Understanding Statistics					 J.R. Rasmussen

					Class 4 Outline

I) Summary of what we covered last class

	A) introduction to statistical inference

	B) Variance in samples 
		1) class example of flipping coin 4 times

		2) Web visits to course Web site  exploring the variability 	
		of the average
			a) example 4.3, page 143: our population of 40 data points
			b) each student drew a sample of size 10 from our 	
			population using Excel
			c) we calculated the average of the samples
			d) we compared the sample results with the actual average

II) Introduction to statistical inference continued

	A) General concept
		1) We want to move from the known sample to the unknown population
		2) New York times poll and statistical inference

	B) Variability of samples

		1) Need to understand if we are going to be able to infer 	
		from the sample to the population
		2) Role of probability
			a) Probability is the means to measure the variability 
			of results of experiments

III) Probability

	A)History of Probability
		1) Chevalier de Méré , Pascal, and Fermat. (1654, France)
		2) Active field today

	B) Basic concepts and examples
		1) In general probability deals with situations with more 	
		than one possible outcome and "measures" the likelihood 	
		of the possible outcomes.

		2) Examples:
			a) weather
			b) flipping a coin
			c) outcomes of an election
			d) rolling two dice

	C) Axioms (Andrei Kolmogorov) and terminology 
		1) example:  flipping a coin 
		2) example:  rolling two dice
			a) simple outcomes
			b) other events:  Pr[the sum on the dice is 5]

	D) The frequency definition
		1) intuitive idea
		2) Flipping a coin
		3) Frequency definition:  page 264 of text

	E) Class participation
		1) I start
		2) students flip coin
		3) how to do on Excel:  Bernoulli trial

Break	

IV) Our four coin example revisited

	A) Overall goal is to understand variability 

	B) Construct the tree of all possible outcomes

	C) Calculate the probability of exactly two heads

	D) Calculate the other probabilities

	E) Group exercise:  how to use Excel to see variability
		1)the event is obtaining exactly two heads in 4 tosses

	F) The binomial distribution on Excel
		1) have each student do one and see how many get 	
			exactly two heads.

	G) Now do 10, 100, etc.:  the frequency command on Excel

V) Homework

	A) Remember assignment 2 is due on Wednesday 10/14/09