For the Coursera students ,we have 59 successes ,and 24 failures, so it

appears that both of these are met, the suc success failure condition is met.

For both of the groups and therefore we can assume.

That the sampling distribution ,of the difference

between ,two proportions is nearly normal.

Now that we got our conditions out of the way.

We can actually calculate our confidence interval.

That's a point estimate so the difference between two sample proportions.

Plus or minus some margin of error, that we

calculate as a Z star, times the standard error.

The sample proportion for Coursera students is .71, and

the sample proportion for Americans is .25, so, our point

estimate is the difference between them, since we are

asked for a 95% confidence interval, the Z star

is 1.96, and we can calculate our standard ,error

as the square root of the sum of two quantities.

So, for the first quantity, we're looking at

the proportion of successes in Coursera times the

proportion of failures divided by the sample size

for the Coursera students ,plus the proportion of

the successes in the US times the proportion of

failures divided by the sample size for the US.

[INAUDIBLE].

The standard error ,then comes out to be .0516 and based

on this, the margin of error comes out to be roughly 10%.

In this case, our overall confidence interval

comes out to be between .36 and .56.

What this means is that we are 95% confident ,that

the proportion of Coursera students who believe that their should be a ban on

possession of handguns ,is 36 to 56%

higher than the proportion of Americans who do.

That's a huge difference even when we

factor in the variability ,around the point estimate.

And, again, this is probably expected based on

how different the composition of the two populations are.

So, we were asked to estimate the difference ,and we made an executive

decision to put the Coursera student

proportion First, and the American proportion second.

But does the order actually matter?

So does our decision actually change things?

The answer is yes and no.

It might change some of the calculations along the

way, but it's not going to change your conclusions.

Remember, this is how we calculate our

confidence interval for the difference between two proportions.

The point estimate ,plus or minus a margin of error.

Your margin of error is bound to be a number that's always, always positive,

because if you think about it, the

standard error is always going to be positive.