### CFA Practice Question

A light bulb manufacturer would like to supply only those bulbs which have a life of 2,000 hours or more. Otherwise, it wants the bulbs to be rejected at the assembly line. The statistician hired by the bulb manufacturer is trying to frame the situation as a hypothesis testing problem. He should specify the null and alternate hypothesis as:
A. H0: average life <= 2,000; H1: average life > 2,000
B. H0: average life >= 2,000; H1: average life < 2,000
C. H0: average life < 2,000; H1: average life >= 2,000
Explanation: The manufacturer is in the business of supplying bulbs which have an average life of 2000 hours or more. So it is logical to assume that the processes usually produce such bulbs and occasionally produce faulty bulbs which have a shorter average life. Hence, the null hypothesis must be that any given bulb has an average life of less than 2000 hours so we can reject it.

User Comment
dealsoutlook Alternative hypothesis is the one that u want to prove and in this case it is which bulbs have life greater than 2000 hrs
ontrack great clarification dealsoutlook! Thanks
Birdy101 why is it not A: as we want to prove that the live is > 2000? Ho is the opppsite thus Ho <= 2000
avgas The question says we want to the ones with 2000 or more.
colinn I think the correct answer should be B: H0: average life >= 2,000; H1: average life < 2,000

One of the few things I remembered from school that the null hypothesis always contains the equality. Reading page 458 of the CFAI book, it lists three possible formulations of hypotheses, and the null either contains =, <=, or >=.
JCopeland From wikipedia: A null hypothesis is a hypothesis that might be falsified using an observed set of data. Did the question not state "a life of 2000 hours or more". If this is in fact true, would disproving not require that the alternative hypothesis be less than. If "a life of 2000 hours or more" is acceptable, having the alternative =2000 as well would create overlap. Am I wrong? So why is the answer not A. I could see if the question framed it as "more than 2000 hours", but it did not.
jpducros The null hypothesis always include the sign =?

However, the explanation may be the following : here we talk about time, which is continuous, so a null hypothesis stated <2000 is equivalent to a null hypothesis stated =<1999,9999 and in that case the null is included. The probability of the bulb having EXACTLY 2000 hour life being null.
Friso I disagree with the answer. I always learned the null hypothesis is the normal(ly distributed) situation, in this case a lightbulb normally should do >= 2000 hours, thus answer B. In that case only 5% (or whatever alpha you choose) would be rejected. Answer C feels to me the manufacturer is throwing out 95% of production...
berns23 boy this one got me good.
Sheeb Amen Colin: The null always contains the "=" sign. Which is why I did not choose C.
harrybay jpducros that would be plausible if they didn't put a = in the alternate hypothesis. You're right but when it comes to a continuous data set it's either you use the = sign or you don't.
dbalakos Heyhey analyst notes watch outt