You are planning to perform analytical procedures related to inventory fraud, and wish to develop a nonfraud hypothesis $(HO)$ expectation using industry data. Specifically, you are interested in the inventory turnover ratio, measured as $[$COGS $/$ Ending Inventory$].$ You are investigating the Scarlet Company.

$($a$)$ What would the Fraud alternative hypothesis $(Ha)$ be if you are checking for a fictitious inventory fraud?

$($b$)$ Following are COGS and Ending Inventory $($EI$)$ balances for several companies in the industry. Develop the $HO$ expectation, making sure to deal appropriately with any pparent data inconsistencies or outliers.

$\backslash$table$[[$Company$,$COGS,EI$],[1,15\mathrm{.}233,10\mathrm{.}028],[2,22\mathrm{.}388,7\mathrm{.}985],[3,2553\mathrm{.}127,551\mathrm{.}082],[4,4\mathrm{.}603,0],[5,460\mathrm{.}114,312\mathrm{.}83],[6,3\mathrm{.}086,1\mathrm{.}235],[7,2887\mathrm{.}055,383\mathrm{.}917],[8,21\mathrm{.}138,5\mathrm{.}529],[9,33\mathrm{.}303,18\mathrm{.}684],[10,1\mathrm{.}064,0\mathrm{.}522],[11,11\mathrm{.}573,3\mathrm{.}088],[12,8\mathrm{.}338,0],[13,7\mathrm{.}45,0\mathrm{.}288],[14,135\mathrm{.}178,87\mathrm{.}7],[15,0\mathrm{.}642,0\mathrm{.}086],[16,1\mathrm{.}47,2\mathrm{.}205],[17,1\mathrm{.}988,1\mathrm{.}315],[18,60\mathrm{.}019,7\mathrm{.}589],[19,2\mathrm{.}892,0]]$

$($c$)$ Assume the Scarlet Company's inventory turnover is $1\mathrm{.}50.$ Is this more consistent with $HO$ or Ha$?$ Explain. $($use both z$-$score and percentile rank tests$)$