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?
what is the std error (std dev of sample means)
what shape would the histogram be?
The sample mean is obviously 78 and I calculate the std error of the sample
means to be 3.
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.
Is it possible to translate it into a z score without any addtional data.
Also I assume that the population itself could take any form skewed, normal
etc and you still end up w/the same std deviation.
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?
Finally what difference does it make how many random samples you take (ie.
100 or 1000). What statistic or parameter does this speak to?
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