Not to disagree with Randy Poe completely, but I think we can say something,
especially if we make _some_ assumptions (mainly, that this comes from an intro
class).
"@Home" wrote:
> I am trying to solve a ? which basically gives the following facts:
>
> population of unknown number
> popu std dev of 27
> pop mean of 78
> sample of size n=81
> 2000 random samples
>
> The ? is:
>
> what is the sample mean?
It will be an average of your 81 measurements, which will be pretty close to
the pop. mean of 78.
>
> what is the std error (std dev of sample means)
It will _estimate_ the stdev of the pop stdev/sqrt(n) = (pretty close to)
27/sqrt(81) = 3.
> what shape would the histogram be?
Central Limit Theorem, Randy! Distribution of sample averages will _tend_
toward a Normal, regardless of underlying pop dist. for n=81, 'tend' will be
pretty darn close.
Since 81 is 3 stdevs from 0, I expect some degree of asymmetry in the original
dist., but it won't be huge. The original dist., of course, could be almost
anything, and still prodcue those two values of the mean and stdev. Without
knowing anything about how the numbers were obtained, we can't say much.
> The sample mean is obviously 78 and I calculate the std error of the sample
> means to be 3.
OK. these do _not_ require any assumption of Normality.
> However I can't put the whole picture together. I suspect the distrib would
> be normal given the 81 samples, but is 3 a low number for a std error.
Could be 0.03, and it would still tend toward a Normal. Just pretty narrow
spread.
> Is it possible to translate it into a z score without any addtional data.
Yes. This may require the assumption of Normal, but thanks to the CLT, you've
pretty much got that.
> Also I assume that the population itself could take any form skewed, normal
> etc and you still end up w/the same std deviation.
Yup.
> In other words is the std deve of 27 and mean of 81 in any way predictive of
> what a histogram of a distribution would look like?
Only tells you the 'central tendency' and the 'dispersion tendency.' Does not
say anything about the rest of the shape.
>
>
> Finally what difference does it make how many random samples you take (ie.
> 100 or 1000).
the more repeat samples, the more smooth your eventual histogram may become -
more 'bins.' What counts with the CLT is n = 81, or lots.
> What statistic or parameter does this speak to?
You tell me, OK?
Jay
BTW, I couldn't send an email to your address. Did I get it wrong?
--
Jay Warner
Principal Scientist
Warner Consulting, Inc.
4444 North Green Bay Road
Racine, WI 53404-1216
USA
Ph: (262) 634-9100
FAX: (262) 681-1133
email: [EMAIL PROTECTED]
web: http://www.a2q.com
The A2Q Method (tm) -- What do you want to improve today?
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
