What is the appropriate statistical test to test the difference in average (mean) between two groups, while the group average is made up of individual averages?

Here is the setup, I have two groups to conduct a/b testing for changing the color of the buy button, and the outcome is the clickthrough rate. I want to restrict that each person from their respective group will be gathered in their first session within a two-week period, a person can view multiple pages and click the buy button during their first session visit. We will calculate the average click-through rate per person, and aggregate the whole group by …

a/b testing b testing color datascience difference mean person rate setup statistical test testing