$2.$ An experiment was performed to study the effect of three different types of $32-$ounce bottles $($A$)$ and three different shelf types $($B$)-$smooth permanent shelves, end $-$aisle displays, with grilled shelves, and beverages coolers$-$on the time it takes to stock ten $12-$bottles cases on the shelves. Three workers $($factors C$)$ were employed in the experiment, and two replicated of a $33$ factorial design were run. The observed time data are shown in the following table. Analyze the data and draw conclusions.

Worker Bottle Type Replicate I Replicate II

Permanent End Aisle Cooler Permanent End Aisle Cooler

$1$ Plastic $3\mathrm{.}554\mathrm{.}145\mathrm{.}803\mathrm{.}364\mathrm{.}195\mathrm{.}25$

$28$ mm glass $4\mathrm{.}014\mathrm{.}385\mathrm{.}483\mathrm{.}524\mathrm{.}264\mathrm{.}90$

$38$ mm glass $4\mathrm{.}204\mathrm{.}255\mathrm{.}753\mathrm{.}684\mathrm{.}375\mathrm{.}58$

$2$ Plastic $4\mathrm{.}805\mathrm{.}226\mathrm{.}214\mathrm{.}404\mathrm{.}755\mathrm{.}88$

$28$ mm glass $4\mathrm{.}525\mathrm{.}156\mathrm{.}284\mathrm{.}444\mathrm{.}656\mathrm{.}20$

$38$ mm glass $4\mathrm{.}965\mathrm{.}176\mathrm{.}054\mathrm{.}394\mathrm{.}756\mathrm{.}38$

$3$ Plastic $4\mathrm{.}103\mathrm{.}945\mathrm{.}143\mathrm{.}654\mathrm{.}084\mathrm{.}49$

$28$ mm glass $4\mathrm{.}304\mathrm{.}534\mathrm{.}994\mathrm{.}044\mathrm{.}084\mathrm{.}59$

$38$ mm glass $4\mathrm{.}174\mathrm{.}864\mathrm{.}853\mathrm{.}884\mathrm{.}484\mathrm{.}93$