Most physics instructors believe that adequate sleep is important in order for students to perform well on problem solving, and many instructors advise students to get plenty of sleep the night before an exam. After years of giving such advice to students at Loyola Marymount University (LMU), one of us decided to find out how many hours students actually do sleep the night before an exam, and how that would relate to their performance. The effect of inadequate sleep on exam performance was explored in a second-semester introductory physics course. At the end of the final exam, students reported the number of hours they slept the night before. Sleep deprivation corresponded to lower final exam scores. The main purpose of this study is to provide evidence that instructors can provide to their students to convince them that their time is better spent sleeping rather than studying all night before an exam.