On 17/09/2009, at 8:06 AM, Bert Gunter wrote:
<snip>
Furthermore, the null can be other than equality -- e.g. that the
mean of
the first population is less than the second.
<snip>
QUIBBLE: Some elementary texts will indeed state the null hypothesis as
``mu_1 <= mu_2'' when the alternative hypothesis is ``mu_1 > mu_2''.
However it seems to me more perspicuous to keep the null hypothesis as
``='' and allow only the alternative to change (i.e. to be one of ``!
='',
``<'', or ``>'').
One calculates one's *test statistic* using the ``='' (which is the
``most extreme'' point of the null hypothesis, the point ``closest'' to
the alternative, i.e. the point least likely to lead one to reject
the null.
Thus confusion amongst the young and naive is minimized if one
insists that
the null hypothesis is always ``=''.
cheers,
Rolf Turner
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