00:01
So we're given a list of the salary in millions of 10 ncaa basketball coaches.
00:08
And we're asked to use that data to find a couple things.
00:13
First, the sample mean.
00:16
Secondly, we want to estimate the population standard deviation.
00:22
And we want to make a 95 % confidence interval for the variance.
00:27
And a 95 % confidence interval for the standard deviation.
00:33
So i have here, this is the formula for the variance, and this is the kai squared formula, which we'll get to in a minute.
00:41
But the first time we want to do is find the sample mean.
00:44
You see this blue column here.
00:47
This is a list of all of the salaries and millions.
00:51
And there are 10 salaries here.
00:55
So what we do is we just add this up and divide by 10.
00:58
And we get 14 .7 divided by 10 or 1 .47.
01:09
So that's our sample mean.
01:11
That is our best estimate for the population mean.
01:19
And from there, we can estimate the population standard deviation using this formula.
01:27
We can either find the variance or the standard deviation, but we need both.
01:33
And i'm not going to calculate it by hand since it would take a.
01:36
A long time, but all you do is you sum up the difference for each value and the mean, you square it.
01:46
So for the first value, it would just be 2 .2 minus 1 .47 squared.
01:57
And you would repeat that for every value on the list.
02:01
And you would, then, i forgot to include this, but you would divide that by n minus one.
02:15
So now we let me erase this before i write down the variance and standard deviation.
02:27
So anyway, when we carry out this laborious calculation or use software to find it, we end up getting a standard deviation of 0 .8757 and a sample variance of 0 .768.
02:53
We want to find a 95 % confidence interval for the variance.
02:59
And to do that, we want to use this kai squared formula.
03:04
We need to take our n -1, so i'll just write the part down...