00:01
So we've been given some sample data.
00:02
The sample size is 571, and out of these, 80 of the participants admitted to illegally downloading music.
00:11
We want a confidence interval for the population proportion of american adults who've done this.
00:17
So the formula for a confidence interval for a population proportion is p -hat, sample proportion, point estimate, plus and minus the margin of error.
00:28
Error.
00:28
Z root p hat 1 minus p hat over n.
00:33
Sometimes they give you a list of formulas, sometimes you just have to memorise them.
00:39
So we have n, we need p hat, that's the proportion of the sample who admitted to this, so 80 out of 571, and we just need z.
00:48
We get that from a level of confidence.
00:52
Now, according to the central limit theorem, if i took every sample of a large enough size, in this case size is 571, took all of the sample proportions and plotted them out, i would see something approximately normal.
01:07
Our sample proportion is somewhere on this curve, we don't know where.
01:10
But to make our interval, we throw it in the middle, and we form an interval around it, wide enough that it would contain the middle 99 % of this curve.
01:20
Curve...