Okay so the publics got used to forming these 95% confidence intervals

from this kind of a statement.

What we're going to do is go backwards now.

We're going to determine what kind of

sample size we need to achieve a certain level of precision.

In advance of doing our survey,

we're going to specify what we want as an outcome.

And then, based on that specification,

calculate what sample size will achieve it.

So in our particular case now, our margin of error is 0.02,

the standard there is half of that.

Two times the standard of error is the margin of error, so we're going to divide

the margin of error by two, .02 divided by 2 is .01 and that is the standard error.

Now in our funny notation here that's the square root of the desired variance.

So I know this notations a little bit hard to keep track of but

just follow the logic.

We'll lay it out in several steps in the next couple of slides.

So the desired variance, which is what we need in that sample sized calculation is

0.1 squared, or 0.0001.

Now that allows us then to calculate a sample size

taking the population variance, s squared, which would be the proportion.

In our particular case, .6 x 1-.6, that's the f squared,

or at least our calculation of a value that's reasonable to use there.

And then we're going to divide by that desired variance, .0001.

Sometimes though, what you'll see are sample size formulas that are based on e.

Rather than converting e to a standard error and

then a variance in using the one formula.

Others prefer to write out a formula that is just based on e, so

don't worry about standard errors, don't worry about these precision levels.

Just figure out what that margin of error is that you want to have, and

then use the following formula.

This leads to confusion.

People will have been trained with one formula and

then they're starting a job in a new firm and that firm doesn't use that approach.

They use a slightly different one.

They may use the formulation that I've been giving us.

And so then it's some confusion here.

So let's just sort of de-confuse this,

sort this out a little bit and talk about then the necessary sample size,

that n prime now, as S squared again in the numerator.

For the denominator what we've got there is the margin of error divided by 2,

which is the standard error we want, squared.

So now we can just write that simply as the formula,

S squared over The quantity e over 2 squared.

And we would then adjust this to account for the finite population size.

We would take tha n prime and divide it by 1 plus n prime over N.