On its website, the Statesman Journal newspaper (Salem1 Oregon1 1999) 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. the size of that difference. Table 10.3 displays mortgage loan rates and the difference between 30-year and 15-year rates for nine randomly selected lending institutions. Assuming that the population of paired differences is normally distributed:
a. Set up the null and alternative hypotheses needed to determine whether there is a difference between mean 30-year rates and mean 15-year rates.
b. Figure 10.10 gives the MINITAB output for testing the hypotheses that you set uµ in µart a. Use the output and critical values to test these hypotheses by setting a equal to .101 .051 .011 and .001. How much evidence is there that mean mortgage loan rates for 30-year and 15-year terms differ?
TABLE 10.3
1999 Mortgage Loan Interest Rates for Nine Randomly Selected Willamette Valley Lending Institutions.

FIGURE 10.10
MINITAB paired Difference f Test of the Mortgage Loan Rate Data

c. Figure 10.1 gives the p-value for testing the hypotheses that you set up in part a. Use the p- value to test these hypotheses by setting a equal to .101 .051 .011 and .001. How much evidence is there that mean mortgage loan rates for 30-year and 15-year terms differ?
d. Calculate a 95 percent confidence interval for the difference between mean mortgage loan rates for 30-year rates versus 15-year rates. Interpret this interval.

Transcribed Image Text:

6.9 6.8 6.7 6.6 6.5 6.4 6.3 6.2 6.1 Annual Percentage Rate Lending Institution American Mortgage N.W. Inc. City and Country Mortgage Commercial Bank Landmark Mortgage Co. Liberty Mortgage, Inc. MaPS Credit Union Mortgage Brokers, Inc. Mortgage First Corp Silver Eagle Mortgage 30-Year 6.715 6.648 6.740 6.597 6.425 6.880 6.900 6.675 6.790 15-Year 6.599 6.367 6,550 6.362 6.162 6.583 6.800 6.394 6.540 Difference 0.116 0.281 0.190 0.235 0.263 0.297 0.100 0.281 0.250 15-Year 30-Year Term 0.3 0.2 0.1 Paired T for 30-Year 15-Year 30-Year 15-Year Difference 9 Mean 6.70778 6.48411 0.223667 StDev 0.14635 0.18396 0.072750 SE Mean 0.04878 0.06132 0.024250 95% CI for mean difference: (0.167746. 0.279587) T-Test of mean di f ference 0 (vs not t= 0): T-value= 9.22 p-value = 0.000