If the first item represents a sample, the first weight, with mean and
standard deviation, then wouldn't twelve such items deal with sample means?
That is if item 1 is measured as xbar 1, then items 2 through 12 would be
xbar 2, xbar 3, xbar 4...., xbar 12. In that case, wouldn't the confidence
interval for the large sample of 12 be determined using the standard error
rather than the standard deviation? In this example, we are not asking the
range for the mean of one item drawn at random, but asking about the range
for the mean of a sample- thus invoking the standard error as denominator?
At 04:06 PM 9/27/99 -0500, Jim Clark wrote:
>Hi
>
>On Mon, 27 Sep 1999, Susan Shapiro wrote:
>> If you know the mean and standard deviation for a population for the weight
>> of one item and you are trying to estimate the probability of a range of
>> weights when 12 items are weighed at the same time, can you simply multiply
>> the mean and SD by 12?
>
>The best way to think of this is in terms of the distribution of
>_mean_weight_ for 12 (or whatever number) items. From the
>Central Limit Theorem, SEmean = SD/sqrt(n), so we can determine
>the probability of the sample mean weight falling within various
>distances of Mu, the population mean (e.g., +/- 1, 2, ...
>SEmean). Once you have figured the desired upper and lower
>boundaries for the mean sample weight, multiply those boundaries
>by 12 to get the total weights. With some algebra, one could
>figure out how to compute the sum boundaries directly. This
>exercise is left for the reader!
>
>Best wishes
>Jim
>
>============================================================================
>James M. Clark (204) 786-9757
>Department of Psychology (204) 774-4134 Fax
>University of Winnipeg 4L05D
>Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED]
>CANADA http://www.uwinnipeg.ca/~clark
>============================================================================
>
>
Dr. Joyce Johnson
Assistant Professor of Psychology
Developmental/ Experimental
Centenary College of Louisiana
PO Box 41188
2911 Centenary Blvd.
Shreveport, LA 71134-1188
<http://www.centenary.edu/~jjohnson>
FAX 318 869 5004
