Michael is interested in obtaining $30-$year fixed mortgage rates in Myrtle Beach, SC$.$ He obtained rate quotes from $6$

lenders, and the APR rates that were quoted to him are given in the following table.

$30-$Year Fixed Mortgage Rates

Lender APR $(\%)$

EverBank $3\mathrm{.}512$

AimLoan $3\mathrm{.}634$

Great Western $4\mathrm{.}040$

Greenlight $4\mathrm{.}220$

Flagstar $4\mathrm{.}202$

AuroraBank $4\mathrm{.}020$

Step $3$ of $3$ : Assuming the population standard deviation for the rates is $0\mathrm{.}5\%$

$,$ calculate the value of $\backslash$chi $2$

$.$ Round any intermediate calculations, if needed, to no less than six decimal places, and round your final answer to three decimal places.