Question

The U.S. Department of Education (USDE) issues periodic reports on variables related to higher education. One concern for the country is the amount of student debt incurred by those attending universities and colleges. Does the type of institution affect debt status? The USDE investigates both the amount of debt owed and the percent of borrowed amount still owed after 12 years. Large amounts of debt make it more difficult for college graduates to buy major purchases such as vehicles and homes. Delaying these types of purchases affects the overall US economy. Does the type of institution attended affect the average percent of borrowed amount still owed after 12 years? To investigate, the USDE sampled average amounts of debt owed among the 4 basic types of institutions: 1) public 4-year institutions, 2) public 2-year institutions, 3) private non-profit institutions, and 4) private for-profit institutions. The data collected is shown in the table below. Part A) Perform the necessary statistical analysis to determine whether the mean percent of borrowed amount still owed after 12 years differs among the 4 classes of higher education institutions. Use an alpha of .05. Be sure to show all required steps. Part B) Provide a post hoc analysis is you find significant differences. Use the confidence interval method as provided by Minitab and as discussed in class.

Amount of Debt Still Owed After 12 Years (in $ thousands)

Public 4 Year	Public 2 Year	Private Non-Profit	Private For-Profit
83.4	50.4	62.4	68.9
70.5	44.2	65.6	70.2
75.1	40.6	42.9	80.2
69.1	48.3	55.6	90.1
72.9	26.3	56.9	75.1
65.3	40.2	38.6	88.2
81.5	36.3	50.5	70.3
64.3	40.5	57.6	68.4

Answer 1

a) H0 : There is no significance difference among the 4 groups of means

H1: There is significance difference among the 4 groups of means

From the given data

									Total	Ti^2/ni
Public 4 Year	83.4	70.5	75.1	69.1	72.9	65.3	81.5	64.3	582.1	42355.05
Public 2 Year	50.4	44.2	40.6	48.3	26.3	40.2	36.3	40.5	326.8	13349.78
Private Non-Profit	62.4	65.6	42.9	55.6	56.9	38.6	50.5	57.6	430.1	23123.25
Private For-Profit	68.9	70.2	80.2	90.1	75.1	88.2	70.3	68.4	611.4	46726.25
								G=	1950.4	125554.3

Here P-value < alpha 0.05 so we reject H0

Thus we conclude that  there is significance difference among the 4 groups of means

b) From the given data