Question: Rates on 30-year fixed mortgages continue to be at historic lows (Chron Business News, September 23, 2010). According to Freddie Mac, the average rate for 30-year fixed loans for the week was 4.37%. An economist wants to test if there is any change in the mortgage rates in the following week. She searches for 30-year fixed loans on google.com in the following week and reports the rates offered by seven banks as: 4.25%, 4.125%, 4.375%, 4.50%, 4.75%, 4.375%, and 4.875%. Assume that rates are normally distributed.
a. State the hypotheses to test if the average mortgage rate differs from 4.37%.
b. What is the value of the test statistic?
c. Compute the critical value(s) of the test with α = 0.05.
d. State your conclusion.