3. A school administrator claims that students whose first language learned is not English score worse on the verbal portion of the SAT exam than students whose first language is English. The mean SAT verbal score of students whose first language is English is 515 with a population standard deviation of 112, on the basis of data obtained from the College Board. SAT verbal scores are normally distributed. In a random sample of 20 students whose first language learned were not English results in a sample mean SAT Verbal Score of 458.

a) Is there significant evidence in the administrator's claim that the SAT Verbal Score will be lower than those students whose first language is English? Provide statistical evidence to support your answer.

b) If your alpha was a .05, what choice should be made and thus what error would be created?

c) If your alpha was a .1, what choice should be made and thus what error would be created?