Two business schools, A and B, located in the same metropolitan area and they are competing for bragging rights. One of the points of competition is average salary of graduating seniors. 30 graduating seniors from A and 25 from B were surveyed. A’s students had an average salary of \$62,000, and B's students had an average salary of \$67,000. Based on historical data, the population standard deviation is assumed to be \$10,000 for A and \$15,000 for B. Construct the hypotheses and conduct the appropriate tests that school B could use to claim that its students have a higher average graduating salary that A. Using a 5% level of significance, and the sample data provided, determine if school B can claim that its average graduating salary is greater than that of school A.