Question: Full-time PhD students receive an average salary of $12.837 according to the U.S. Department of Education. The dean of graduate studies at a large state university feels that PhD students in his state earn more than this. He surveys 44 randomly selected students and finds their average salary is $14, 445 with a standard deviation of $1500. With α = 0.05 is the dean correct? Show the math and explain your answer.