Question

College students are accumulating increasing amounts of debt while they pursue their degrees. This debt has a significant economic affect as the new graduates strive to begin their life after graduation. Nationally, the mean debt of recent graduates from all public 4-year institutions was $27995.

How does the loan debt of recent graduates of North Carolina's public colleges and universities compare to student loan debt nationally? To answer this question, use the data in this Excel file Student Debt Recent UNC System Grads that shows the student debt of recent graduates from 12 UNC System schools to perform the hypothesis test:

H₀: μ = 27995, H_a: μ < 27995

where μ is the mean student loan debt of all recent graduates from UNC System schools.

Name	Institution Sector	Average debt of graduates
Appalachian State University	Public, 4-year or above	$22,855
East Carolina University	Public, 4-year or above	$28,918
North Carolina A & T State University	Public, 4-year or above	$34,379
North Carolina State University	Public, 4-year or above	$24,053
University of North Carolina School of the Arts	Public, 4-year or above	$28,551
University of North Carolina Wilmington	Public, 4-year or above	$24,605
University of North Carolina at Asheville	Public, 4-year or above	$23,824
University of North Carolina at Chapel Hill	Public, 4-year or above	$22,214
University of North Carolina at Charlotte	Public, 4-year or above	$27,453
University of North Carolina at Greensboro	Public, 4-year or above	$26,841
University of North Carolina at Pembroke	Public, 4-year or above	$25,831
Western Carolina University	Public, 4-year or above	$15,669

Question 1: What is the value of the test statistic t for this hypothesis test? (round x and s to the nearest whole number).

Question 2: What is the P-value for this hypothesis test? (use 4 decimal places in your answer)

Question 3: What is the correct conclusion for this hypothesis test?

a) The null hypothesis H₀: μ = 27995 is false with probability equal to the P-value, so reject H₀.

b) The null hypothesis H₀: μ = 27995 is true with probability equal to the P-value, so reject H₀.    

c) Reject the null hypothesis H₀: μ = 27995; the probability we have made a mistake is equal to the P-value.

d) Do not reject the null hypothesis H₀: μ = 27995 and conclude that the mean loan debt of recent UNC System graduates does not differ significantly from the national average.

e) Reject the null hypothesis H₀: μ = 27995 and conclude that the mean student loan debt of recent UNC System graduates is less than the national average.

Answer 1

using excel>addin>phstat>one sample t

we have

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	27995
Level of Significance	0.05
Sample Size	12
Sample Mean	25432.75
Sample Standard Deviation	4529.117296
Intermediate Calculations
Standard Error of the Mean	1307.4435
Degrees of Freedom	11
t Test Statistic	-1.9597
Lower-Tail Test
Lower Critical Value	-1.7959
p-Value	0.0379
Reject the null hypothesis

H0: μ = 27995, Ha: μ < 27995

Ans 1 ) the value of the test statistic t =-1.9597

Ans 2: the P-value for this hypothesis test is 0.0379

ans 3: What is the correct conclusion for this hypothesis test

Reject the null hypothesis H₀: μ = 27995 and conclude that the mean student loan debt of recent UNC System graduates is less than the national average