00:01
We want to estimate a population mean.
00:02
We don't know how big our sample should be, but imagine if i did know my sample size n.
00:07
I'd take my sample and find x bar, the sample mean.
00:11
I would then make a confidence interval to estimate the population mean.
00:15
The formula for that is x bar, point estimates, plus and minus the margin of error, z sigma over root n.
00:24
I will just focus on this margin of error since we are told we want the sampling distribution error to be 0 .25.
00:31
Now if i solve for n, i will know the sample size necessary to make this true.
00:37
So let's rearrange to solve for n.
00:39
I'll multiply by root n, divide by 0 .25, square both sides.
00:48
We have a couple of unknowns here.
00:50
Sigma is the population standard deviation.
00:54
We're given sigma squared as being 3 .9, so i'll just put this as root 3 .9 for now.
00:59
It's getting squared anyway.
01:02
And z we get from the level of confidence.
01:08
The central limit theorem tells me that as sample size increases, sample means become more and more normally distributed compared to the population.
01:17
If n is at least 30, you can treat them as approximately normal...