Principles of Managerial Statistics and Data Science

10Hypothesis Testing for One Population

10.1 Introduction

Three adventurers are in a hot‐air balloon. Soon, they find themselves lost in a canyon in the middle of nowhere. One of the three says, “I've got an idea. We can call for help in this canyon and the echo will carry our voices far.” So he leans over the basket and yells out,

“Hello! Where are we?”

They hear his voice echoing in the distance. Fifteen minutes pass. Then they hear this echoing voice:

“Hello! You're lost!!”

One of the three says, “That must have been a statistician.” Puzzled, his friend asks, “Why do you say that?” He replied, “For three reasons. One – he took a long time to answer, two – he was absolutely correct, and three – his answer was absolutely useless.”¹

This joke has some truth to it, in the sense that statisticians do not always communicate well their results. But, we have all heard it, communication is a two‐way street. The issue is also due to the lack of understanding of statistics in part of the receiver of the “statistical message.” We have previously seen multiple concepts that are not straightforward to understand, such as the interpretation of the results from confidence intervals and the meaning of the correlation coefficient. Hypothesis testing is one of the most used statistical methods, yet the most misunderstood topic in statistics.

In practice, we often have to make decisions in situations involving uncertainty. As a result of this uncertainty, we cannot guarantee a good final result. ...