00:01
We have been given some sample data.
00:02
Sample size n is 64.
00:06
The sample mean x bar is 22.
00:10
The population standard deviation sigma is 6.
00:14
We want to take this and make a confidence interval for the population mean.
00:19
The formula for this is the point estimate x bar plus and minus the margin of error z sigma over root n.
00:29
Sigma over root n is the standard error.
00:32
Z is our critical value.
00:34
It's not the only type of critical value.
00:35
There's also t.
00:37
But z is preferable and we do meet the requirements to use it.
00:40
Big requirement being sigma should be known.
00:44
We do know sigma.
00:45
Even so you can still use z anyway if you have a large sample, which we do.
00:53
So what is z? well we get it from the level of confidence.
00:58
So the central limit theorem, clt, tells me that as sample size increases, sample means get more and more normally distributed.
01:09
So if i were to take every possible sample of this size, get the sample means, plot them out, i would get something approximately normal.
01:19
And to make the interval, we put the point estimate in the middle here, form the interval around it, containing 90 % of the area of this curve for 90 % confidence.
01:29
Alpha refers to the significance, the area outside the interval.
01:34
That would be 10%.
01:35
So split that into two for each tail.
01:38
Each tail is 5%.
01:39
Z is the z score to exclude these tails...