Question

michael is interested in obtaining 30-year fixed mortgage rates in myrtle beach, sc. he obtained rate quotes from 10 lenders, and the apr rates that were quoted to him are given in the following table. 30-year fixed mortgage rates lender apr (%) everbank 3.529 aimloan 3.653 great western 4.059 greenlight 4.239 flagstar 4.219 aurorabank 4.039 quicken 4.449 roundpoint 4.143 lendingtree 4.269 rocket 4.410 step 2 of 3 : how many degrees of freedom are associated with this chi-square distribution?

Answer 1

To calculate the degrees of freedom for a chi-square distribution with 10 lender APR quotes, we subtract 1 from the number of categories, resulting in 9 degrees of freedom assuming no other constraints.

Step-by-step explanation:

The question pertains to calculating the degrees of freedom associated with a chi-square distribution given a list of annual percentage rates (APRs) quoted by lenders for a 30-year fixed mortgage.

When we discuss degrees of freedom in the context of a chi-square distribution in statistics, it typically relates to the number of categories or classes minus any constraints that are applied to the data.

In this case, Michael has rate quotes from 10 lenders, which means there are 10 categories. However, when calculating the degrees of freedom for a chi-square test (which is not fully detailed here), we usually subtract 1 to account for the overall constraint that the sum of observed and expected frequencies is fixed. Therefore, the degrees of freedom would be 10 - 1, which equals 9.

This is under the assumption that a chi-square test is being conducted with no further constraints than the sum of frequencies.