there are two populations (which i want to show they differ significantly). but the problem is i dont have the mean and std of two groups, independently.

but i have means and std deviation of these populations mixed and the ratio of them in the mixture. is there any way to analyse these data in order to show the difference?

Let s clarify it with an example:

population 1: physicians

population 2: nurses

the goal is to prove there is a significant difference in incomes

we have mean and std of these populations

population 3: 80 physicians, 80 nurses

population 4: 100 physicians, 30 nurses

population 5: 20 physicians, 120 nurses

is there any test to prove our hypothesis (income differences)??