Day I Don't Know but I'm Pretty Much Done!

Sooo I wanted to try a confidence interval of just one proportion to see another way of rejecting the hypothesis. So I did a confidence interval for the national data, which would look like

.7059+/- (1.96)*sqrt(.7059*.2941/20562119)

This gave me the interval (.7057, .7061), which is really ridiculously small, but unsurprisingly so, considering the size of the n. If we do the same for my sample data, we get (.9133, .9933), which also doesn't fit into the other proportion. Therefore we can reject the null hypothesis that p1=p2.

Yet another way to do this, and probably the easier way, is to do the 1-proportion z-test, where we put in the assumed value, the national proportion (I was first unsure of doing this considering that this data was also gathered by another amateur person, but since we are assuming, I'll accept it) as p0, and then put x in as 102 and n in as 107 with the proportion not equal to p0. When I calculated, I got the same z-value and p-value as I did with the 2-proportion z-test, cementing that this null hypothesis should be rejected.

I think that's it. I've tried pretty much everything I can think of to test this hypothesis. While there are a few flaws in my executing the data and in using the normal model cautiously, I believe that even with the perfect data, we would find that we had to reject the null hypothesis, just because of the sheer difference in proportions. I believe this also shows the increase in social networking importance and how the amount of kids using Facebook is in fact much larger than originally thought. It looks like Facebook will be here to stay. Now, about Twitter...