00:01
So we're given a sample size of 22 people.
00:06
And we're told that the sample standard deviation of the waiting time was 3 .6 minutes.
00:12
And we want to make a 98 % confidence interval about the population variance, sigma squared, and the standard deviation sigma.
00:22
And the formula is given here.
00:24
So the variance is n minus 1 s squared over kai squared.
00:34
Alpha over 2 knowing the degrees of freedom, and that is the lower bound on the variance, the upper bound on the variance is n minus 1 sample variance all over kai squared 1 minus alpha over 2, noting the degrees of freedom.
00:50
And the degrees of freedom is given as n minus 1, so 22 minus 1 is 21, so 21 degrees of freedom.
00:59
So it's going to give us the lower and upper bound for our variance to find the, standard deviation, we just take this square root.
01:10
Well, thank you, because we just got to get rid of the square.
01:12
There we go.
01:13
So let's do the variance first.
01:16
And i use my spreadsheet to get these kai squared values, 38 .93 for this lower bound value and the 8 .897 for the upper bound value of the chi squared statistic.
01:30
Oh, and the alpha is, i like to think about it as the value that makes this confidence interval 100%.
01:37
So now it's a matter of subject.
01:39
Restituting in our values.
01:41
So we get 21 times 3 .6 squared all over this kai squared value, 38 .93...