A left tailed test is used when the alternative hypothesis involves a less-than inequality symbol. A right tailed when it involves a greater-than symbol. And a two tailed when it involves a not-equal to.
Gender can be used in a hypothesis test of two populations if the samples are random, independent, and greater than 30. Here, one sample would consist of more than 30 randomly chosen males and the other of more than 30 randomly chosen females. The 30 or more condition can be eliminated if the populations are normally distributed and have a known standard deviation.
I would use a two population test in my statistics class.