00:01
We're looking to estimate the population mean for the time college students spend watching online videos each day.
00:06
But we're not going to be asking every college student how much time they spend.
00:10
We'll be taking a sample and using that.
00:13
We don't know what sample size is necessary.
00:15
Imagine if we knew the sample size n.
00:18
We'd go ahead, take the sample, and find x bar, the sample mean.
00:22
From this we would be making a confidence interval for the population mean.
00:26
The formula we would use is x bar, the point estimate, plus and minus the margin of error, z sigma over root n.
00:36
But i'm just going to focus on this margin of error because we've been told our estimate must be within 0 .25 minutes.
00:45
So i'll set this as less than or equal to 0 .25.
00:49
Now if i solve for n, i'll know the sample size necessary.
00:54
We have too many unknowns right now luckily we've been given sigma, population standard deviation, 1 .3.
01:02
Z we get from the level of confidence.
01:06
Now as the sample size increases, the distribution of sample means becomes more and more normally distributed.
01:16
So if n is at least 30, we can treat it as approximately normal.
01:20
That's the central limit theorem...