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 4.35%? Test the hypothesis at a 10% level of significance. (You may find it useful to reference the appropriate table: z table or t table) Financial Institution APR G Squared Financial 4.720 % Best Possible Mortgage 4.780 Hersch Financial Group 4.670 Total Mortgages Services 4.130 Wells Fargo 4.280 Quicken Loans 4.175 Amerisave 4.805 Source: MSN Money.com; data retrieved October 1, 2010. a. Select the null and the alternative hypotheses. H0: µ ≥ 4.35; HA: µ < 4.35 H0: µ ≤ 4.35; HA: µ > 4.35 H0: μ = 4.35; HA: μ ≠ 4.35 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. 0.05 p-value < 0.10 0.025 p-value < 0.05 0.01 p-value < 0.025 p-value 0.10 p-value < 0.01 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 = 0.100. The mean mortgage rate equals 4.35%. The mean mortgage rate does not equal 4.35%. The mean mortgage rate is less than 4.35%. The mean mortgage rate exceeds 4.35%.

Answer 1

Solution:

Claim: the mean mortgage rate for the population exceeds 4.35%

Part a) Select the null and the alternative hypotheses.

H0: µ ≤ 4.35; HA: µ > 4.35

Part b) Calculate the value of the test statistic.

Since sample size n = 7 is small and population standard deviation is unknown , we use one sample t test for mean.

where

Thus we need to make following table:

	x	x^2
Financial Institution APR G Squared Financial	4.720	22.278400
Best Possible Mortgage	4.780	22.848400
Hersch Financial Group	4.670	21.808900
Total Mortgages Services	4.130	17.056900
Wells Fargo	4.280	18.318400
Quicken Loans	4.175	17.430625
Amerisave	4.805	23.088025

Thus we get:

Thus we get:

Part c) Find the p-value.

df = n- 1 = 7 - 1 = 6

Look in t table for df = 6 row and find interval in which t = 1.40 fall

then find corresponding one tail area.

t = 1.40 fall between 1.134 and 1.440

corresponding one tail area is between 0.10 and 0.15

Thus p-value range is:

0.10 < p-value < 0.15

Thus correct option is: p-value > 0.10

Part d) What is the conclusion?

Since p-value > 0.10 level of significance, we fail to reject H0.

Thus correct option is:
Do not reject H0 since the p-value is greater than significance level.

Part e) Make an inference at α = 0.100.

The mean mortgage rate equals 4.35%.