[2](10) Simple random samples of high-interest (5.36%) mortgages and low interes

Question

[2](10) Simple random samples of high-interest (5.36%) mortgages and low interest (3.77%) mortga were obtained. For the 40 high-interest mortgages, the borrowers had a mean FICO credit score of 594.8 and standard deviation of 12.2. For the 40 low-interest mortgages, the borrowers had a mean FICO credit score of 785.2 and standard deviation of 16.3. Use a 0.01 significance level, we wish to test the claim that t mean FICO score of borrowers with high-interest mortgage is lower than the mean FICO score of borrowers with low-interest mortgage. ge a) Set up the null and alternative hypotheses. Ho Hi: b) Perform the hypothesis test you set up in a). c) Does the FICO credit rating score appear to affect mortgage payments? If so, how?

Explanation / Answer

Given that,
mean(x)=594.8
standard deviation , s.d1=12.2
number(n1)=40
y(mean)=785.2
standard deviation, s.d2 =16.3
number(n2)=40
null, Ho: u1 = u2
alternate, H1: u1 < u2
level of significance, = 0.01
from standard normal table,left tailed t /2 =2.426
since our test is left-tailed
reject Ho, if to < -2.426
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =594.8-785.2/sqrt((148.84/40)+(265.69/40))
to =-59.1451
| to | =59.1451
critical value
the value of |t | with min (n1-1, n2-1) i.e 39 d.f is 2.426
we got |to| = 59.14513 & | t | = 2.426
make decision
hence value of | to | > | t | and here we reject Ho
p-value:left tail - Ha : ( p < -59.1451 ) = 0
hence value of p0.01 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 < u2
test statistic: -59.1451
critical value: -2.426
decision: reject Ho
p-value: 0

fico credit rating payments appears to be affect since it is
claim that high interest mortgage is lower than the low intrest rates

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