Question 1174679: A mortgage is a type of loan that is secured by a designated
piece of property. If the borrower defaults on the loan, the
lender can sell the property to recover the outstanding debt.
The following data are outstanding principal balance of home
mortgages foreclosed by the bank due to default by the
borrower during the last 3 years obtained from a random
sample of 12 foreclosed mortgages:
95,982; 81,422; 39,888; 46,836; 66,899; 69,110; 59,200; 62,331; 105,812; 55,545; 56,635; 72,123
Test the claim that the average outstanding balance of home
mortgages is less than 80,000.
a. Using a 0.05 level of significance.
b. Using a 0.10 level of significance.
c. Using a 0.01 level of significance.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho: mean >=$80000
Ha: mean < $80000
alpha=0.05 (initially) p{reject Ho|Ho true}
test stat is a t df=11 reject Ho if t < -1.796
mean is $67698.58
s is $19,184.79
calculation t=(x bar-mean)/s/sqrt(n)=-12301.42*sqrt(12)/19184.79
=-2.22
Will reject the hypothesis at both the 5% and the 10% level.
At the 1% level, the critical value is -2.718 and would fail to reject at that significance level.
p-value=0.024
This means that at the 0.05 and 0.10 levels of significance we conclude that the true value of the average outstanding value of the mortgages is < $80000 but not conclude that at the 1% level.
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