There are two questions lurking here:
(1) Which is the null hypothesis and which the alternative?
(2) In which direction ought a one-sided hypothesis to be specified?
Duncan addressed (2); jjl's professor was dealing with (1):
The null hypothesis is the one that permits you to define a sampling
distribution for the statistic you will observe. A disribution cannot
be specified for an hypothetical inequality: so the "null" hypothesis
is always the one that contains an equals sign (=).
jjl's professor is correct: if you wish to decide between the one-sided
alternatives {Mu < 150 psi} and {Mu >= 150 psi}, the null hypothesis
must be the latter: {Mu >= 150 psi}.
There remains (2), whether this pair of hypotheses properly addresses
the question you want to ask of the universe of discourse.
(In other words, in which direction do you want the burden of proof?)
Duncan's response addressed this question, but not the other.
On this point, jjl's intuition with respect to the INequalities is
correct: you want the alternative hypothesis to contain {Mu > 150 psi},
because deciding that this is true supports the requirement specified,
that the breaking strength be at least 150 psi, and only the decision to
reject a null hypothesis entails a P-value that one can invoke as prima
facie evidence for the decision. (Which of course is the reason for the
textbook's choice of null and alternative, for an analogous problem.)
But if the one-sided alternative hypothesis contains {Mu > 150 psi},
then the corresponding null hypothesis (which must contain "=") must be
{Mu <= 150 psi}.
<End of Stats 101 lecture. Time to slope off to class... -- DFB.>
On Wed, 24 Sep 2003, jjl wrote (edited):
> 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
>
> My professor said it should be another way around:
> Null: Mu>=150
> Alternative: Mu<150
>
> In my textbook (design and analysis of experients, Montgomery 5th),
> there is an example as:
> The manufacturer wants to know if the lot average breaking strength
> exceeeds 200 psi with the following hypothesis test:
> Null: Mu <=200
> Alternative: Mu>200
>
> Could someone point me on what is a good way to specify hypothesis
> test. Thanks.
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