Please answer all of the questions and all calculations.

A sociology professor is interested in determining whether sociology/criminal justice students have a higher GRE verbal score than the average student at the school.

He takes a sample of 90 students and obtains a mean GRE verbal score of 568 for his sample of sociology/criminal justice students. He knows the population standard deviation is 99 and the population mean verbal GRE score for all school students is 554.

Use the following information to conduct a test of the hypothesis that sociology/criminal justice undergraduates have higher GRE verbal scores than the average school student.

Set a = 0.05 and run the appropriate hypothesis test.

Please show all steps of hypothesis testing.