#### Overview of this book

Python, one of the world's most popular programming languages, has a number of powerful packages to help you tackle complex mathematical problems in a simple and efficient way. These core capabilities help programmers pave the way for building exciting applications in various domains, such as machine learning and data science, using knowledge in the computational mathematics domain. The book teaches you how to solve problems faced in a wide variety of mathematical fields, including calculus, probability, statistics and data science, graph theory, optimization, and geometry. You'll start by developing core skills and learning about packages covered in Python’s scientific stack, including NumPy, SciPy, and Matplotlib. As you advance, you'll get to grips with more advanced topics of calculus, probability, and networks (graph theory). After you gain a solid understanding of these topics, you'll discover Python's applications in data science and statistics, forecasting, geometry, and optimization. The final chapters will take you through a collection of miscellaneous problems, including working with specific data formats and accelerating code. By the end of this book, you'll have an arsenal of practical coding solutions that can be used and modified to solve a wide range of practical problems in computational mathematics and data science.
Preface
Basic Packages, Functions, and Concepts
Free Chapter
Mathematical Plotting with Matplotlib
Working with Randomness and Probability
Geometric Problems
Finding Optimal Solutions
Miscellaneous Topics
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# Testing hypotheses using t-tests

One of the most common tasks in statistics is to test the validity of a hypothesis about the mean of a normally distributed population given that you have collected sample data from that population. For example, in quality control, we might wish to test that the thickness of a sheet produced at a mill is 2 mm. To test this, we would randomly select sample sheets and measure the thickness to obtain our sample data. Then, we can use a t-test to test our null hypothesis, H0, that the mean paper thickness is 2 mm, against the alternative hypothesis, H1, that the mean paper thickness is not 2 mm. We use the SciPy stats module to compute a t statisticand a p value. If the p value is below 0.05, then we accept the null hypothesis with 5% significance (95% confidence). If the p value is larger than 0.05, then we must reject the null hypothesis in favor of our alternative hypothesis.

In this recipe, we will see how to use a t-test to test whether...