A researcher wants to know if the annual yields for securities of different maturities have different annual rates of returns. To conduct the test, she draws samples of instruments with $30$ year yields and $15$ year yields from a number of banks. His data is shown in the table below.

$\backslash$table$[[,$Annual Percentage Yield$],[$Institution$,30$ Year,$15$ Year,Difference$],[1,6\mathrm{.}715,6\mathrm{.}599,0\mathrm{.}116],[2,6\mathrm{.}648,6\mathrm{.}36,0\mathrm{.}281],[3,6\mathrm{.}74,6\mathrm{.}550,0\mathrm{.}190],[4,6\mathrm{.}597,6\mathrm{.}36,0\mathrm{.}235],[5,6\mathrm{.}425,6\mathrm{.}162,0\mathrm{.}263],[6,6\mathrm{.}88,6\mathrm{.}583,0\mathrm{.}297],[7,6\mathrm{.}9,6\mathrm{.}800,0\mathrm{.}100],[8,6\mathrm{.}675,6\mathrm{.}394,0\mathrm{.}281],[9,6\mathrm{.}79,6\mathrm{.}540,0\mathrm{.}250]]$

Conduct the appropriate hypothesis testing procedure to determine if the paired observations are different