Performing hypothesis testing for two means

In this section, we will explore the process of comparing two sample means using hypothesis testing. When comparing two sample means, we want to determine whether a significant difference exists between the means of two distinct populations or groups.

Suppose now we have two groups of samples. These two groups could represent a specific value before and after treatment for each sample. Our objective is thus to compare the sample statistics of these two groups, such as the sample mean, and determine whether the treatment has an effect. To do this, we can perform a hypothesis test to compare mean values from the two independent distributions using either bootstrap simulation or t-test approximation.

When using the t-test in the hypothesis test to compare the mean values of two independent samples, the two-sample t-test assumes normal distribution for the data, and that the variances of the two populations are equal. However, in cases...