Hypothesis Testing

Mastering the Art of Statistical Decision Making through Hypothesis Testing

What you'll learn

Identify the key components of hypothesis testing, including null and alternative hypotheses, significance levels, and types of errors.

Explain the rationale behind different types of hypothesis tests (e.g., t-tests, z-tests) and when each is appropriate to use.

Apply the hypothesis testing framework to real-world data, performing tests to evaluate claims about population parameters.

Analyze the results of hypothesis tests by interpreting p-values, confidence intervals, and the significance of results.

Evaluate the outcomes of hypothesis tests, assessing the risk of Type I and Type II errors and the implications of these risks in decision-making.

Create and communicate clear reports of statistical findings, including all relevant assumptions, calculations, and interpretations of hypothesis test results.

Requirements

Comfort with elementary algebra and interpreting mathematical expressions.

Familiarity with basic probability concepts and rules.

Ability to interpret and construct graphs, such as histograms and box plots.

Description

This course provides a comprehensive introduction to hypothesis testing, one of the most fundamental techniques in inferential statistics. The course is designed to guide students through the process of making data-driven decisions by evaluating claims about populations based on sample data. Beginning with the essential concepts of null and alternative hypotheses, students will learn how to construct testable statements about population parameters and will explore the reasoning behind the formulation of these hypotheses. The course will emphasize the critical role of hypothesis testing in drawing conclusions in various real-world contexts, from scientific research to business decision-making.A key focus of the course will be the framework for making decisions using sample data. Students will develop a deep understanding of statistical significance and the logic behind rejecting or failing to reject a null hypothesis. They will also become familiar with the critical concepts of Type I and Type II errors, learning how to interpret p-values and confidence levels, and gaining insights into how these affect conclusions in hypothesis testing. Throughout the course, students will engage with one-sample and two-sample t-tests, z-tests for population proportions.By the end of the course, students will have the tools and knowledge to apply hypothesis testing to a range of research and business problems. They will also be equipped to critically evaluate the results of hypothesis tests reported in academic studies and the media. With an emphasis on both theoretical understanding and practical application, the course prepares students to confidently use hypothesis testing in their future academic and professional endeavors.

Overview

Section 1: Introduction

Lecture 1 1925 Hypothesis Testing

Section 2: OneNote Practice Problems

Lecture 2 OneNote Resource

Lecture 3 1977 Hypothesis Testing 1 Tail Upper - STDp Known

Lecture 4 1979 Hypothesis Testing 1 Tail Lower - STDp Known

Lecture 5 1981 Hypothesis Testing 2 Tail - STDp Known

Lecture 6 1983 Hypothesis Testing t Distribution 1 Tail Upper- STDp Not Known

Lecture 7 1985 Hypothesis Testing t Distribution 1 Tail Lower- STDp Not Known

Lecture 8 1987 Hypothesis Testing t Distribution 2 Tail- STDp Not Known

Undergraduate students seeking a deeper understanding of hypothesis testing in statistics.,Students in psychology, economics, biology, business, public health, and social sciences.,Individuals who have completed an introductory statistics course and want to further their knowledge of inferential statistics.,Students preparing for careers in research or data analysis.,Learners interested in applying statistical techniques to real-world problems, such as experiments and business performance evaluation.,Those planning to pursue advanced studies or careers in academia, industry, or government requiring strong statistical decision-making skills.