Is it possible to analyse two mixed group?

#1
This is the problem:
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)??
 

Karabiner

TS Contributor
#3
we have mean and std of these populations
population 3: 80 physicians, 80 nurses
These are samples, not populations, by the way.
You could calculate the Pearson correlation coefficient between proportion of nurses in the respective samples,
and mean income in the respective samples. But with just n=3 samples, a test of statistical significance wil not
be possible, I suppose.

With kind regards

Karabiner