

Basic knowledge of set theory and calculus
Familiarity with probability concepts (covered in "A Gentle Introduction to Probability")
Understanding of random variables (from the "Random Variables" course)
Basic statistical knowledge (from "A Gentle Introduction to Statistics")
Some experience with computer programming, particularly in Excel or R

Course Content

Introduction to confidence intervals and their applications
Formulation and interpretation of confidence intervals for various distributions
Normal distribution confidence intervals (mean, variance, difference of means)
Bernoulli proportion confidence intervals
Introduction to hypothesis testing and its importance
Types of errors in hypothesis testing and mitigation strategies
Hypothesis tests for normal distributions (mean, variance, difference of means)
Bernoulli proportion hypothesis tests
Goodness-of-fit tests and their applications

Who This Course Is For

Data analysts and statisticians looking to enhance their skills
Researchers who need to interpret and present statistical findings
Business professionals making data-driven decisions
Students pursuing careers in data science, economics, or related fields
Anyone interested in deepening their understanding of statistical methodologies

Real-World Applications

Market research: Estimating consumer preferences and market trends
Quality control: Assessing product quality and comparing manufacturing processes
Medical research: Evaluating drug efficacy and treatment outcomes
Finance: Analyzing investment risks and returns
Social sciences: Conducting and interpreting survey results
Environmental studies: Monitoring and predicting climate changes
Sports analytics: Evaluating player performance and team strategies

Syllabus

Module 1: Confidence Intervals

Lessons 1-10 covering various aspects of confidence intervals

Module 2: Hypothesis Testing

Lessons 1-15 covering introduction, errors, and various types of hypothesis tests