00:01
So we're looking at a sample and we found that the sample proportion p -hat was 50%.
00:07
So that's the proportion of the poll who got at least some news from twitter.
00:13
We're also given the standard error.
00:16
Okay, so what is the standard error? well, the poll followed a binomial distribution.
00:22
N independent trials, two outcomes, they get at least some of their news from twitter or they don't.
00:28
Same probability p, the population proportion, whatever it is, of each person meeting the criteria.
00:34
The binomial variable is x, the number from the sample to meet the criteria.
00:40
Now we don't know the sample size, so we don't even know how many, but i can take a normal approximation to the binomial and then i divide this distribution by n to turn it into a probability distribution for p -hat.
00:56
So this is the sampling distribution.
00:58
0 .5 is somewhere on this curve, we don't know where.
01:02
The mean of the original binomial is np, with a standard deviation of root np 1 minus p.
01:10
So these are the mean and standard deviation of x.
01:13
If i divide these by n, i get the mean and standard deviation of the sampling distribution, p and p 1 minus p over n, all in this square root sign.
01:24
This is the standard error.
01:28
The standard error is a standard deviation of a sampling distribution, in this case the sample proportion.
01:34
So that's 2 .6%.
01:36
Actually i will put these in a percentage form.
01:45
If you're doing calculations, typically you don't want to use percentages, it doesn't go very well, but this is a rare case where it's not going to matter, as the calculations we're doing are quite simple.
01:57
Okay, we want a 99 % confidence interval for the population proportion.
02:05
Well, so i said 50 % is somewhere on this curve, but to make my interval i put it in the centre and form an interval around it containing 99 % of the distribution.
02:17
That leaves 1 % in the tails, so each tail is half a percent.
02:22
Because this is a normal curve, i can represent this interval as the centre plus and minus some number of standard deviations...