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 4.40%? Test the hypothesis at a 1% level of significance.

APR G Squared Financial 4.830 %

Best Possible Mortgage 4.640 %

Hersch Financial Group 4.135

Total Mortgages Services 4.255

Wells Fargo 4.620

Quicken Loans 4.720

Amerisave 4.665

Source: MSN Money.com; data retrieved October 1, 2010.

a. Select the null and the alternative hypotheses.

H0: µ ≥ 4.40; HA: µ < 4.40

H0: µ ≤ 4.40; HA: µ > 4.40

H0: μ = 4.40; HA: μ ≠ 4.40

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

c. Find the p-value.

0.025 p-value < 0.05

0.01 p-value < 0.025

p-value < 0.01

0.05 p-value < 0.10

p-value 0.10

d. What is the conclusion?

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

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

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

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

e. Make an inference at α = 0.010.

The mean mortgage rate equals 4.4%.

The mean mortgage rate does not equal 4.4%.

The mean mortgage rate is less than 4.4%.

The mean mortgage rate exceeds 4.4%.

Answer 1

For doing hypothesis testing first we need to calculate mean and standard deviation:

Mean = (4.830+4.640+4.135+4.255+4.620+4.720+4.665)/7 = 4.5521

Standard Deviation s = 0.2558

Answer a)

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ ≤ 4.40

Ha:μ > 4.40

This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

Answer b): 1.57 (Rounded to 2 decimal places)

Answer c)

The p-value is p = 0.0834 (Obtained using online p-value calculator for t = 1.57 and df = 7 -1 = 6)

Answer d) Do not reject H0 since the p-value is greater than significance level.

Explanation

Since p=0.0834 ≥ 0.01, it is concluded that the null hypothesis is not rejected. There is not enough evidence to support the claim that the mean mortgage rate for the population exceeds 4.40% at 1% significant level.

We can answer 4 parts only