Edith Educationer wants to take a closer look at the 10 honors students in her Statistics course (n = 10). She believes they are the smartest kids in...

  Edith Educationer wants to take a closer look at the 10 honors students in her Statistics course (n = 10).  She believes they are the smartest kids in the state!  She gives the students a state-normed statistics test, which has a state average of 48.2 (µ= 48.2).  Her sample of 10 students had an average of 54.3 on the exam and a standard deviation of 8.2 points (s = 8.2).  Is there enough evidence to conclude that Edith's class is performing better (have a higher score) than other students in the state?  

Conduct a hypothesis test, use the traditional method to solve this problem using α = 0.01.