Question: Salaries Student Services. 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 45 officials in student services earned an average of x = $50,340 each year.

(a) Assume that \(\sigma \) = $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 \(\sigma \) = $10,780 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?

(c) Assume that \(\sigma \) = $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 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?