Discussion:
It looks like you selected your IV and DV appropriately. Remember to fully describe your variables by indicating the variable name, label, and measurement level. Also indicate the data set for your variables. The variable race is nominal. Nominal variables are also categorical. Race is measured, it is just measured on a nominal measurement level.
Your research hypothesis is good. However, be careful when stating the null hypothesis. It is incorrect to imply that all means differ. Instead you should make a statement that "at least one mean differs" or "not all means are equal". Notice how this is different from saying that "all means differ."
Be sure to fully report your results. First you must review the Levene's test for the assumption of equal variances.
Then you must report the F-test for the ANOVA.
Then you must report an appropriate post hoc test to determine which means differ. One post hoc test that does not assume equal variances is the Games-Howell test; report the results of this test if the Levene's test has a p-value less than
One post hoc test that does assume equal variances is the Bonferroni test; report the results of this test of the Levene's test has a p-value greater than