Question

Test the Hypotheses Below Null Hypothesis: Mean Student Debt in 2011 is equal to Mean Student...

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?

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

Homework Answers

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

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