Headhunters locate candidates to fill vacant senior positions in companies. These placement companies are typically paid a percentage of the salary of the filled position. A placement company that  specializes in biostatistics is considering a  move into information technology (IT). It earns a  fee of 15% of the starting salary for each person it places. Its numerous placements in biostatistics had an average starting salary of $125,000. Its first 50 placements in IT had an average starting salary of $140,000 1s = +20,0002 but produced higher costs at the agency. If each placement in IT has cost the placement company $1,200 more than each placement in biostatistics, should the firm continue its push into the IT industry?

(a)  State the null and alternative hypotheses.   Describe the parameters.

(b)  Describe Type I and Type II errors in this context.

(c)  Find the -value of the test. Do the data supply  enough evidence to reject the null hypothesis if  ? (Assume that the data meet the sample  size condition.)