In a certain state, officials at the Department of Education wanted to investigate whether seniors in high school are absent more often than other high school students. At the end of the school year, a random sample of $50$ seniors from the state was selected, and their attendance records were analyzed.
The mean number of days these seniors were absent from school was $6.2$ with a standard deviation of $2.1$. Attendance records were also analyzed for a second, independent random sample of $50$ high school students in the state who were not seniors. The mean number of days these students were absent was $5.7$ days with a standard deviation of $1.6$. No outliers were found in either sample.
Does the data provide convincing evidence at the $\alpha=0.05$ level that seniors in high school have more absences on average than other high school students?