Asignificant amount of teaching assistant and instructor time is allocated to grading homework assignments, especially in large enrolment courses. However, the benefits of such a time- consuming activity are unknown and not well documented. Our goal is to examine the impact that different homework grading policies have on students' final examination performance. We are interested not only in the overall student performance, but also in the performance of specific student subgroups with varying backgrounds, as well as the impact of homework on the type of learning that takes place in the course. The study was conducted in a Numerical Methods course at the University of South Florida over a period of three years encompassing data from over 300 Mechanical Engineering students. Statistical analysis of data regarding the impact of homework grading policies on student subgroups based on several factors is presented. Our results indicate that there is no statistically significant difference in student examination performance when homework is graded versus when homework is assigned but not graded. However, certain grading policies did seem to put some subgroups of students at a disadvantage. While grading homework may not be critical in improving student examination performance, it is important to ensure that students practice the concepts.