3436384042444648505254565814890138059901175677900122279016689388156256694Securit
ID: 2946835 • Letter: 3
Question
3436384042444648505254565814890138059901175677900122279016689388156256694Securitization of mortgages is a process in which banks bundle mortgages and sell them to investors who then bear the risk of default instead of the bank. Atif suspects that securitized mortgages are more likely to be defaulted upon than the mortgages the banks retain. He discovers that mortgages to borrowers with FICO credit scores of 620 or higher are far more likely to be securitized than those with lower FICO scores. Atif then seeks to find evidence that banks are manipulating the FICO credit scores of riskier borrowers to make their mortgages easier to resell.
Atif finds that applicants in 2001 with a FICO score of 620 have an average income of $47,287, but he does not know the population's standard deviation, nor its distribution.
He obtains a simple random sample of 47 mortgage applications with a FICO score of 619. The stem?and?leaf plot to the right shows Atif's sample data, rounded to the nearest hundred. The sample mean is $47,587, and the sample standard deviation is $4,912.
Atif wants to use a t-test at an ? of 0.05 to test the hypothesis that all borrowers with a FICO score of 619 have an average income higher than $47,287. Identify whether each of the following five statements is true or false.
The sample is a simple random sample.
The population standard deviation is not known.
There are no outliers in the sample.
The population is normally distributed,
or the sample size is large enough.
The requirements for a t-test are met.
Explanation / Answer
The sample is a simple random sample -true (given)
The population standard deviation is not known -true
There are no outliers in the sample. --(stem leaf mplot is not given for this)
The population is normally distributed,
or the sample size is large enough. -True (sample is large enough as n>30)
The requirements for a t-test are met. -True
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