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 4.2%? Test the hypothesis at the 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 4.125 % Best Possible Mortgage 4.250 Hersch Financial Group 4.250 Total Mortgages Services 4.375 Wells Fargo 4.375 Quicken Loans 4.500 Amerisave 4.750 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 ≥ 4.2; HA: µ < 4.2 H0: µ ≤ 4.2; HA: µ > 4.2 H0: μ = 4.2; HA: μ ≠ 4.2 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. p-value < 0.01 0.01 ≤ p-value < 0.025 0.025 ≤ p-value < 0.05 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 = 0.10. 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

for hypothesis:

H0: µ ≤ 4.2; HA: µ > 4.2

test statistic t =2.27

0.025 ≤ p-value < 0.05

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

The mean mortgage rate exceeds 4.2%.