anova $2)$ A company is contemplating redesigning one of its business process to reduce the

time required to complete the process and reduce operating costs. The company

has developed a simulation model for its current process design and two proposed

design changes. $20$ replications were performed using common random numbers.

The following table displays the completion times in hours for the current design and

each proposed design.

Replication Completion Time Current Design $($hours$)$ Completion Time Proposed Design A $($hours$)$ Completion Time Proposed Design B $($hours$)$

$18\mathrm{.}117\mathrm{.}526\mathrm{.}81$

$211\mathrm{.}7813\mathrm{.}358\mathrm{.}9$

$310\mathrm{.}4311\mathrm{.}558$

$47\mathrm{.}716\mathrm{.}667\mathrm{.}17$

$510\mathrm{.}811\mathrm{.}437\mathrm{.}52$

$67\mathrm{.}687\mathrm{.}436\mathrm{.}7$

$711\mathrm{.}3611\mathrm{.}098\mathrm{.}38$

$810\mathrm{.}1110\mathrm{.}267\mathrm{.}73$

$911\mathrm{.}113\mathrm{.}68\mathrm{.}87$

$108\mathrm{.}211\mathrm{.}878\mathrm{.}33$

$118\mathrm{.}929\mathrm{.}277\mathrm{.}49$

$1212\mathrm{.}9614\mathrm{.}739\mathrm{.}87$

$1311\mathrm{.}4714\mathrm{.}018\mathrm{.}87$

$148\mathrm{.}487\mathrm{.}337\mathrm{.}44$

$1511\mathrm{.}8812\mathrm{.}579\mathrm{.}47$

$168\mathrm{.}458\mathrm{.}187\mathrm{.}37$

$1712\mathrm{.}512\mathrm{.}29\mathrm{.}22$

$1811\mathrm{.}1311\mathrm{.}298\mathrm{.}51$

$1912\mathrm{.}6716\mathrm{.}2110\mathrm{.}48$

$208\mathrm{.}1814\mathrm{.}169\mathrm{.}16$

b$)$ Calculate the sample mean and variance for the completion times for each

design and discuss the apparent effectiveness of the proposed design changes

with respect to reducing the process completion time.