Hypothesis testing isn't just for population means and standard deviations. You can use this procedure to test many different kinds of propositions. For example, a jury trial can be seen as a hypothesis test with a null hypothesis of "innocent" and an alternative hypothesis of "guilty."

One particularly interesting application of hypothesis testing comes from the Royal Mint in England. The Royal Mint has been producing coins for more than 1,100 years. It currently produces coins for circulation in the United Kingdom, as well as commemorative coins. It also produces coins and medals for foreign governments.

Throughout the Royal Mint's history, producing coins of consistent quality has been a constant challenge. Testing the quality of each coin would be a huge burden, so during the late 13th century, the Royal Mint developed a process for testing the quality of its coins based on randomly chosen samples. This process is known as the "Trial of the Pyx." (The Pyx refers to wooden chests that contain the random samples of coins; the name derives from the Pyx Chamber in Westminster Abbey where the chests were once kept.)

As part of the trial, samples of coins produced throughout the year are set aside to determine whether they have the proper weight, diameter, and chemical composition. The coins are then presented to a jury for testing. (Members of the jury were originally goldsmiths, who had expertise in assessing the weight and purity of gold and silver.)

The Trial of the Pyx can be seen as a hypothesis test, where the null and alternative hypotheses are as follows:

  • Null hypothesis: The coins conform to the required weight, diameter, and composition.

  • Alternative hypothesis: The coins don't conform to the required weight, diameter, and composition.

The coins being tested are compared with a standard coin, known as a Trial Plate. If the coins are significantly different from the Trial Plate, the null hypothesis is rejected. This outcome indicates that the production process is flawed and needs to be fixed. Otherwise, the null hypothesis is not rejected, and the coins are acceptable.

Although the Trial of the Pyx predates the formal development of hypothesis testing by hundreds of years, it's an excellent example of how you can use hypothesis testing to draw conclusions from sample data with a high level of confidence. In fact, the Royal Mint was able to establish a reputation for producing coins of consistent quality; clearly, its testing procedures were a major source of its success.