00:01
So we have been given some sample data.
00:03
Our sample size is 200.
00:06
And we have this weighted average of 41 % of these students reporting food insecurities.
00:12
So let's report that as a sample proportion of 41%.
00:17
And we're looking at a confidence interval for the percentage based on this sample.
00:21
So i've immediately turned it into a proportion.
00:24
All of my calculations will be in decimal form because percentages don't play very well with calculations.
00:29
We will turn it back into a percentage at the end.
00:32
The form we look for this confidence interval is p -hat, point estimate, plus minus the margin of error, z -route.
00:41
P -hat, 1 minus p -hat, over n.
00:44
So i have n, i have p -hat, i just need z.
00:47
We get that from a level of confidence.
00:49
If we took every sample of this size, took the sample proportions and plotted them out, we would see something approximately normal, thanks to the central limit theorem.
00:58
Now, my p hat rolls somewhere on this curve.
01:01
I don't know where.
01:02
But to make my interval, we put it in the centre, form the interval around it.
01:08
And this interval has to be wide enough to contain the middle 95 % of the sampling distribution for 95 % confidence.
01:15
That leaves 5 % in the tails, so each tail is 2 .5%...