School officials in St. Louis County believe that their schools differ from other school in the state in terms of safety. To examine this, you survey a random sample of 64 high school principals in St. Louis County and ask them how many violent incidents occurred at their school in the past year. You find that this sample reported an average of 25.2 violent incidents in the past year. You know that average number of violent offenses reported by all high school principals in Missouri is 27.2, with a population standard deviation of 8.8.

a) Did principals in St. Louis County report a significantly different number of violent incidents than principals in Missouri as a whole? Use alpha = .05 and show all steps of your hypothesis test