Transcript Unit #2 – Confidence Intervals (An Overview)

Unit #2 – Confidence
Intervals
(An Overview)
©2005 Dr. B. C. Paul
Unit #2 Covers Confidence
Intervals

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.
Too Many Normal Distributions

Normal distribution is defined by its mean and
standard deviation


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.

Has the form
Z
X 

Just Any Normal Distribution
Our formula converts that point
To an equal point on the standard
Normal distribution.
Stdev=1
0
Our Value X
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?
Things in Common

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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

Look for the pattern.