Question

A mortgage specialist would like to analyze the average mortgage rates for Atlanta, Georgia. He collects data on the annual percentage rates (APR in %) for 30-year fixed loans as shown in the following table. 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 4.50%? Test the hypothesis at a 10% level of significance.

Calculate the value of the test statistic.

Financial Institution	APR
G Squared Financial		4.835	%
Best Possible Mortgage		4.305
Hersch Financial Group		4.680
Total Mortgages Services		4.440
Wells Fargo		4.860
Quicken Loans		4.300
Amerisave		4.835

Answer 1

Solution:

We have to test if the mean mortgage rate for the population exceeds 4.50%.

Level of significance =

We are given following data set:

Financial Institution	APR
G Squared Financial	4.835
Best Possible Mortgage	4.305
Hersch Financial Group	4.68
Total Mortgages Services	4.44
Wells Fargo	4.86
Quicken Loans	4.3
Amerisave	4.835

We use following steps:

Step 1) State H0 and H1:

Vs

Step 2) Find test statistic:

Since sample size is small, population standard deviation is unknown and rates are randomly drawn from a normally distributed population, we use t test statistic.

we need to find sample mean and sample standard deviation.

Thus we need to make following table:

x : APR	x^2
4.835	23.377225
4.305	18.533025
4.68	21.902400
4.44	19.713600
4.86	23.619600
4.3	18.490000
4.835	23.377225

Thus

Thus t test statistic is:

Step 3) Find t critical value:

df = n - 1 = 7 - 1 = 6

Level of significance =

t critical value = 1.440

Step 4) Decision rule:

Reject H0, if t test statistic value > t critical value = 1.440, otherwise we fail to reject H0.

Since t test statistic value = t = 1.124 < t critical value = 1.440, we fail to reject H0.

Step 5) Conclusion:

Since we failed to reject H0, there is not sufficient evidence to conclude that the mean mortgage rate for the population exceeds 4.50%