Greetings. In this set of lectures we'll build on

something that we started to look at at the end of lecture six,

to show how to consistently compute 95 percent confidence intervals for

single sample somebody measures as

a confidence interval for the underlying population value.

So, we'll look at it for sample means,

create confidence interval for the underlying population mean,

use the sample proportion and information in the sample to create

underlying confidence intervals for

the population level proportion and we'll do the same thing for incidence rates.

You use the sample based data to a 95 percent confidence interval for

the unknown true incidence rate in the population from which the data is selected.

What you'll see throughout this process that is

regardless of what we're computing a confidence interval for,

the procedure is pretty straight forward.

What's a little more and a little harder to get one's head

around is the idea of what a confidence interval is and what it's accounting for.

So, we'll spend some time talking about what 95 percent confidence

really means with respect to uncertainty about our sample based estimate.

Then at the last part of this lecture we will show that some of

the ideas we've developed require ample samples of

data for that predictable pattern under

the CLT to kick in and when we have smaller samples, doesn't necessarily hold.

We'll talk about some ways to get around that.

These will be handled by the computer,

they're not that different than what we

will be doing for the rest of the lecture and it's not something

you have to worry about learning to do

analytically and looking things up in tables et cetera.

But I want to put it out there because

sometimes you'll see confidence intervals that look

slightly different than the ones we've showed you how to calculate by hand.

Again, I want to focus on the main idea which is that

regardless of whether confidence interval is created based on a larger sample

using CLT-based methods or smaller sample using other methods

the interpretation and understanding it provides are the same.