Supplementary exercise 4.9 of IPS7e
-----------------------------------

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. We use the Probability 
applet to carry out the simulation, as described in the exercise. The
PSLS applet does not allow a sample size of 20, so we use 15 (the default)
instead for part (a). 

It is recommended to type the results (number of heads ~ Internet users)
into a column in a Minitab worksheet, in order to facilitate processing
of the results.

Minitab commands and output for the two distributions (obtained in one session
with the Probability applet, resetting between the two series):

MTB > name c1 "count15"
MTB > name c2 "count200"
* type the counts into these columns *

MTB > Name C3 'prop15'
MTB > Let 'prop15' = 'count15'/15
MTB > Name C4 'prop200'
MTB > Let 'prop200' = 'count200'/200
MTB > Describe 'prop15' 'prop200'.
Descriptive Statistics: prop15, prop200 

Variable   N  N*     Mean  SE Mean    StDev  Minimum       Q1   Median       Q3  Maximum
prop15    25   0   0.2747   0.0201   0.1006   0.0667   0.2000   0.2667   0.3333   0.4667
prop200   25   0  0.30440  0.00711  0.03554  0.24000  0.28250  0.30500  0.32500  0.39500

MTB > Dotplot 'prop15' 'prop200';
SUBC>   Overlay.
Dotplot of prop15, prop200 

MTB > Boxplot 'prop15' 'prop200';
SUBC>   Overlay;
SUBC>   IQRBox;
SUBC>   Outlier.
Boxplot of prop15, prop200 

MTB > Stem-and-Leaf 'prop15' 'prop200';
SUBC>   Increment .05.
Stem-and-Leaf Display: prop15, prop200 

Stem-and-leaf of prop15  N  = 25
Leaf Unit = 0.010

 1   0  6
 2   1  3
 2   1
 9   2  0000000
(8)  2  66666666
 8   3  3333
 4   3
 4   4  0
 3   4  666

Stem-and-leaf of prop200  N  = 25
Leaf Unit = 0.010

 2    2  44
 11   2  568889999
(12)  3  000112222444
 2    3  59

We may manually align the two stemplots to faciliate the comparison:

prop15               prop200
 1   0  6
 2   1  3
 2   1
 9   2  0000000      2    2  44
(8)  2  66666666     11   2  568889999
 8   3  3333        (12)  3  000112222444
 4   3               2    3  59
 4   4  0
 3   4  666

Comments:
---------
As also indicated in the exercise, the distribution for 15 tosses is
more variable and not centered as closely to the true probability (0.3)
as the distribution for 200 tosses. See Exercise 4.10 for a numerical
comparison of the variability based on a larger number of repetitions.