00:01
We have been given some sample data.
00:02
The sample size n is 90.
00:08
The sample mean x -bar is 4 days.
00:11
We also know the population standard deviation sigma is 3 .5 days.
00:17
What is the confidence interval for the population mean? the average length of stay for all patients.
00:23
The formula for this is x -bar, point estimate, plus and minus the margin of error z sigma over root n.
00:31
Z is our critical value here.
00:34
It's not the only critical value, there's also t, but z is preferable and we can use it because sigma is known.
00:41
We didn't know sigma if we only had the population, the sample standard deviation rather.
00:46
We might have to use t.
00:49
Okay, so what is z? well, we get it from the level of confidence.
00:58
The central limit theorem tells me that as sample size increases, sample means become more and more normally distributed...