The assignment aims to compare the performance of deleting nodes from a custom NumberList with that of the standard library (STL) list. The author hypothesizes that the NumberList's deleteNode method will be faster than STL's erase function. Three sample data sets of 20000, 30000, and 50000 are used to test this hypothesis, and the results show that deleting nodes in the NumberList is indeed faster than in the STL list.