Name:________________________
Sampling   SEM

*Card hands
https://davidwills.us/math103/cardhand.html

freq dist, histogram, stats ***

Card value: Ace is 1, 2 2, ..., Jack 11, Queen 12, King 13.   Mean of the population of 52 cards is 7.0

Card hand of size 3 (sample size n=3) 
Take 20 samples, adding each's mean into "Frequency distribution, histogram, and statistics" input textbox. 
And here: __________________________________________________________________________
This is a (very incomplete) sampling distribution of the mean. 
  The actual sampling distribution has N=52C3=_____ samples means.

Calculate the mean of those 20 means. =_________  (the mean of the 20 sample means)
                  and their s=________  (the SD of the 20 sample means)


Samples always have sampling error: they aren't exact mini-mes of the population.


Card hand of size 10 (sample size n=10)
Take 20 samples, adding each's mean into "Frequency distribution, histogram, and statistics" input textbox. 
And here: __________________________________________________________________________
This is a (very incomplete) sampling distribution of the mean.
  The actual sampling distribution has N= 52C10≈________ samples means

Calculate the mean of those 20 means. =_________  (the mean of the 20 sample means)
                  and their s=________  (the SD of the 20 sample means)



The two means of these sampling distributions of the means of n=3 and n=10 don't differ much. 
But their standard deviations are significantly different:
the smaller sample size n=3 sample means have a __________ SD, indicating those samples 
are more spread out, have more variation, than 
the larger sample size n=10 sample means with a __________ SD, 

and so the larger sample size n makes it more likely that a sample you take
 has a mean closer to the population mean.

What does having a larger sample size n probably get you:_______________________


The SDs indicate that the _______ the sample size, the sample means have _____ variation.
The SDs indicate that the _______ the sample size, the sample means have _____ variation.

So if there is a population that we want to estimate its mean by taking one sample
we would want the sample size n to be as ________ as possible.