$4\mathrm{.}14.$ An aluminum master alloy manufacturer produces

grain refiners in ingot form. The company produces the prod$-$

uct in four furnaces. Each furnace is known to have its own

unique operating characteristics, so any experiment run in the

foundry that involves more than one furnace will consider fur$-$

naces as a nuisance variable. The process engineers suspect

that stirring rate affects the grain size of the product. Each fur$-$

nace can be run at four different stirring rates. A randomized

block design is run for a particular refiner, and the resulting

grain size data is as follows.

$($a$)$ Is there any evidence that stirring rate affects grain size?

Make sure I need this as hand solution stepwise only