Question: Salaries College Officials. How much money do these people make each year? You read in a paper that 45 Officials in student services earned an average of xbar = $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 o = $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 o = $4,830 for salaries of college officials in student services. Find a 90% confidence interval for the population means salary oif such personnel. What is the margin of error?

(d) Compare the margins of error for parts (d) thru (c). As the standard deviation decreases, does the margin of error decrease?

(e) Compare the lengths of the confidence intervals for parts (e) thru (c). As the standard deviation decreases, does the length of a 90% confidence interval decrease?