**(9.5 points) 2.** The mean income per year of employees who produce internal and external newsletters and magazines for corporations was reported to be $51,500. These editors and designers work on corporate publications but not on marketing materials. As a result of poor economic conditions and oversupply, these corporate communications workers may be experiencing a decrease in salary. A random sample of 38 corporate communications workers revealed that x̄ = $49,762. Conduct a hypothesis test to determine whether there is any evidence to suggest that the mean income per year of corporate communications workers has decreased. Assume that the population standard deviation is $3750. Please use 4 decimal places for all critical values.

(6 pts.) b) Is there any evidence to suggest the true mean income per year of corporate communications workers has decreased? Perform the hypothesis test at a 1% significance level. Include the complete four step hypothesis test with all of the work.

(2 pts.) c) Calculate **and interpret** the appropriate 99% bound that is consistent with what you did in part b).

(1 pt.) d) If the employer also found a cheaper medical insurance that reduced the amount of money that the employees have to pay for health insurance by $300 per year**, in practical terms**, are the employees are really taking home less money than before? Please explain your answer.