Question

Simple random samples of high-interest mortgages and low-interest mortgages were obtained. For the 35 high-interest mortgages, the borrowers had a mean FICO score of 701 and a standard deviation of 47. For the 29 low-interest mortgages, the borrowers had a mean FICO credit score of 745 and a standard deviation of 21. Test the claim that the mean FICO score of borrowers with high-interest mortgages is different than the mean FICO score of borrowers with low-interest mortgages at the 0.2 significance level.

The test statistic is: ["-4.9718", "-2.5647", "-3.9974", "-1.5463", "-2.9644", "-3.2456", "-4.1334", "-1.7893"]           

The Critical Value is: +/- ["2.772", "1.313", "3.012", "2.403", "1.687", "2.032"]           

Based on this we: ["Reject the null hypothesis", "Fail to reject the null hypothesis"]   

Conclusion: There ["does", "does not"] appear to be enough evidence to support the claim that the mean FICO score of borrowers with high-interest mortgages is different than the mean FICO score of borrowers with low-interest mortgages.

**NOTE the values in-between " " are possible answer choices

Answer 1

Sample #1   ---->   1          
mean of sample 1,    x̅1=   701.00          
standard deviation of sample 1,   s1 =    47          
size of sample 1,    n1=   35          
                  
Sample #2   ---->   2          
mean of sample 2,    x̅2=   745.000          
standard deviation of sample 2,   s2 =    21.00          
size of sample 2,    n2=   29          
                  
difference in sample means = x̅1-x̅2 =    701.000   -   745.0000   =   -44.0000
                  
std error , SE =    √(s1²/n1+s2²/n2) =    8.8499          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -44.0000   /   8.8499   ) =   -4.9718

DF = min(n1-1 , n2-1 )=   28
  
  
t-critical value , t* = ±1.313

Reject the null hypothesis

There ["does", ] appear to be enough evidence to support the claim that the mean FICO score of borrowers with high-interest mortgages is different than the mean FICO score of borrowers with low-interest mortgages.

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