First, 'hash table' isn't a sorting algorithm. If you apply 'hash table' to an array the result is not a sorted array.
Second, assuming that numberOfYearsOld takes on at most 100 unique values (which I think is reasonable), the best you can hope for is for every hash table insertion and lookup to require you to traverse an average of 5000 students (because on average you will have to look through half of a list of 10,000 students). If you used this as an intermediate step in a real sorting algorithm, your sort would take O(n^2) time.
Second, assuming that numberOfYearsOld takes on at most 100 unique values (which I think is reasonable), the best you can hope for is for every hash table insertion and lookup to require you to traverse an average of 5000 students (because on average you will have to look through half of a list of 10,000 students). If you used this as an intermediate step in a real sorting algorithm, your sort would take O(n^2) time.