00:01
We want to find a 99 % confidence interval of a mean waiting time at a drive -in.
00:05
We have a sample of n equals 54, the sample size, and the sample mean, x bar, is 9 .2 minutes.
00:14
The sample standard deviation, s, is 2 .6 minutes, and it's a 99 % confidence interval.
00:21
So how do we work this out? we use this formula.
00:26
X bar plus or minus the margin of error, which is zs over 3.
00:31
Root m.
00:35
If your sample size is big enough, typically over 30, you can use the central limit theorem, which says that your sample means are normally distributed.
00:45
So we have our sample mean here, and it is part of a normal distribution.
00:50
So if i draw a normal distribution around this, i'm putting down a lower bound and an upbound, and i'm saying i'm 99 % confident that any other sample mean would fall within this interval.
01:05
And the population mean is included there.
01:09
So i'm 99 % confident, but the population mean will be somewhere in this interval.
01:14
1 % of the possibility is excluded in the tables.
01:18
Each tail is 0 .5%.
01:22
And this is where we get our z from.
01:24
Z, the critical value, is the z score in the normal distribution to exclude a tail of 0 .005...