Radford Neal wrote:
>
> In article <[EMAIL PROTECTED]>,
> Jo <[EMAIL PROTECTED]> wrote:
>
> >The time that students spend at part time jobs per week is approximately
> >Normally distributed with standard deviation 8 hours. A random sample of 130
> >students is taken and the sample mean is 11.4 hours.
> >
> >How do I find the 90% lower confidence limit for the true mean (mu)?
>
> You don't, since the assumptions stated are false. It's not possible
> for the time to have a mean of around 11 and standard deviation of 8,
> since that would produce substantial numbers of students who work for
> a negative number of hours, which is clearly impossible.
Quibble 1 (silly): as the 11.4 is a *sample* mean, the true mean might
be considerably higher (it's not likely but it *might* happen). In which
case the distribution could be very close to normal.
Quibble 2 (not quite silly): What do you mean by "approximately"? In
this context, the only rational interpretation is "close enough that the
sampling distribution with N=130 is very close to normal."
By that interpretation, a population distribution with 50% of students
working 3.4 hours per week and the rest working 19.4 hours per week is
approximately normal. (As is just about anything that doesn't spend its
time smoking behind the gym with the Cauchy distribution...)
That said, it's a silly question based on a silly assumption (that you
know the SD and not the mean.) Jo, I wouldn't blame you for not doing
this question, but I'm not doing it for you.
-Robert Dawson
.
.
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