Day 08: Statistics for Business Applications

1. Parameters describe populations;
2. Parameters are almost always unknown;
3. We take random samples of a population as data, and
4. we estimate parameter values from statistics calculated on the samples.

Basic idea:

• The variable of interest x is distributed with mean mu, with spread parameter (standard deviation) sigma; we want to estimate mu.
• Instead of relying on a single value to estimate the parameter mu (the population mean), we use a sample of values, and take an average!
• How is xbar distributed?
  • With the same mean mu,
  • with smaller standard deviation, and
  • more and more normally as the sample size gets big!

Recall the dice applet - normal curves arise in the strangest places! (Figure 9.3, p. 273, for example)

• Toss a coin - tails, lose a dollar; head, win a dollar.
• The distrIllustrates Chebysheff's Theorem - the 1-(1/k^2) rule
• 8 tosses, and compute the mean loss per turn
• Uniform distribution -> normal
• The hexstat demonstrator