00:01
So in this question we have 95 % confidence, we have n is 21 and s is 65 .7.
00:11
Now our degrees of freedom are going to be n minus 1, so that's 20.
00:16
Now for chi -squared left we want the probability that chi -squared with 20 degrees of freedom is greater, sorry, is less than chi -squared left, is 1 minus our confidence level divided by 2, so that's 0 .025.
00:32
So we want the quantile of the chi -squared distribution which contains 0 .025 probability to its left when we have 20 degrees of freedom, and that gives chi -squared left is 9 .5908.
00:48
Rounding to three decimal places, 9 .591.
00:53
For chi -squared right we have that the probability chi -squared with 20 degrees of freedom is greater than chi -squared right is 1 minus our confidence level over 2, 0 .025.
01:05
So we look for the quantile of the chi -squared distribution which has 2 .5 probability to its right now, or 97 .5 to its left when we have 20 degrees of freedom...