Confidence interval for the population mean.
Consider college officials in admissions, registration, counselling, financial aid, campus ministry, food services, and so on. How much money do these people make each year? Suppose you read in your local paper that 45 officials in student services earned an average of x = $50,340 each year.
(a) Assume that σ = $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) Suppose that σ = $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) Presume that σ = $44830 for salaries of college officials in student services. Find a 90% confidence interval for the population means salary of such personnel. What is the margin of error?
(d) Evaluate the margins of errors for parts (a) through (c). As the standard deviation decreases, does the margin of error decrease?
(e) Evaluate 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?