Final answer:
The t-test for independent samples is the hypothesis-testing procedure when two different groups are compared, and population variance is unknown. It provides a way to either reject or not reject the null hypothesis based on sample data. The conclusion is tied to the levels of significance and potential errors known as Type 1 and Type 2.
Step-by-step explanation:
The procedure you are referring to in the question is known as the t-test for independent samples (or independent two-sample t-test) when comparing two separate groups of people and the population variance is unknown. This statistical method is used to determine whether there is a significant difference between the means of two groups, which could be related to almost any feature such as scores, measurements, or quantities.
In hypothesis testing, we encounter two main decisions: either we reject the null hypothesis, or we do not reject the null hypothesis. Failure to reject the null hypothesis does not necessarily mean it is true; it simply indicates that there is not enough evidence to prove it false, given a pre-determined level of significance. Conversely, rejecting the null hypothesis suggests that the sample data provides sufficient evidence to conclude that the null hypothesis is not true.
Type 1 error occurs when we incorrectly reject a true null hypothesis, whereas Type 2 error happens when we fail to reject a false null hypothesis.