The test of significance is designed to assess the strength of the evidence against the null hypothesis.
To prove the statement of the prosecutor, evidence must be convincing enough to convict the defendant; this is analogous to sufficient statistical significance in a hypothesis test.
However, this does not necessarily mean that the alternative hypothesis is true due to the potential presence of a type I error.
In order to quantify the statistical significance, the test statistic variables are assumed to follow a certain probability distribution such as the normal distribution or t-distribution to determine the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct, which is defined as the p-value.
In the metaphor of a trial, the announcement may be "with tolerance for the probability α of an incorrect conviction, the defendant is guilty."
The concept of an alternative hypothesis in testing was devised by Jerzy Neyman and Egon Pearson, and it is used in the Neyman–Pearson lemma.
However it was not part of Ronald Fisher's formulation of statistical hypothesis testing, and he opposed its use.