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 4.30%? 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 4.860 %

Best Possible Mortgage 4.460

Hersch Financial Group 4.495

Total Mortgages Services 4.850

Wells Fargo 4.245

Quicken Loans 4.435

Amerisave 4.465

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

Answer 1

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (4.5443 - 4.3)/(0.2275/sqrt(7))
t = 2.84