Luxco a whilesale lightbulb manufacturer has two factories F

Luxco, a whilesale lightbulb manufacturer, has two factories. Factory A sells bubls 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 ins 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 0.6 percent. We\'re better at both regular and softglow bulbs by half of a tenth of a percent each.\"

\"Au contraire,\" counter the manager of B, \"each of our 3000 bubl lots contains only 11 bad bulbs, while A\'s 3000 bubllots contain 13. So our 0.37 percent bad bulb rate beats their 0.43 percent\"

Who is right?

Solution

To compare the proportion of A and B

set null hypotheses

H0: pA = pB

Ha: pA not equal to pB

This is a two tailed test for proportions

As sample size is large, we use z test

Both are not significantly diferent. Hence both claims are wrong.