1. Unit #2 – Confidence Intervals (An Overview) ©2005 Dr. B. C. Paul

2. Unit #2 Covers Confidence Intervals What is a confidence interval? What is a confidence interval? Imagine that what ever we are studying has a normal distribution. If I take a sample where is it most Likely to come from. Suppose I pull a sample and its value is from Way out here? What do I know? - that was pretty unlikely to happen – in fact – at some Point I’m going to wonder whether I really got it from that population Confidence Interval Problems all have the flavor of deciding how far out in The tails, how rare, the sample is or would be if you could get it.

3. Too Many Normal Distributions Normal distribution is defined by its mean and standard deviation Normal distribution is defined by its mean and standard deviation There are endless possibilities There are endless possibilities We start by standardizing our results to a standard normal distribution with a mean of 0 and an stdev of 1. We start by standardizing our results to a standard normal distribution with a mean of 0 and an stdev of 1. Has the form Has the form

4. Just Any Normal Distribution Our Value X Our formula converts that point To an equal point on the standard Normal distribution. 0 Stdev=1

5. Once We Are On A Standard Normal Distribution we look at how extreme a value we have What % of the Values are More Extreme than this?

6. Things in Common All the techniques we will learn in unit 2 are just about finding out how far out in the tails a value would be All the techniques we will learn in unit 2 are just about finding out how far out in the tails a value would be We may work the normalizing formula forward or rearrange it and backsolve something We may work the normalizing formula forward or rearrange it and backsolve something Look for the pattern. Look for the pattern.