Final answer:
Statistical hypothesis tests, such as the t-test, are used to determine if experimental findings support a hypothesis or are due to chance, with the goal to limit the probability of making errors, and the power of the test quantifies the likelihood of correctly identifying true effects.
Step-by-step explanation:
The mathematical tools to evaluate the likelihood that the experiment's findings support a hypothesis or are due to chance are known as statistical hypothesis tests. These tests involve establishing a null hypothesis, which assumes no effect or change in a variable of interest, and then using inferential statistics to determine the probability of observing the collected data if the null hypothesis were true. Commonly, a threshold probability, such as a 5% chance, is set for making Type I errors, which is rejecting a true null hypothesis. A well-known statistical test is the t-test, which may be used to compare means between groups or against a hypothesized value. The power of the test, 1 – ß, is the probability of correctly identifying a true effect when it exists, and a higher power is considered more desirable in hypothesis testing.