In paper manufacturing, pulp brightness is an important performance characteristic.

Customers require maximum pulp brightness with maximum uniformity $($minimum

variance$).$ The company is testing two bleaching chemicals for effectiveness in achieving a

brightness of $90.$ Assume that the data are normally distributed. $($a$)$ State and test the

hypothesis that the brightness variances of the two chemicals are equal at

$=0\mathrm{.}05.($b$)$

State and test the hypothesis that the brightness means for the two chemicals are equal at

$$

$=0\mathrm{.}05.($c$)$ Which chemical best fulfills the requirements of maximum brightness at

minimum variance?