00:01
So we want to find a confidence interval here.
00:03
And the information we've been given is a sample of size 100, so n is 100, a sample mean, x bar, of 180 centimetres, and the population variance, sigma squared, is 49.
00:20
Okay, first thing i'm going to do, square root that variance, to get the population standard deviation.
00:27
So that's going to be seven.
00:28
So the formula for a confidence interval for a population mean is x bar plus and minus the margin of error, z sigma over root n.
00:40
So we use z here because we know the population standard deviation.
00:46
Okay, so we have most of this information.
00:49
We have x bar, we have sigma, we have n, we just need z.
00:53
We get that from the level of confidence.
00:55
So this formula is based on the normal distribution.
00:59
And by the central limit theorem, if you have a sample of size at least 30, which we do, then the sample means are approximately normally distributed.
01:09
So if i put x bar in the middle and make a normal distribution around it, the other sample means and the population mean will follow this curve.
01:19
If i put down my interval, say, okay, i want 95 % of the area of this curve in the interval.
01:26
Only 5 % is in the tails.
01:28
So that's where it comes from.
01:31
This is the standard deviation of v -sampling distribution, aka the standard error.
01:39
And this is how many standard deviations away we're going.
01:46
Each tail is 2 .5%...