00:01
So you want to determine a confidence interval for the standard deviation and the variance.
00:04
And so we'll find both of them kind of at the same time.
00:07
And the first thing i like to do is draw my little chi -squared distribution here, just kind of a generic one.
00:14
And we want to put 95 % in here, so .025 in the upper tail and .025 in the lower tail.
00:22
And so this area to the right of that is .975.
00:27
And that's usually the way we have to look up our value in our table.
00:30
And so our degrees of freedom will be 22.
00:33
So let me look those values up for you.
00:35
And i'll hopefully change to a green color here.
00:38
So we want to have 23 degrees of freedom.
00:40
And we have .975 in that upper tail and 22 degrees of freedom, i'm sorry.
00:48
And that's going to correspond with 10 .982, 10 .982.
00:55
Now let's find for the upper tail that has .025 and .025 with 22 is the 36 .781, 36 .781.
01:10
Now we're ready to find that interval.
01:14
So let's find the variance first and then we'll square root to find the other.
01:19
So we have our sample size less 1.
01:22
And then we take our sample standard deviation squared.
01:26
And then we divide that first one by the larger of the two values.
01:33
And then we take our 22 times that 2 .4 squared.
01:38
And then divide that by the smaller chi -squared value.
01:43
And so i'll put these in.
01:45
And as i do them, i'll kind of store them too.
01:47
And i'm actually going to write what the standard deviation value will be.
01:51
Because all we do is square root that answer...