Sampling to the Fore!

Statistics, Obamas, and Internet Memes Statistics made visible!!The Principle of Statistical InferenceOne of the many reasons for doing Statistics, besides the fact that it is more fun than one may have sitting down, is that it enables one to draw tentative conclusions about unexamined populations based on carefully examined samples.  In fact, the difference between probability, statistics, and process control can be visualized by means of a sample taken from a box full of beads, some percentage of which are red and the others white.

1. Probability. Knowing the proportion of red beads in the box, how many red beads will show up in a sample of n beads?
2. Statistics.  Knowing the number of red beads in a sample of n beads, what is the proportion of red beads in the box? 
3. Process Control.  Is there a box?
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