#### Overview of this book

Are you looking to start developing artificial intelligence applications? Do you need a refresher on key mathematical concepts? Full of engaging practical exercises, The Statistics and Calculus with Python Workshop will show you how to apply your understanding of advanced mathematics in the context of Python. The book begins by giving you a high-level overview of the libraries you'll use while performing statistics with Python. As you progress, you'll perform various mathematical tasks using the Python programming language, such as solving algebraic functions with Python starting with basic functions, and then working through transformations and solving equations. Later chapters in the book will cover statistics and calculus concepts and how to use them to solve problems and gain useful insights. Finally, you'll study differential equations with an emphasis on numerical methods and learn about algorithms that directly calculate values of functions. By the end of this book, you’ll have learned how to apply essential statistics and calculus concepts to develop robust Python applications that solve business challenges.
Preface
1. Fundamentals of Python
Free Chapter
2. Python's Main Tools for Statistics
3. Python's Statistical Toolbox
4. Functions and Algebra with Python
5. More Mathematics with Python
6. Matrices and Markov Chains with Python
7. Doing Basic Statistics with Python
8. Foundational Probability Concepts and Their Applications
9. Intermediate Statistics with Python
10. Foundational Calculus with Python
11. More Calculus with Python
12. Intermediate Calculus with Python

# Inferential Statistics

Unlike descriptive statistics, where our goal is to describe various characteristics of a dataset using specific quantities, with inferential statistics, we'd like to perform a particular statistical modeling process on our dataset so that we can infer further information, either about the dataset itself or even about unseen data points that are from the same population.

In this section, we will go through a number of different methods of inferential statistics. From these discussions, we will see that each method is designed for specific data and situations, and it is the responsibility of the statistician or machine learning engineer to appropriately apply them.

The first method that we will discuss is one of the most fundamental in classical statistics: t-tests.

## T-Tests

In general, t-tests (also known as Student's t-tests) are used to compare two mean (average) statistics and conclude whether they are different enough from each other...