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 4.20%? 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 4.255 % Best Possible Mortgage 4.265 Hersch Financial Group 4.200 Total Mortgages Services 4.540 Wells Fargo 4.175 Quicken Loans 4.225 Amerisave 4.490 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 ≥ 4.20; HA: µ < 4.20 H0: µ ≤ 4.20; HA: µ > 4.20 H0: μ = 4.20; HA: μ ≠ 4.20

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? 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 α = 0.100. The mean mortgage rate equals 4.2%. The mean mortgage rate does not equal 4.2%. The mean mortgage rate exceeds 4.2%. The mean mortgage rate is less than 4.2%.

Answer 1

Ans a) since population standard deviation is unknown so we will use t test

using minitab stat>basic stat> one sample t

we have

One-Sample T: institutions

Test of μ = 4.2 vs > 4.2

Variable N Mean StDev SE Mean 90% Lower Bound T P
institutions 7 4.3071 0.1460 0.0552 4.2277 1.94 0.050221.

a. H0: μ = 4.20

HA: µ > 4.20 (one-tailed )

b. test statistic t = 1.94

c. the p-value. is 0.050221.

0.05< p-value < 0.10

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

e. at α = 0.100The mean mortgage rate exceeds 4.2%.