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. (You may find it useful to reference the appropriate table: z table or t table) 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 Source: MSN Money.com; data retrieved October 1, 2010. Click here for the Excel Data File a. Select the null and the alternative hypotheses. H0: µ ≥ 4.45; HA: µ < 4.45 H0: µ ≤ 4.45; HA: µ > 4.45 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.) 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 = 0.010. The mean mortgage rate equals 4.45%. The mean mortgage rate does not equal 4.45%. The mean mortgage rate does not exceed 4.45%. The mean mortgage rate exceeds 4.45%.

Answer 1

(a)

Correct option:

H0: µ ≤ 4.45; HA: µ > 4.45

(b)

From the given data, the following statistics are calculated:

n = 7

= 31.975/7 = 4.5679

s = 0.3146

SE = s/

= 0.3146/

= 0.1189

Test Statistic is given by:

t = (4.5679 - 4.45)/0.1189

= 0.57

the value of the test statistic = 0.57

(c)

t score = 0.57

ndf = 7 - 1 = 6

One Tail - Right Side Test

By Technology, p - value = 0.2947

Correct option:

p - value > 0.10

(d)

Correct option:

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

(e)

Correct option:

The mean mortgage rate does not exceed 4.45%.