On Wed, 24 Sep 2003 11:50:52 GMT, "jjl" <[EMAIL PROTECTED]> wrote:
> I have a question regarding how to specify hypothesis, i.e null and > alternative. > > Example is as follows: > > The breaking strength of a fiber is required to be at least 150 psi. A > random sample of four speciments is tested .... > > I set up the hypothesis test as follows: > > Null: Mu<150 > Alternative: Mu>=150 1. I like what David Jones has posted, most recently, "As said in another post, the null hypothesis is the one which one is prepared to accept unless there is strong evidence to the contrary." - I wanted to add to this, the idea that if you are going to be scientific, the 'null' is the one that is probably 'hostile' or inconvenient. 2. On the other hand, this is another classroom exercise that, it seems to me, is doomed to controversy, by poor exposition. In a situation like that of the example, I would be tempted to place a CI around the observations, and toss that information to whoever asked. Different observers might disagree on what is more appropriate as the null. Is a conclusion really possible from the terse introduction? 3. [ What about Tolerance intervals, instead of CIs ? ] Further, the problem (as stated) seems *misguided*, from a manufacturer's perspective, unless a lot more is said. Fishing lines? Climbers' ropes? I immediately thought of problems where I want *every* fiber to meet a criterion, and not just their average. The problem did not *say* average.... IMHO, the manufacturer's standard should probably be written with at least this much complexity: "We want 950 out of every 1000 fibers to measure 150 psi, for 99% of the batches." - You could specify the mean needed to hit that mark, if you had a really good estimate of the standard deviation. Next, for a real problem, you would want add one more level of 'assurance', based on the confidence you place in your sample of 4. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html "Taxes are the price we pay for civilization." . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
