In a study of student loan subsidies, the Department of Education reported that four-year Stafford Loan borrowers will owe an average of $12,168 upon graduation (USA Today, April 5, 1995). Assume that this average or mean amount owed is based on a sample of 480 student loans and that the population standard deviation for the amount owed upon graduation is $2200.
a. Develop a 90 % confidence interval estimation of the mean.
b. Develop a 95 % confidence interval estimation of the mean.
c. Discuss what happens to the width of the confidence interval as the confidence level is increased. Does this seem reasonable? Explain.
d. If you were to decrease the width of the 95% confidence interval by 25% of its current width, how much samples do you need to collect?