Faculty members in a state university system who resign within 10 years of initial em- ployment are entitled to receive the money paid into a retirement system, plus 4% per year. Unfortunately, experience has shown that the state is extremely slow in return- ing this money. Concerned about such a practice, a local teachers organization decides to investigate. After a confrontation with the teachers' union, the state promised to make reimbursements within 60 days. Monitoring of the next 40 resignations yields an average of 61 days, with a standard deviation of 10 days. (a) Set up the appropriate hypothesis tests for this investigation. (b) Test the null hypothesis using an alpha level of 0:01, draw out a graphical repre- sentation of the test. Include critical values, and test statistic value. What is your conclusion regarding the population parameter mu ( state your answer in the context of the problem).