Amstat News 2011 reports an survey of salaries in the United States of full professors with 6-10 years of service at the given rank. The average salary of 59 statisticians is $168,500 with an estimated standard deviation of $41,480. The average salary of 37 biostatisticians is $188,100 with an estimated standard deivaition of $41,185. Test whether the mean yearly income of biostatisticians is at least $10,000 greater than the mean income of statisticians. State the statistical model and hypothesis.