Consider college officials in admissions, registration, counseling, financial aid, campus ministry, food services, and so on, How much money do these people make each year? Suppose you read in your local newspaper that 43 officials in student services earned an average of x = $50,340 each year (a) Assume that o = $16,560 for salaries of college officials in student services. Find a 90% confidence interval for the population mean salaries of such personnel. What is the margin of error? (Round your answers to the nearest whole number.) lower limit upper limit margin of error (b) Assume that a = $10,060 for salaries of college officials in student services. Find a 90% confidence interval for the population mean salaries of such personnel. What is the margin of error? (Round your answers to the nearest whole number.) lower limit upper limit margin of error $ (c) Assume that o = $5,000 for salaries of college officials in student services. Find a 90% confidence interval for the population mean salaries of such personnel. What is the margin of error? (Round your answers to the nearest whole number) lower limit upper limit 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? O As the standard deviation decreases, the margin of error decreases. O As the standard deviation decreases, the margin of error remains the same. O As the standard deviation decreases, the margin of error increases. (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? O As the standard deviation decreases, the confidence interval decreases in length. O As the standard deviation decreases, the confidence interval remains the same length. As the standard deviation decreases, the confidence interval increases in length