A mortgage specialist would like to analyze the average mortgage rates for Atlan

Question

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 4.30%? Test the hypothesis at a 5% level of significance. Use Table 2.

a. Use the p-value approach..

Calculate the value of the test statistic:

b. Calculate the critical value:

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 4.30%? Test the hypothesis at a 5% level of significance. Use Table 2.

Explanation / Answer

Given that,
population mean(u)=4.3
sample mean, x =4.48
standard deviation, s =0.2041
number (n)=7
null, Ho: =4.3
alternate, H1: >4.3
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.943
since our test is right-tailed
reject Ho, if to > 1.943
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =4.48-4.3/(0.2041/sqrt(7))
to =2.3333
| to | =2.3333
critical value
the value of |t | with n-1 = 6 d.f is 1.943
we got |to| =2.3333 & | t | =1.943
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 2.3333 ) = 0.02919
hence value of p0.05 > 0.02919,here we reject Ho
ANSWERS
---------------
null, Ho: =4.3
alternate, H1: >4.3
test statistic: 2.3333
critical value: 1.943
decision: reject Ho
p-value: 0.02919

we have evidence to conclude that the mean mortgage rate for the population exceeds 4.30%

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