"What is the hypothesis being tested?

'Is there a stat significant difference between each ethnicity in the category of final points?"

No, think substantively rather than statistically in this case. 'Does average final exam score vary by ethnicity and/or gender?'

H0: mean final exam score does not vary by ethnicity or gender.

H1: at least one ethnicity has a different mean exam score from one other ethnicity, or at least one gender has a different mean exam score from one of the other genders. (How many gender categories are in your sample?)

I think you're correct about two-way ANOVA with Tukey post hoc being the way to go.

Let me double check H0 and H1 are stated correctly.