00:01
We have been given some data here.
00:03
We've been given a population mean mu, 27, a population standard deviation, sigma, as being 8, but we aren't looking at individual observations, we are looking at a mean from a sample of size 68.
00:16
Our sample mean x bar is 26.
00:20
We want to know the standard score of this sample mean.
00:24
So a z -score, standard score, is telling you how many standard deviations away from the mean a value is for an individual observation.
00:40
We're looking at a sample mean, so what we need to know is how many standard deviations of the sampling distribution is this away from the mean of the sampling distribution.
00:49
And what do i mean by sampling distribution? well, if we look at the central limit theorem, this tells me that as sample size increases, sample means become more and more normally distributed compared to the population.
01:04
If n is at least 30, they are approximately normally distributed.
01:08
So if you took every sample of size 68, took the sample means, plotted them out, you'd get something approximately normal.
01:15
The theorem tells me that the mean of the means is the same as the population mean.
01:21
The standard deviation of the sample means, or standard error, is sigma over root n, so 8 over root 68...