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 4.25%? Test the hypothesis at a 5% level of significance. (You may find it useful to reference the appropriate table: z table or t table) Financial Institution APR G Squared Financial 4.855 % Best Possible Mortgage 4.325 Hersch Financial Group 4.685 Total Mortgages Services 4.095 Wells Fargo 4.615 Quicken Loans 4.575 Amerisave 4.825

a. What is the null and alternative hypotheses?

b. Calculate the value of the test statistic?

c. Find the p-value

d. What is the conclusion?

• Reject H₀ since the p-value is greater than significance level.

• Reject H₀ since the p-value is smaller than significance level.

• Do not reject H₀ since the p-value is greater than significance level.

• Do not reject H₀ since the p-value is smaller than significance level.

e. Make an inference at   αα = 0.050.

• The mean mortgage rate equals 4.25%.

• The mean mortgage rate does not equal 4.25%.

• The mean mortgage rate exceeds 4.25%.

• The mean mortgage rate is less than 4.25%.

Answer 1

Ans:

sample mean=4.568

sample standard deviation=0.273

n=7

a)

b)

Test statistic:

t=(4.568-4.25)/(0.273/SQRT(7))

t=3.082

df=7-1=6

c)p-value=tdist(3.082,6,1)=0.0108

d)Reject H₀ since the p-value is smaller than significance level.

e)The mean mortgage rate exceeds 4.25%.