Our goal is to estimate what percent

of Americans have good intuition about experimental design.

Our parameter of interest here is the

percentage of all Americans who have good intuition

about experimental design, and we're going to denote

this unknown population parameter, P, for population proportion.

Our point estimate is the percentage of sampled

Americans who have good intuition about experimental design.

And we're going to denote this p-hat, and this is our known sample proportion.

In fact that is 571 divided by 670.

The total sample size roughly 85%.

When it comes to estimation of an unknown population parameter, we know that it

always follows the same structure, the point

estimate plus or minus a margin of error.

In this case our point estimate is our sample proportion p-hat.

And our margin of error can be calculated as z

star our critical value, times the standard error of p-hat.

So, once again, the only new concept here is going to

be how to calculate the standard error for the sample proportion.

And in fact, we were already introduced to this

when we talked about the central limit therum for proportions.

So, to calculate the standard error for proportion,

for calculating a confidence interval, we would use the

formula that's based on the central limit theorem, square

root of p-hat times one minus p-hat over n.

Remember that when we initially introduced this formula we had used

p instead of p-hat in the calculation of the standard error.

Well, but we also said that if you don't

know p, or true population parameter, you would be plugging

in your sample proportion, and in fact, in most

instances, we don't know what the true population parameter is.

That's why we're calculating a confidence interval in the first place.