Question 436815
{{{H[0] : mu[2] <= 2*mu[1]}}}
{{{H[a] : mu[2] > 2*mu[1]}}}
where {{{mu[2]}}}= average lifetime of new lightbulb, and 
{{{mu[1]}}} = average lifetime of old lightbulb.

Commentary:  Lightbulb lifetime is usually normally distributed, and thus the random variable {{{X[2] - 2X[1]}}} is normally distributed with mean {{{mu[2] - 2mu[1]}} and variance {{{sigma[2]^2 + 4sigma[1]^2}}}.  I'm mentioning this information because all we really need are estimates of the standard deviations of the two samples to carry out a test of significance (plus the sample size for your competitor's lghtbulbs.)  In this case a large sample z-test is recommendable, and the hypotheses can be rephrased as 
{{{H[0] : mu[2] - 2*mu[1]<= 0}}}
{{{H[a] : mu[2] - 2*mu[1] > 0}}}.