We studied the effect of such stereotypes in an experimental market, where subjects were hired to perform an arithmetic task that, on average, both genders perform equally well.
If this is actually what they did, then it's a bit shady. Most of the data shows that men and women are the same on average, but men have a higher variance. So if managers are hiring the best, you'll get more men. Of course, the paper is paywalled, so who knows?
It is nice to know that objective measurements can reduce bias. Score 1 for hiring by github. I'd be curious to see what happens with incentives taken into account - make the employees do math problems and the manager gets $1 for every correct answer.