Question: Suppose that you read in your local newspaper that 45 officials in student services earned an average \(\bar{X}\) =$50,340 each year.

a. assume that =$16,920, for salaries of college officials in student services. Find a 90% confidence interval for the population mean salary of such personnel. What is the margin of error?

b. assume that = $ 10,780 for salaries of college officials in student services. Find a 90% confidence for the population mean salary of such personnel. What is the margin of error?

c. assume that $4830 for salaries of college officials in student services. Find a 90% confidence interval for the population mean salary of such personnel. What is the margin of error?

d. Compare the margins of error for parts a through c. as the standard deviation decreases, does the margin of error decrease?

e. Compare the lengths of the confidence intervals for parts a through c. as the standard deviation decreases, does the length of a 90% confidence interval decrease?