OKAY, so let's do this shindig:
Statistic: difference of sample proportions
p1= 102/107 (observed) p2= 14514800/20562119 (expected)
p1= 95.3% p2= 70.59%
p1-p2= .2473710184
Standard Deviation of Statistics: sqrt[(.9533*.0467/107)+(.7059*.2941/20562119)]
= .0204 standard deviations
95% confidence interval, two-tail; critical value= 1.96
Confidence Interval: .2474 +/- 1.96*(.0204)
(.207416, .287384)
The true difference between probability 1 and probability 2 is between .207 and .287. Unfortunately, this does not land within enough standard deviations to fail to reject, so we would reject the hypothesis that p1 is equal to p2.
We are 95% confident that between 20% and 29% more students use Facebook at North Penn compared with a national average.
ReplyDeleteMake sure that conditions are met to construct this interval. Also, I would've liked to have seen some randomization employed (which is very hard to do).