Question

Test the Hypotheses Below
Null Hypothesis: Mean Student Debt in 2011 is equal to Mean Student Debt in 2007
Alternative Hypothesis: Mean Student Debt in 2011 is not equal to Mean Student Debt in 2007
Alpha Level = 0.05

	Variable 1	Variable 2
Mean	3925.76	2876.82
Variance	222129.8188	140278.3547
Observations	50	50
Pooled Variance	181204.0867
Hypothesized Mean Difference	0
df	98
t Stat	12.32073615
P(T<=t) one-tail	6.27467E-22
t Critical one-tail	1.660551217
P(T<=t) two-tail	1.25493E-21
t Critical two-tail	1.984467455

1. Run the appropriate t-test (assuming either equal or unequal variances based on your conclusion in 1e above) using an alpha level of 0.05 to determine if there is a difference between the debt amounts in the two years and answer the following questions.
   
   1. What is the Null and Alterative Hypotheses for the T-Test for the differences between debt amounts in the two years?
      
      Null Hypothesis:
      
      Alterative Hypothesis:
      
   2. Which of the two years has the higher mean?  
      
      
   3. Is this a one-tailed or two-tailed test?  Explain?

4. What is the t Test Statistics?  What is the p-value?
   
5. Based on the statistical output, would you conclude that means are equal or not equal?  Why?

Answer 1

1. the Null and Alternative Hypotheses for the T-Test for the differences between debt amounts in the two ye

   1. Null Hypothesis: Mean Student Debt in 2011 is equal to Mean Student Debt in 2007
      Alternative Hypothesis: Mean Student Debt in 2011 is not equal to Mean Student Debt in 2007

      b )for student debt have higher mean from given output t
   2. wo-tailed test becasue alternative hypothesis is two-tailed

d ) the t Test Statistics is 12.32073615

the p-value is 1.25493E-21

e ) since p value is less than 0.05 so we conclude that Mean Student Debt in 2011 is not equal to Mean Student Debt in 2007