I need help with stats

#1
I have couple of questions that I don't know how to answer.


how the standard error of the mean is calculated. Is the standard error of the mean smaller or larger in samples of 13 than in samples of 25? Why?


Which one of the alternative explanations does statistical testing examine?

thanks
 
#2
Ok, first it's important to distinguish between a sample and a population.

Imagine you're interested in 100 people's height, the population is all 100, but a sample is any subset of these. Because the sample is always less and might not be representative it has a higher error associated with it.

standard deviation of population (or variance squared)
=squareroot of (((sum of each data point - mean) squared)/N).


standard deviation of sample (or variance squared)
=squareroot of (((sum of each data point - mean) squared)/(N-1)).

The reason you take the square root is so the units of the error are the same as the units of the mean so you can say.
height = 1.8 +/- 0.25m instead of height -1.8m +/-0.05 m^2

I hope this helps