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 4.45%? Test the hypothesis at a 1% level of significance.

Financial Institution APR

G Squared Financial 4.025 %

Best Possible Mortgage 4.840

Hersch Financial Group 4.785

Total Mortgages Services 4.850

Wells Fargo 4.465

Quicken Loans 4.705

Amerisave 4.305

a. Select the null and the alternative hypotheses.

a. H0: µ ≥ 4.45; HA: µ < 4.45

b. H0: µ ≤ 4.45; HA: µ > 4.45

c. H0: μ = 4.45; HA: μ ≠ 4.45

b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

_______Test Statistic

c. Find the p-value.

a. 0.05 p-value < 0.10

b. 0.025 p-value < 0.05

c. 0.01 p-value < 0.025

d. p-value 0.10

e. p-value < 0.01

d. What is the conclusion?

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

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

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

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

e. Make an inference at α = 0.010.

a. The mean mortgage rate equals 4.45%.

b.  The mean mortgage rate does not equal 4.45%.

c. The mean mortgage rate does not exceed 4.45%.

d. The mean mortgage rate exceeds 4.45%.

Answer 1

a)

b. H0: µ ≤ 4.45; HA: µ > 4.45

b)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (4.5679 - 4.45)/(0.3146/sqrt(7))
t = 0.99

c)

P-value Approach
P-value = 0.1802
d. p-value > 0.10

d)

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

e)

c. The mean mortgage rate does not exceed 4.45%.