Question: The average college student goes through 500 disposable cups in a year. To raise environmental awareness, a student group at a large University to help count how many cups were used by students on their campus. A random sample of 50 students’ results found that they used a mean of 476 cups \(\sigma \) =42 cups. At \(\alpha \) = 0.01, is there sufficient evidence to conclude that the mean differs from 500?