Then I propose such a scientific study be performed.
I don't like appeals to "common sense" in political matters (and unfortunately gender and sexuality is very political right now). Because, hey, if you're wrong, wouldn't that be an interesting result?
http://www.bloomberg.com/politics/articles/2015-05-22/americ...
All things must often appeal to common sense regardless of the politics behind the issue. Males have penises and females don't, does a scientific study need to be conducted to prove this point? No. Because if we needed a scientific study for every possible issue without regard to common sense we would make zero progress on any topic.
What you've described is what I refer to as "sex" while totally ignoring the topic of gender. https://en.wikipedia.org/wiki/Sex_and_gender_distinction
I'm not sure what your politics are, but a lot of people who have traveled down this path in a conversation ended up expressing very intolerant opinions towards transgendered people. If you do feel contempt for someone whose gender identity and/or assumed gender role doesn't match their biological sex, please don't share that opinion with me.
They have not found a definitive biological causal mechanism that causes transgendered traits. They have found correlations between certain biological mechanisms and transgendered traits. However these findings lead to only about a 70% correlation at most.
Please note that the 70% correlation cannot be ignored. It indicates high likelihood of a causal connection. It is unwise to dismiss this correlation even if it is below a 95% criteria. My intuition tells me that 70% is only a statistic for a single causative biological agent out of several. Once all biological markers are discovered and correlated together, I believe that the number will be 99%.
Please also note that the correlation between the XX chromosomes and the female gender is above 95%, same with the XY chromosomes and the male gender. These correlations meet your criteria. There is no scientific study that proves this but you will note through common sense that males and females tend to act within their gender role over 95% of the time.