Show by how much a fair coin can deviate from 50% in different size samples.
NOTE to students -- I have not yet prepare the excel sheet, but you can do this one on your own:
Step 1: Set value of p in cell B1
Step 2:
In cells A1:A1000, write =if(rand()<$B$1,1,0) -- this will generate 1000 IID Bernoullis with P(Bi=1)=p
Step 3: Compute Averages; start from A1:A10, to avoid initial fluctuations
Enter "=average($A$1:A10)" in cell B10, and copy this down to B1000
In cell C10 enter "=$B$1" and copy it down to C1000
Step 4: Draw a graph which plots the averages in B10:B1000 and also the value of p in C10:C1000. NOte the convergence of the averages to p
ANOTHER WAY to do this would be to write "=average($A$1:A10)-$B$1" in cell B10 and copy this down to B1000 -- this looks at the differences between observed sample averages and theoretical probability p. This should center around 0 and show convergence to 0