[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Luxco, a wholesale lightbulb manufacturer, has two factories. Factory A

sells bulbs in lots that consists of 1000 regular and 2000 softglow bulbs each. Random sampling has shown that on the average there tend to be about 2 bad regular bulbs and 11 bad softglow bulbs per lot. At factory B the lot size is reversed---there are 2000 regular and 1000 softglow per lot---and there tend to be 5 bad regular and 6 bad softglow bulbs per lot. The manager of factory A asserts, “We're obviously the better producer; our bad bulb rates are .2 percent and .55 percent compared to B's .25 percent and .6 percent. We're better at both regular and softglow bulbs by half of a tenth of a percent each.” “Au contraire,” counters the manager of B, “each of our 3000 bulb lots contains only 11 bad bulbs, while A's 3000 bulb lots contain 13. So our .37 percent bad bulb rate beats their .43 percent.”

Who is right?