In this article, the authors focus on hypothesis testing--that peculiarly statistical way of deciding things. Statistical methods for testing hypotheses were developed in the 1920s and 1930s by some of the most famous statisticians, in particular Ronald Fisher, Jerzy Neyman and Egon Pearson, who laid the foundations of almost all modern methods of statistical inference, introducing concepts and terminology (such as consistency, efficiency, sufficiency, likelihood, null and alternative hypotheses, critical region, power, and uniformly most powerful test) that are today familiar to every statistician. However, most statisticians are doing statistics that rarely give much thought to the philosophical foundations on which their methods rest. This lack of attention extends also to statistics education. Here, the authors present some questions and answers on hypothesis testing, which are important to the development of a deep and balanced understanding of statistics.