Randomization Test using R:

The conduct of a randomization or permutation test for the equality of two population means is as follows. Under the null hypothesis, there is no difference in the populations. Thus, the assignment of values to one population or the other is regarded as one arbitrary permutation. The question is how unusual is the test statistic under this permutation in relation to other permutations. For problem 9.2.20, consider the fixed and ARM rates. As the data appear, compute the difference in mean rates between them. Then combined the values from ARM and fixed into one vector. Sample without replacement from that vector a set of 10 rates. The sample function will help. The rates chosen represent one rate plan; the rates not chosen represent the other. For each of these permutations, take the difference of means between the rates chosen and the rates not chosen. Keep track for 1000 permutations of the test statistic. Use R to determine how many of the test statistics resulting from permuted rates are more unusual than the initial difference between rates from the way the data are given in the problem. The proportion of the mean difference in rates more unusual (extreme) than the initial difference is interpretable as a p-value. Report your p-value from the randomization test.

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9.2.20. 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 inter- est rate. Since the ARM offers less certainty, its rates are usually lower than those of fixed-rate mortgages. Test this hypothesis at the a = 0.01 level using the following sam- ple of mortgage offerings for a loan of $250,000. Do not assume the variances are equal. $250,000 Mortgage Rates 30-Year Fixed ARM 3.525 3.625 3.383 3.625 3.661 3.791 3.941 3.781 3.660 3.733 2.923 3.385 3.154 3.363 3.226 3.283 3.427 3.437 3.746 3.438 9.2.20. 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 inter- est rate. Since the ARM offers less certainty, its rates are usually lower than those of fixed-rate mortgages. Test this hypothesis at the a = 0.01 level using the following sam- ple of mortgage offerings for a loan of $250,000. Do not assume the variances are equal. $250,000 Mortgage Rates 30-Year Fixed ARM 3.525 3.625 3.383 3.625 3.661 3.791 3.941 3.781 3.660 3.733 2.923 3.385 3.154 3.363 3.226 3.283 3.427 3.437 3.746 3.438