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 x¯ = $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.

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.

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

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.