Two popular forms of mortgage are the thirty-year fixed-rate mortgage, where the

Question

Two popular forms of mortgage are the thirty-year fixed-rate mortgage, where the borrower has thirty years to repay the loan at a constant rate, and the adjustable-rate mortgage (ARM), one version of which is for five years with the possibility of yearly changes in the interest rate. Since the ARM offers less certainty, its rates are usually lower than those of fixed-rate mortgages. However, such vehicles should show more variability in rates. Test this hypothesis at the 0.10 level of significance using the following samples of mortgage offerings for a loan of $160,000 (the borrower needs $200,000, but must pay $40,000 up front).

Explanation / Answer

From given samples, the sample standard deviation for the 30-year fixed is 0.31339, and                                                                                        sample standard deviation for ARM is 0.50775.

HO: Population standard deviation for ARM = Population standard deviation for the 30-year fixed

HA: Population standard deviation for ARM > population standard deviation for the 30-year fixed

Alpha = 0.10

Test statistic, F = 0.50775^2/0.31339^2 = 2.625

This is the right tailed test (greater than), looking up on an F distribution table, under area in right tail = 0.10 and degrees of freedom in numerator = 4, and degrees of freedom in the denominator = 7, critical value is 2.96.

Since test statistic, F of 2.625 is less than the critical value of 2.96, we do NOT reject null hypothesis.

Conclusion: There is NOT sufficient evidence at a 0.10 level of significance that there is more variability in ARM

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