00:01
We have been given some sample data.
00:02
The sample size n is 10.
00:05
The sample mean x bar is 5 .1.
00:10
The population standard deviation sigma is 0 .75.
00:14
We want a confidence interval for the population mean.
00:19
Okay so the formula we need is the point estimate x bar plus and minus the margin of error z sigma over root n.
00:29
So sigma over root n is the standard error, that's the standard deviation of sampling distribution.
00:36
Z is our critical value.
00:37
It's not the only critical value, there's also t but i'm using z because z is preferable and we meet the requirement that sigma is known.
00:49
So what is z? well the central limit theorem tells me that as sample size increases, sample means become more and more normally distributed compared to their original distribution.
01:00
If n is at least 30, they're approximately normally distributed regardless of the shape of the distribution, population distribution...