Question: Rates on 30 year fixed mortgages continue to be at historic lows

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 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. Specify the critical value(s) with α = 0.05.
c. What is the value of the test statistic?
d. At the 5% significance level, does the average mortgage rate differ from 4.37%? Explain.

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