(Round all intermediate calculations to at least 4 decimal places.) A mortgage s

Question

(Round all intermediate calculations to at least 4 decimal places.) A mortgage specialist would like to analyze the average mortgage rates for Atlanta, Georgia. He studies the following sample APR quotes. These are the annual percentage rates (APR) for 30-year fixed loans. If he is willing to assume that these rates are randomly drawn from a normally distributed population, can he conclude that the mean mortgage rate for the population exceeds 4.35%? Test the hypothesis at a 10% level of significance. Use Table 2 Financial Institution APR 4.615% G Squared Financial 4.430 Best Possible Mortgage 4.585 Hersch Financial Group 4.790 Total Mortgages Services 4.865 Wells Fargo Quicken Loans 4.415 4.060 Amerisave SOURCE: MSN Money.com; data retrieved October 1, 2010. Click here for the Excel Data File Use the p-value approach. a-1. Select the null and the alternative hypotheses. O Ho: u24.35; HA: u

Explanation / Answer

Given that,
population mean(u)=4.35
sample mean, x =4.5371
standard deviation, s =0.2689
number (n)=7
null, Ho: =4.35
alternate, the mean mortage value of the sample is exceeds 4.35%, H1: >4.35
level of significance, = 0.1
from standard normal table,right tailed t /2 =1.44
since our test is right-tailed
reject Ho, if to > 1.44
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =4.5371-4.35/(0.2689/sqrt(7))
to =1.841
| to | =1.841
critical value
the value of |t | with n-1 = 6 d.f is 1.44
we got |to| =1.841 & | t | =1.44
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 1.8409 ) = 0.05762
hence value of p0.1 > 0.05762,here we reject Ho

ANSWERS
---------------
null, Ho: =4.35
alternate, H1: >4.35
test statistic: 1.841
critical value: 1.44
decision: reject Ho
p-value: 0.05762, 0.05<p<0.010
the mean mortage value of the sample is exceeds 4.35%

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