Supplementary exercise 4.10 of IPS7e
------------------------------------
(continuation of supplementary exercise 4.9)

Simulation of draws of Internet users' age group; specifically whether a 
randomly selected Internet user is of age 18-29 years. The (true) 
probability of this event is assumed to be 0.3.

The following commands in Minitab will simulate 100 draws of 20 Internet
users and convert to percentages, and then do the same for draws of
samples of size 320:

MTB > Base 250905.
MTB > Random 100 c1;
SUBC>   Binomial 20 .3.
MTB > Name C2 'prop20'
MTB > Let 'prop20' = c1/20*100

MTB > Random 100 c3;
SUBC>   Binomial 320 .3.
MTB > Name C4 'prop320'
MTB > Let 'prop320' = c3/320*100

MTB > Describe 'prop20' 'prop320'.
Descriptive Statistics: prop20, prop320 

Variable    N  N*    Mean  SE Mean  StDev  Minimum      Q1  Median      Q3  Maximum
prop20    100   0   29.95     1.05  10.46     5.00   21.25   30.00   40.00    55.00
prop320   100   0  30.003    0.272  2.719   22.188  27.891  30.000  32.109   35.625

MTB > GSummary 'prop20' 'prop320'.
Summary Report for prop20 
Summary Report for prop320 


Comments:
---------
Both distributions look reasonably symmetric and bell-shaped. They are
both centered approximately around 0.3 (their means are very close to
0.3), but the spread of the distribution for sample size 320 is much
smaller. Theoretically (we will see these formulae in Session 5), the 
standard deviation should be sqrt(320/20)=4 times larger for sample size 20 
than for sample size 320, and this matches quite well (10.46/2.719=3.85).