On its website, the Statesman Journal newspaper (Salem, Oregon, 2005) reports mo
ID: 3303776 • Letter: O
Question
On its website, the Statesman Journal newspaper (Salem, Oregon, 2005) reports mortgage loan interest rates for 30-year and 15-year fixed-rate mortgage loans for a number of Willamette Valley lending institutions. Of interest is whether there is any systematic difference between 30-year rates and 15-year rates (expressed as annual percentage rate or APR) and, if there is, what is the size of that difference. The following table displays the 30-year rate and the 15-year rate for each of nine lending institutions. Also given is the difference between the 30-year rate and the 15-year rate for each lending institution. Use the table to compare the 30-year rates and the 15-year rates. Also, calculate the average of the differences between the rates. (Input the amount as positive value. Round your answer to 4 decimal places.)
Lending Institution 30-Year 15-Year Difference Blue Ribbon Home Mortgage 3.304 3.509 -.205 Coast To Coast Mortgage Lending 4.971 3.935 1.036 Community Mortgage Services Inc. 5.865 3.122 2.743 Liberty Mortgage 6.265 2.509 3.756 Jim Morrison's MBI 3.043 2.745 .298 Professional Valley Mortgage 5.570 3.859 1.711 Mortgage First 4.092 3.215 .877 Professional Mortgage Corporation 3.343 3.265 .078 Resident Lending Group Inc. 5.707 2.858 2.849 Term of Mortgage 0-Year 5-Vear Boxplot of Differerce AD
Explanation / Answer
Studying the box plot of mortgage rat efor 30 year and 15 year, one can see that median (note the horizontal bar within the box) is located at much higher side for 30 year compared to 15 year. Moreover, the distribution of data for 30 year mortgage term data is right skewed, with medin lying close to third qurtile, and distribution of data of mortage term for 15 year is roughly symmetrical with median and mean at same position. Thus, it indicates that the 30 year rates are >= 15 year rates.
The variability is larger for 30 year rates.
Averag eof the difference, dbar=sigma d/n=13.143/9=1.46
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