St. West High School requires that students are assigned an average of $3.5$ hours of homework each night. The school board, however, believes that the average amount of time per night for the assigned homework is not $3.5$ hours. Subsequently, the school board decides to take a random sample of $87$ St. West High School students in order to determine whether there is convincing evidence to support their suspicion. The board finds that the sample of students were assigned an average of $3.7$ hours on homework per night with a standard deviation of $1.1$ hours. **Assuming that all the necessary conditions are met, what is the $p$-value associated with the hypothesis test the school board would use to determine whether or not St. West students are being assigned an average of $3.5$ hours of homework per night?** [[☃ radio 2]]