Suppose employers care about overall productivity Z$,$ which is made up of two components, $x$ and $Y,$ such that $Z=x+Y($and employers know this productivity function$).$ Suppose there are two groups $($tall and short individuals$)$ whose average Zs are the same $($i$.$e$.Z_T=Z_S),$ but $Y_T>Y_S{x}_T$ and $Y_T>Y_S(and$ again, employers know these population averages$).(Averages$ are given $by$ bold font.$)$ Researchers decide $to$ run a resume$-$based audit study where they randomize heights but hold constant $Y.$ They provide $no$ information $onX.$ Which $of$ the following results would provide suggestive evidence $of$ statistical discrimination?

The call$-$back rate $is$ higher for short individuals than tall individuals

The call$-$back rate $is$ the same for both groups

The call$-$back rate $is$ higher for tall individuals than short individuals

$We$ can't use differences $in$ call$-$back rates $to$ find evidence $of$ statistical discrimination.